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def/lionfix{filled{gsave lioncolour fill grestore}if stroke}def/toefix{gsave lioncolour fill grestore stroke} def/ea{/savematrix mtrx currentmatrix deftranslate 5 -1 roll rotate scale 0 0 1 5 -2 roll arcsavematrix setmatrix}def/ec{/savematrix mtrx currentmatrix deftranslate 5 -1 roll rotate scale 0 0 1 5 -2 roll arcnsavematrix setmatrix}def/db /rlineto load def /dt /lineto load def /mt /moveto load def/lion1{0.77 0.77 scale-200 -600 translate406 338 mt 440 375 45 -115 38 arc120 -90 90 15 11 445 425 ea120 -90 90 15 15 402 442 ea130 -143 25 33 20 360 454 ea360 485 32 217 73 arcn 397 507 dt464 524 45 241 70 arc 464 554 20 36 -133 arcn377 396 161 63 97 arc 362 494 62 93 227 arc512 690 308 235 255 arc 437 373 16 70 -105 arcn420 360 dt -100 20 db -50 0 db -20 40 db262 55 125 80 55 200 465 ea270 -41 185 23 15 265 517 ea260 540 dt -4 20 db -6 10 db -16 -2 db -14 -8 db90 -90 90 40 20 200 560 ea-14 8 db -16 2 db -6 -10 db -4 -20 db90 -5 221 23 15 135 517 ea98 55 125 80 55 200 465 ea420 340 285 164 183 arc} def/lion2{126 299 27 70 126 arc98 333 15 271 190 arcn287 438 230 207 170 arcn307 0 145 50 25 33 522 ea240 485 240 162 177 arc20 496 18 177 270 arc96 -10 190 26 12 7 450 ea111 -25 180 36 12 15 388 ea 40 350 dt119 -30 190 33 10 36 318 ea 70 296 dt127 -15 180 28 7 66 260 ea130 213 45 138 120 arcn120 296 36 -75 -40 arc}def/lion3{69 255 81 11 -37 arcn-123 362 300 -33 -47 arcn40 57 160 30 11 49 98 ea40 175 350 40 15 57 90 ea72 150 345 50 18 115 123 ea90 150 330 45 14 155 177 ea80 150 340 50 10 186 230 ea110 105 240 32 22 218 284 ea}def/lion4{332 247 36 115 210 arc307 160 31 40 -55 arcn160 390 305 -58 -70 arcn22 30 160 20 7 243 90 ea27 170 330 30 12 250 77 ea 288 90 dt60 125 300 45 15 312 100 ea 340 125 dt72 155 360 30 12 356 140 ea380 190 25 210 400 arc90 230 50 18 13 383 208 ec363 240 22 300 356 arc}def/lion5{476 296 108 212 242 arc412 171 32 50 -30 arcn55 90 310 40 20 420 84 ea498 102 54 200 235 arc93 200 360 40 11 470 105 ea95 165 350 30 8 474 173 ea479 205 5 210 360 arc 490 270 dt470 260 13 350 195 arcn348 247 108 10 60 arc}def/lion6{90 0 360 30 15 72 445 ea toefix243 324 108 180 208 arc stroke}def/lion7{10 0 360 30 20 53 148 ea toefix}def/lion8{-5 0 360 33 13 243 115 ea toefix}def/lion9{50 0 360 27 13 393 103 ea toefix317 280 mt 335 292 18 235 380 arc385 238 dt stroke}def/lion10{160 360 mt 4 -20 db 16 -20 db 16 20 db 4 20 db 10 -14 db10 -6 db 10 6 db 10 24 db 14 0 db 16 10 db strokegsave 200 490 translate1 1 2{pop 16 0 mt 24 40 db -26 -20 db lioneyecolour fill-1 1 scale}for grestore90 90 270 60 25 200 465 ea 200 450 dt closepath 1 setlinewidth stroke500 710 203 240 271 arc stroke} def/lion11{280 280 dt 262 203 18 133 220 arc228 156 36 42 -50 arcn52 38 315 44 23 160 20 ea 195 40 dt67 135 322 44 17 220 54 ea85 100 305 27 20 263 90 ea75 130 340 22 10 293 118 ea314 137 8 -150 40 arc380 197 72 202 148 arcn250 317 99 323 350 arc422 334 72 208 248 arc47 360 240 24 11 394 242 ec60 60 310 30 20 364 178 ea65 110 340 30 15 408 196 ea72 150 350 15 8 435 239 ea450 260 11 220 40 arc505 375 108 237 200 arcn}def/lion12{30 0 360 30 20 135 56 ea toefix35 0 360 22 15 352 212 ea toefix280 280 mt 347 300 dt stroke}def/lion13{0 45 -40 31 20 178 242 ec40 90 310 31 20 137 168 ea 170 174 dt80 90 320 41 20 189 163 ea82 160 310 35 20 226 218 ea73 180 325 25 10 263 266 ea 333 284 dt341 260 18 145 215 arc325 183 27 30 -58 arcn37 90 320 35 15 287 84 ea80 50 280 23 12 325 80 ea75 160 335 25 17 350 124 ea112 140 290 15 11 378 154 ea 383 170 dt395 180 9 265 31 arc462 230 72 210 180 arcn405 160 32 60 -10 arcn82 90 340 34 17 432 13 ea105 150 330 35 15 455 63 ea100 160 330 30 11 466 126 ea 461 161 dt80 180 345 26 8 475 187 ea125 180 60 40 15 456 251 ec325 265 108 14 43 arc}def/lion14{335 306 22 265 336 arc 390 230 dt stroke10 0 360 25 13 122 198 ea toefix13 0 360 22 13 266 106 ea toefix60 0 360 28 15 400 24 ea toefix}def/lion15{69 255 81 11 -40 arcn40 57 160 30 11 49 123 ea40 175 350 40 15 57 113 ea72 150 320 50 18 115 145 ea90 120 270 27 15 155 188 ea80 170 340 50 10 186 230 ea110 105 240 32 22 218 284 ea}def/lion16{10 0 360 30 20 53 168 ea toefix}def/cuarms{/arg exch def gsave 0.05 0.05 scale arg type /booleantype eq { /arg arg {1} {0} ifelse def} if arg 3 eq { % colour definitions /erminecolour { 0 0 0 setrgbcolor } def /lioncolour { 1 .9 0 setrgbcolor } def /lioneyecolour { 1 0 0 setrgbcolor } def /bgcolour { 1 0 0 setrgbcolor } def /crosscolour { 1 1 1 setrgbcolor } def /bookcolour { 1 0 0 setrgbcolor } def /bktrimcolour { 1 .9 0 setrgbcolor } def /filled true def } { /erminecolour { 0 setgray } def /lioncolour { 1 setgray } def /lioneyecolour { 0 setgray } def /bgcolour { 0 setgray } def /crosscolour { 1 setgray } def /bookcolour { 0 setgray } def /bktrimcolour { 1 setgray } def /filled arg 1 eq def } ifelse 1 1 2 {pop %repeat for symmetry %outline bgcolour 0 1475 moveto 600 1475 lineto 600 343 0 0 500 arcto 4 {pop} repeat 0 0 lineto gsave crosscolour fill grestore 15 setlinewidth stroke 125 1475 moveto 125 1000 lineto 600 1000 lineto filled {600 1475 lineto fill} if 125 75 moveto 125 700 lineto 600 700 lineto filled {600 343 0 0 500 arcto 4 {pop} repeat fill} {20 setlinewidth stroke} ifelse %ermine [[0 1170] [63 1045] [63 1295] [225 850] [375 850] [525 850] [300 730] [450 730] [0 275] [0 540] [63 120] [63 400]] { aload pop gsave translate 0 115 10 0 360 arc erminecolour fill 172 107 170 180 210 arc 8 20 lineto 0 0 lineto -8 20 lineto -172 107 170 -30 0 arc closepath fill grestore } forall %book gsave 0 745 translate 0 0 moveto 60 0 lineto 60 -80 lineto 100 -80 lineto 100 0 lineto 140 0 lineto 140 225 lineto 70 213 20 37 143 arc 0 213 20 37 90 arc bookcolour fill bktrimcolour 70 213 12 0 180 arc 58 183 lineto 82 183 lineto fill 0 213 12 0 90 arc 0 183 lineto 12 183 lineto fill 80 -22 12 0 180 arc 80 -43 12 180 0 arc fill 80 -67 6 0 360 arc fill 105 25 8 0 360 arc fill 105 180 8 0 360 arc fill 0 -90 90 50 25 0 112.5 ea 0 90 -90 45 20 0 112.5 ec fill 0 -90 90 20 5 0 112.5 ea fill grestore -1 1 scale }for%point of shield0 0 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adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cpfillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17{2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 addchg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop}forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get Amul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)(LaserWriter 16/600)]{A length product length le{A length product exch 0exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelseend{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemaskgrestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot}imagemask grestore}}ifelse B/QV{gsave newpath transform round exch roundexch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlinetofill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S pdelta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 Srmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end%%EndProcSet%%BeginProcSet: pstricks.pro%!% PostScript prologue for pstricks.tex.% Version 97 patch 3, 98/06/01% For distribution, see pstricks.tex.%/tx@Dict 200 dict def tx@Dict begin/ADict 25 dict def/CM { matrix currentmatrix } bind def/SLW /setlinewidth load def/CLW /currentlinewidth load def/CP /currentpoint load def/ED { exch def } bind def/L /lineto load def/T /translate load def/TMatrix { } def/RAngle { 0 } def/Atan { /atan load stopped { pop pop 0 } if } def/Div { dup 0 eq { pop } { div } ifelse } def/NET { neg exch neg exch T } def/Pyth { dup mul exch dup mul add sqrt } def/PtoC { 2 copy cos mul 3 1 roll sin mul } def/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def }def/PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def} { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ }/pathforall load stopped { pop pop pop pop } if z } def/STP { .996264 dup scale } def/STV { SDict begin normalscale end STP } def/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 defPathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul ymul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ]0 } ifelse setdash stroke } def/DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt{ /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y adddef } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1setlinecap stroke } def/LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25% DG/SR modification begin - Dec. 12, 1997 - Patch 2%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED aitransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a% DG/SR modification endDiv cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }% defa mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestorepop pop } def% DG/SR modification end/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub negexch 3 index sub exch Atan rotate newpath } def/EndArrow { @mtrx setmatrix CP grestore end } def/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fillgrestore } def/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0CLW moveto } def/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0CLW moveto } def/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto }def/SD { 0 360 arc fill } def/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DSCLW sub SD } if 0 DS z add CLW 4 div sub moveto } def/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {/closepath load } /pathforall load stopped { pop pop pop pop CP /movetoload } if ] cvx newpath 3 1 roll T exec } def/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exchcvi def } def/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } iff { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 subdef n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }ifelse { pop } repeat a } def/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eqand { pop pop /n n 1 sub def } if } def/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll LinetoLineto pop pop closepath } ifelse } def/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mulneg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w adddef } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrxsetmatrix } def% DG modification begin - Jan. 15, 1997%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx%setmatrix } def/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dupCLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)% setmatrix } defsetmatrix pop } def% DG/SR modification end/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pythdef } def/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pythdef } def/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c expmul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cosabs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mulm mul neg def } def/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }def/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def/NC { CC x1 y1 x2 y2 x y curveto } def/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def/NAC { x2 y2 x y curveto CC x1 y1 } def/EAC { x2 y2 x y ArrowB curveto pop pop } def/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub defn { NC } repeat EOC } ifelse } def/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { poppop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }repeat closepath pop pop } ifelse } def/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }def/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrixrotate matrix concatmatrix exch findfont exch makefont setfont } def/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 linetox1 y1 lineto closepath } def/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 divexch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arctox2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }ifelse } def/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {pop pop Rect } { OvalFrame } ifelse } def/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 62 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }ifelse } def/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }def/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowAx0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0y0 x0 2 mul x1 sub y1 ] def } def/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 }if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy divround cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx divround cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def }if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def }{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 addexch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy ndiv ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt {dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dupstringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i iw add def } repeat grestore gsave n 0 gt% DG/SR modification begin - Nov. 7, 1997 - Patch 1%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }% DG/SR modification end{ 2 setlinecap } ifelse /i y1 def /f x1 dx muln 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx ndiv 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvsdup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto gexch t L stroke /i i h add def } repeat grestore } def/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 01 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x addexch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div cmul neg d } def/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def/Rot { CP CP translate 3 -1 roll neg rotate NET } def/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngledup a add ] cvx def } def/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]cvx def } def/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b sabs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c bdiv w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {h1 abs h sub dup s mul abs } ifelse } def/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div smul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 addexch } def/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def} if } ifelse } def/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnitneg exch neg exch idtransform T moveto } def /BOL { BeginOL } def/IfVisible true def } defend% END pstricks.pro%%EndProcSet%%BeginProcSet: pst-dots.pro%!PS-Adobe-2.0%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07.%%Creator: Timothy Van Zandt <tvz@Princeton.EDU>%%Creation Date: May 7, 199310 dict dup begin /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /FontBBox [ 0 0 0 0 ] def /Encoding 256 array def 0 1 255 { Encoding exch /.notdef put } for Encoding dup (b) 0 get /Bullet put dup (c) 0 get /Circle put dup (C) 0 get /BoldCircle put dup (u) 0 get /SolidTriangle put dup (t) 0 get /Triangle put dup (T) 0 get /BoldTriangle put dup (r) 0 get /SolidSquare put dup (s) 0 get /Square put dup (S) 0 get /BoldSquare put dup (q) 0 get /SolidPentagon put dup (p) 0 get /Pentagon put (P) 0 get /BoldPentagon put /Metrics 13 dict def Metrics begin /Bullet 1000 def /Circle 1000 def /BoldCircle 1000 def /SolidTriangle 1344 def /Triangle 1344 def /BoldTriangle 1344 def /SolidSquare 886 def /Square 886 def /BoldSquare 886 def /SolidPentagon 1093.2 def /Pentagon 1093.2 def /BoldPentagon 1093.2 def /.notdef 0 def end /BBoxes 13 dict def BBoxes begin /Circle { -550 -550 550 550 } def /BoldCircle /Circle load def /Bullet /Circle load def /Triangle { -571.5 -330 571.5 660 } def /BoldTriangle /Triangle load def /SolidTriangle /Triangle load def /Square { -450 -450 450 450 } def /BoldSquare /Square load def /SolidSquare /Square load def /Pentagon { -546.6 -465 546.6 574.7 } def /BoldPentagon /Pentagon load def /SolidPentagon /Pentagon load def /.notdef { 0 0 0 0 } def end /CharProcs 20 dict def CharProcs begin /Adjust { 2 copy dtransform floor .5 add exch floor .5 add exch idtransform 3 -1 roll div 3 1 roll exch div exch scale } def /CirclePath { 0 0 500 0 360 arc closepath } def /Bullet { 500 500 Adjust CirclePath fill } def /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath } def /SolidTriangle { TrianglePath fill } def /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath } def /SolidSquare { SquarePath fill } def /Square { SquarePath .89 .89 scale SquarePath eofill } def /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def /PentagonPath { -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto 0 574.7 lineto -546.6 177.6 lineto closepath } def /SolidPentagon { PentagonPath fill } def /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def /.notdef { } def end /BuildGlyph { exch begin Metrics 1 index get exec 0 BBoxes 3 index get exec setcachedevice CharProcs begin load exec end end } def /BuildChar { 1 index /Encoding get exch get 1 index /BuildGlyph get exec } bind defend/PSTricksDotFont exch definefont pop% END pst-dots.pro%%EndProcSet%%BeginProcSet: pst-node.pro%!% PostScript prologue for pst-node.tex.% Version 97 patch 1, 97/05/09.% For distribution, see pstricks.tex.%/tx@NodeDict 400 dict def tx@NodeDict begintx@Dict begin /T /translate load def end/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next endgrestore } def/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def} def/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exchSin mul } def } def/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def }ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dxdup Sin mul Cos Div } ifelse } def/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub/u ED /NodePos { GetRnodePos } def } def/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dupCos mul exch Sin mul } def/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w hmul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul} ifelse } def/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /dED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def dsub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atansin def /NodePos { TriNodePos } def } def/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Coshh mul Atan dup cos ww mul exch sin hh mul } def/GetCenter { begin X Y NodeMtrx transform CM itransform end } def/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { DistDist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg }{ 0 Dist Sin mul } ifelse } ifelse Do } def/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransformexch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrxdtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED popXYPos } ifelse } def/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1roll sin mul sub exch } ifelse } def/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleAAddOffset yA add /yA1 ED xA add /xA1 ED } def/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleBAddOffset yB add /yB1 ED xB add /xB1 ED } def/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmAAngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do EDArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED} ifelse } def/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmBAngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do EDArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED} ifelse } def/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict bknown and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yAED /xA ED NodeB GetCenter /yB ED /xB ED } if } def/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t submul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop} repeat LPutLine cleartomark } def/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bxsub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul muladd cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul addy0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mulmul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def} def/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd } def/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def} def/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomarkVPosEnd } def/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvxdef grestore exec /LPutVar /SaveLPutVar load def } def/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add defGetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {LPutVar VPutLine } def LPutVar } def/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop popend } def/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA subAtan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }ifelse } def/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmAGetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dictbegin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrxitransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate defxA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrxtransform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def }{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dictbegin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvxdef /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } ifxB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB EDGetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict beginfalse Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin falseLine end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def% DG/SR modification begin - May 9, 1997 - Patch 1%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp rr mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA addexch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED% DG/SR modification end} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a addAngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 rDiv def /y ED /x ED } def/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cosmul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dyadd xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVartx@Dict begin false Polygon end } def/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atandef /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r divdef /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add defGetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mulsub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn }{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 00 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat }ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le {r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC }{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul addadd AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t submul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 tsub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelsey0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos {LPutPos } def } def/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yBsub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xBw sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub negexch X sub neg exch moveto setmatrix CP grestore } def/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0def } ifelse LPutCoor } def/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg }if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED }def/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } ifr Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED }defend% END pst-node.pro%%EndProcSet%%BeginProcSet: pst-text.pro%!% PostScript header file pst-text.pro% Version 97, 94/04/20% For distribution, see pstricks.tex./tx@TextPathDict 40 dict deftx@TextPathDict begin% Syntax: <dist> PathPosition -% Function: Searches for position of currentpath distance <dist> from% beginning. Sets (X,Y)=position, and Angle=tangent./PathPosition{ /targetdist exch def /pathdist 0 def /continue true def /X { newx } def /Y { newy } def /Angle 0 def gsave flattenpath { movetoproc } { linetoproc } { } { firstx firsty linetoproc } /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if grestore} def/movetoproc { continue { @movetoproc } { pop pop } ifelse } def/@movetoproc{ /newy exch def /newx exch def /firstx newx def /firsty newy def} def/linetoproc { continue { @linetoproc } { pop pop } ifelse } def/@linetoproc{ /oldx newx def /oldy newy def /newy exch def /newx exch def /dx newx oldx sub def /dy newy oldy sub def /dist dx dup mul dy dup mul add sqrt def /pathdist pathdist dist add def pathdist targetdist ge { pathdist targetdist sub dist div dup dy mul neg newy add /Y exch def dx mul neg newx add /X exch def /Angle dy dx atan def /continue false def } if} def/TextPathShow{ /String exch def /CharCount 0 def String length { String CharCount 1 getinterval ShowChar /CharCount CharCount 1 add def } repeat} def% Syntax: <pathlength> <position> InitTextPath -/InitTextPath{ gsave currentpoint /Y exch def /X exch def exch X Hoffset sub sub mul Voffset Hoffset sub add neg X add /Hoffset exch def /Voffset Y def grestore} def/Transform{ PathPosition dup Angle cos mul Y add exch Angle sin mul neg X add exch translate Angle rotate} def/ShowChar{ /Char exch def gsave Char end stringwidth tx@TextPathDict begin 2 div /Sy exch def 2 div /Sx exch def currentpoint Voffset sub Sy add exch Hoffset sub Sx add Transform Sx neg Sy neg moveto Char end tx@TextPathSavedShow tx@TextPathDict begin grestore Sx 2 mul Sy 2 mul rmoveto} defend% END pst-text.pro%%EndProcSet%%BeginProcSet: special.pro%!TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc 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known { true setstrokeadjust /t { } def }{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 addexch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy ndiv ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt {dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dupstringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i iw add def } repeat grestore gsave n 0 gt% DG/SR modification begin - Nov. 7, 1997 - Patch 1%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }% DG/SR modification end{ 2 setlinecap } ifelse /i y1 def /f x1 dx muln 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx ndiv 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvsdup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto gexch t L stroke /i i h add def } repeat grestore } def/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 01 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x addexch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div cmul neg d } def/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def/Rot { CP CP translate 3 -1 roll neg rotate NET } def/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngledup a add ] cvx def } def/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]cvx def } def/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b sabs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c bdiv w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {h1 abs h sub dup s mul abs } ifelse } def/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div smul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 addexch } def/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def} if } ifelse } def/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnitneg exch neg exch idtransform T moveto } def /BOL { BeginOL } def/IfVisible true def } defend% END pstricks.pro%%EndProcSet%%BeginProcSet: pst-dots.pro%!PS-Adobe-2.0%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07.%%Creator: Timothy Van Zandt <tvz@Princeton.EDU>%%Creation Date: May 7, 199310 dict dup begin /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /FontBBox [ 0 0 0 0 ] def /Encoding 256 array def 0 1 255 { Encoding exch /.notdef put } for Encoding dup (b) 0 get /Bullet put dup (c) 0 get /Circle put dup (C) 0 get /BoldCircle put dup (u) 0 get /SolidTriangle put dup (t) 0 get /Triangle put dup (T) 0 get /BoldTriangle put dup (r) 0 get /SolidSquare put dup (s) 0 get /Square put dup (S) 0 get /BoldSquare put dup (q) 0 get /SolidPentagon put dup (p) 0 get /Pentagon put (P) 0 get /BoldPentagon put /Metrics 13 dict def Metrics begin /Bullet 1000 def /Circle 1000 def /BoldCircle 1000 def /SolidTriangle 1344 def /Triangle 1344 def /BoldTriangle 1344 def /SolidSquare 886 def /Square 886 def /BoldSquare 886 def /SolidPentagon 1093.2 def /Pentagon 1093.2 def /BoldPentagon 1093.2 def /.notdef 0 def end /BBoxes 13 dict def BBoxes begin /Circle { -550 -550 550 550 } def /BoldCircle /Circle load def /Bullet /Circle load def /Triangle { -571.5 -330 571.5 660 } def /BoldTriangle /Triangle load def /SolidTriangle /Triangle load def /Square { -450 -450 450 450 } def /BoldSquare /Square load def /SolidSquare /Square load def /Pentagon { -546.6 -465 546.6 574.7 } def /BoldPentagon /Pentagon load def /SolidPentagon /Pentagon load def /.notdef { 0 0 0 0 } def end /CharProcs 20 dict def CharProcs begin /Adjust { 2 copy dtransform floor .5 add exch floor .5 add exch idtransform 3 -1 roll div 3 1 roll exch div exch scale } def /CirclePath { 0 0 500 0 360 arc closepath } def /Bullet { 500 500 Adjust CirclePath fill } def /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath } def /SolidTriangle { TrianglePath fill } def /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath } def /SolidSquare { SquarePath fill } def /Square { SquarePath .89 .89 scale SquarePath eofill } def /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def /PentagonPath { -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto 0 574.7 lineto -546.6 177.6 lineto closepath } def /SolidPentagon { PentagonPath fill } def /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def /.notdef { } def end /BuildGlyph { exch begin Metrics 1 index get exec 0 BBoxes 3 index get exec setcachedevice CharProcs begin load exec end end } def /BuildChar { 1 index /Encoding get exch get 1 index /BuildGlyph get exec } bind defend/PSTricksDotFont exch definefont pop% END pst-dots.pro%%EndProcSet%%BeginProcSet: pst-node.pro%!% PostScript prologue for pst-node.tex.% Version 97 patch 1, 97/05/09.% For distribution, see pstricks.tex.%/tx@NodeDict 400 dict def tx@NodeDict begintx@Dict begin /T /translate load def end/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next endgrestore } def/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def} def/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exchSin mul } def } def/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def }ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dxdup Sin mul Cos Div } ifelse } def/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub/u ED /NodePos { GetRnodePos } def } def/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dupCos mul exch Sin mul } def/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w hmul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul} ifelse } def/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /dED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def dsub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atansin def /NodePos { TriNodePos } def } def/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Coshh mul Atan dup cos ww mul exch sin hh mul } def/GetCenter { begin X Y NodeMtrx transform CM itransform end } def/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { DistDist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg }{ 0 Dist Sin mul } ifelse } ifelse Do } def/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransformexch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrxdtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED popXYPos } ifelse } def/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1roll sin mul sub exch } ifelse } def/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleAAddOffset yA add /yA1 ED xA add /xA1 ED } def/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleBAddOffset yB add /yB1 ED xB add /xB1 ED } def/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmAAngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do EDArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED} ifelse } def/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmBAngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do EDArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED} ifelse } def/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict bknown and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yAED /xA ED NodeB GetCenter /yB ED /xB ED } if } def/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t submul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop} repeat LPutLine cleartomark } def/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bxsub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul muladd cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul addy0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mulmul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def} def/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd } def/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def} def/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomarkVPosEnd } def/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvxdef grestore exec /LPutVar /SaveLPutVar load def } def/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add defGetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {LPutVar VPutLine } def LPutVar } def/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop popend } def/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA subAtan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }ifelse } def/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmAGetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dictbegin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrxitransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate defxA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrxtransform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def }{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dictbegin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvxdef /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } ifxB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB EDGetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict beginfalse Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin falseLine end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def% DG/SR modification begin - May 9, 1997 - Patch 1%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp rr mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA addexch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED% DG/SR modification end} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a addAngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 rDiv def /y ED /x ED } def/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cosmul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dyadd xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVartx@Dict begin false Polygon end } def/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atandef /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r divdef /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add defGetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mulsub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn }{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 00 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat }ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le {r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC }{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul addadd AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t submul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 tsub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelsey0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos {LPutPos } def } def/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yBsub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xBw sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub negexch X sub neg exch moveto setmatrix CP grestore } def/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0def } ifelse LPutCoor } def/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg }if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED }def/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } ifr Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED }defend% END pst-node.pro%%EndProcSet%%BeginProcSet: pst-text.pro%!% PostScript header file pst-text.pro% Version 97, 94/04/20% For distribution, see pstricks.tex./tx@TextPathDict 40 dict deftx@TextPathDict begin% Syntax: <dist> PathPosition -% Function: Searches for position of currentpath distance <dist> from% beginning. Sets (X,Y)=position, and Angle=tangent./PathPosition{ /targetdist exch def /pathdist 0 def /continue true def /X { newx } def /Y { newy } def /Angle 0 def gsave flattenpath { movetoproc } { linetoproc } { } { firstx firsty linetoproc } /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if grestore} def/movetoproc { continue { @movetoproc } { pop pop } ifelse } def/@movetoproc{ /newy exch def /newx exch def /firstx newx def /firsty newy def} def/linetoproc { continue { @linetoproc } { pop pop } ifelse } def/@linetoproc{ /oldx newx def /oldy newy def /newy exch def /newx exch def /dx newx oldx sub def /dy newy oldy sub def /dist dx dup mul dy dup mul add sqrt def /pathdist pathdist dist add def pathdist targetdist ge { pathdist targetdist sub dist div dup dy mul neg newy add /Y exch def dx mul neg newx add /X exch def /Angle dy dx atan def /continue false def } if} def/TextPathShow{ /String exch def /CharCount 0 def String length { String CharCount 1 getinterval ShowChar 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def a r /arcto load stopped { 5 } { 4 }ifelse { pop } repeat a } def/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eqand { pop pop /n n 1 sub def } if } def/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll LinetoLineto pop pop closepath } ifelse } def/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mulneg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w adddef } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrxsetmatrix } def% DG modification begin - Jan. 15, 1997%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx%setmatrix } def/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dupCLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)% setmatrix } defsetmatrix pop } def% DG/SR modification end/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pythdef } def/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pythdef } def/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c expmul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cosabs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mulm mul neg def } def/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }def/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def/NC { CC x1 y1 x2 y2 x y curveto } def/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def/NAC { x2 y2 x y curveto CC x1 y1 } def/EAC { x2 y2 x y ArrowB curveto pop pop } def/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub defn { NC } repeat EOC } ifelse } def/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { poppop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }repeat closepath pop pop } ifelse } def/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }def/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrixrotate matrix concatmatrix exch findfont exch makefont setfont } def/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 linetox1 y1 lineto closepath } def/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 divexch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arctox2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }ifelse } def/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {pop pop Rect } { OvalFrame } ifelse } def/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 62 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }ifelse } def/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }def/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowAx0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0y0 x0 2 mul x1 sub y1 ] def } def/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 }if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy divround cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx divround cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def }if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def }{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 addexch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy ndiv ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt {dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dupstringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i iw add def } repeat grestore gsave n 0 gt% DG/SR modification begin - Nov. 7, 1997 - Patch 1%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }% DG/SR modification end{ 2 setlinecap } ifelse /i y1 def /f x1 dx muln 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx ndiv 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvsdup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto gexch t L stroke /i i h add def } repeat grestore } def/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 01 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x addexch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div cmul neg d } def/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def/Rot { CP CP translate 3 -1 roll neg rotate NET } def/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngledup a add ] cvx def } def/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]cvx def } def/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b sabs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c bdiv w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {h1 abs h sub dup s mul abs } ifelse } def/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div smul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 addexch } def/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def} if } ifelse } def/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnitneg exch neg exch idtransform T moveto } def /BOL { BeginOL } def/IfVisible true def } defend% END pstricks.pro%%EndProcSet%%BeginProcSet: pst-dots.pro%!PS-Adobe-2.0%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07.%%Creator: Timothy Van Zandt <tvz@Princeton.EDU>%%Creation Date: May 7, 199310 dict dup begin /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /FontBBox [ 0 0 0 0 ] def /Encoding 256 array def 0 1 255 { Encoding exch /.notdef put } for Encoding dup (b) 0 get /Bullet put dup (c) 0 get /Circle put dup (C) 0 get /BoldCircle put dup (u) 0 get /SolidTriangle put dup (t) 0 get /Triangle put dup (T) 0 get /BoldTriangle put dup (r) 0 get /SolidSquare put dup (s) 0 get /Square put dup (S) 0 get /BoldSquare put dup (q) 0 get /SolidPentagon put dup (p) 0 get /Pentagon put (P) 0 get /BoldPentagon put /Metrics 13 dict def Metrics begin /Bullet 1000 def /Circle 1000 def /BoldCircle 1000 def /SolidTriangle 1344 def /Triangle 1344 def /BoldTriangle 1344 def /SolidSquare 886 def /Square 886 def /BoldSquare 886 def /SolidPentagon 1093.2 def /Pentagon 1093.2 def /BoldPentagon 1093.2 def /.notdef 0 def end /BBoxes 13 dict def BBoxes begin /Circle { -550 -550 550 550 } def /BoldCircle /Circle load def /Bullet /Circle load def /Triangle { -571.5 -330 571.5 660 } def /BoldTriangle /Triangle load def /SolidTriangle /Triangle load def /Square { -450 -450 450 450 } def /BoldSquare /Square load def /SolidSquare /Square load def /Pentagon { -546.6 -465 546.6 574.7 } def /BoldPentagon /Pentagon load def /SolidPentagon /Pentagon load def /.notdef { 0 0 0 0 } def end /CharProcs 20 dict def CharProcs begin /Adjust { 2 copy dtransform floor .5 add exch floor .5 add exch idtransform 3 -1 roll div 3 1 roll exch div exch scale } def /CirclePath { 0 0 500 0 360 arc closepath } def /Bullet { 500 500 Adjust CirclePath fill } def /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath } def /SolidTriangle { TrianglePath fill } def /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath } def /SolidSquare { SquarePath fill } def /Square { SquarePath .89 .89 scale SquarePath eofill } def /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def /PentagonPath { -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto 0 574.7 lineto -546.6 177.6 lineto closepath } def /SolidPentagon { PentagonPath fill } def /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def /.notdef { } def end /BuildGlyph { exch begin Metrics 1 index get exec 0 BBoxes 3 index get exec setcachedevice CharProcs begin load exec end end } def /BuildChar { 1 index /Encoding get exch get 1 index /BuildGlyph get exec } bind defend/PSTricksDotFont exch definefont pop% END pst-dots.pro%%EndProcSet%%BeginProcSet: pst-node.pro%!% PostScript prologue for pst-node.tex.% Version 97 patch 1, 97/05/09.% For distribution, see pstricks.tex.%/tx@NodeDict 400 dict def tx@NodeDict begintx@Dict begin /T /translate load def end/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next endgrestore } def/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def} def/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exchSin mul } def } def/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def }ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dxdup Sin mul Cos Div } ifelse } def/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub/u ED /NodePos { GetRnodePos } def } def/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dupCos mul exch Sin mul } def/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w hmul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul} ifelse } def/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /dED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def dsub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atansin def /NodePos { TriNodePos } def } def/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Coshh mul Atan dup cos ww mul exch sin hh mul } def/GetCenter { begin X Y NodeMtrx transform CM itransform end } def/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { DistDist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg }{ 0 Dist Sin mul } ifelse } ifelse Do } def/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransformexch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrxdtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED popXYPos } ifelse } def/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1roll sin mul sub exch } ifelse } def/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleAAddOffset yA add /yA1 ED xA add /xA1 ED } def/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleBAddOffset yB add /yB1 ED xB add /xB1 ED } def/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmAAngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do EDArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED} ifelse } def/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmBAngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do EDArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED} ifelse } def/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict bknown and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yAED /xA ED NodeB GetCenter /yB ED /xB ED } if } def/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t submul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop} repeat LPutLine cleartomark } def/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bxsub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul muladd cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul addy0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mulmul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def} def/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd } def/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def} def/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomarkVPosEnd } def/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvxdef grestore exec /LPutVar /SaveLPutVar load def } def/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add defGetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {LPutVar VPutLine } def LPutVar } def/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop popend } def/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA subAtan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }ifelse } def/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmAGetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dictbegin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrxitransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate defxA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrxtransform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def }{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dictbegin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvxdef /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } ifxB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB EDGetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict beginfalse Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin falseLine end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def% DG/SR modification begin - May 9, 1997 - Patch 1%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp rr mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA addexch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED% DG/SR modification end} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a addAngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 rDiv def /y ED /x ED } def/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cosmul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dyadd xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVartx@Dict begin false Polygon end } def/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atandef /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r divdef /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add defGetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mulsub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn }{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 00 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat }ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le {r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC }{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul addadd AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t submul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 tsub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelsey0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos {LPutPos } def } def/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yBsub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xBw sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos{ LPutLines } def /VPutPos@ { 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/currentlinewidth load def/CP /currentpoint load def/ED { exch def } bind def/L /lineto load def/T /translate load def/TMatrix { } def/RAngle { 0 } def/Atan { /atan load stopped { pop pop 0 } if } def/Div { dup 0 eq { pop } { div } ifelse } def/NET { neg exch neg exch T } def/Pyth { dup mul exch dup mul add sqrt } def/PtoC { 2 copy cos mul 3 1 roll sin mul } def/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def }def/PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def} { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ }/pathforall load stopped { pop pop pop pop } if z } def/STP { .996264 dup scale } def/STV { SDict begin normalscale end STP } def/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 defPathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul ymul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ]0 } ifelse setdash stroke } def/DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt{ /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y adddef } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1setlinecap stroke } def/LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25% DG/SR modification begin - Dec. 12, 1997 - Patch 2%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED aitransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a% DG/SR modification endDiv cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }% defa mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestorepop pop } def% DG/SR modification end/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub negexch 3 index sub exch Atan rotate newpath } def/EndArrow { @mtrx setmatrix CP grestore end } def/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fillgrestore } def/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0CLW moveto } def/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0CLW moveto } def/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto }def/SD { 0 360 arc fill } def/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DSCLW sub SD } if 0 DS z add CLW 4 div sub moveto } def/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {/closepath load } /pathforall load stopped { pop pop pop pop CP /movetoload } if ] cvx newpath 3 1 roll T exec } def/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exchcvi def } def/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } iff { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 subdef n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }ifelse { pop } repeat a } def/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eqand { pop pop /n n 1 sub def } if } def/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll LinetoLineto pop pop closepath } ifelse } def/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mulneg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w adddef } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrxsetmatrix } def% DG modification begin - Jan. 15, 1997%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx%setmatrix } def/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dupCLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)% setmatrix } defsetmatrix pop } def% DG/SR modification end/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pythdef } def/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pythdef } def/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c expmul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cosabs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mulm mul neg def } def/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }def/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def/NC { CC x1 y1 x2 y2 x y curveto } def/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def/NAC { x2 y2 x y curveto CC x1 y1 } def/EAC { x2 y2 x y ArrowB curveto pop pop } def/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub defn { NC } repeat EOC } ifelse } def/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { poppop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }repeat closepath pop pop } ifelse } def/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }def/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrixrotate matrix concatmatrix exch findfont exch makefont setfont } def/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 linetox1 y1 lineto closepath } def/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 divexch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arctox2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }ifelse } def/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {pop pop Rect } { OvalFrame } ifelse } def/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 62 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }ifelse } def/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }def/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowAx0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0y0 x0 2 mul x1 sub y1 ] def } def/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 }if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy divround cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx divround cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def }if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def }{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 addexch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy ndiv ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt {dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dupstringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i iw add def } repeat grestore gsave n 0 gt% DG/SR modification begin - Nov. 7, 1997 - Patch 1%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }% DG/SR modification end{ 2 setlinecap } ifelse /i y1 def /f x1 dx muln 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx ndiv 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvsdup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto gexch t L stroke /i i h add def } repeat grestore } def/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 01 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x addexch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div cmul neg d } def/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def/Rot { CP CP translate 3 -1 roll neg rotate NET } def/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngledup a add ] cvx def } def/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]cvx def } def/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b sabs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c bdiv w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {h1 abs h sub dup s mul abs } ifelse } def/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div smul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 addexch } def/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def} if } ifelse } def/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnitneg exch neg exch idtransform T moveto } def /BOL { BeginOL } def/IfVisible true def } defend% END pstricks.pro%%EndProcSet%%BeginProcSet: pst-dots.pro%!PS-Adobe-2.0%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07.%%Creator: Timothy Van Zandt <tvz@Princeton.EDU>%%Creation Date: May 7, 199310 dict dup begin /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /FontBBox [ 0 0 0 0 ] def /Encoding 256 array def 0 1 255 { Encoding exch /.notdef put } for Encoding dup (b) 0 get /Bullet put dup (c) 0 get /Circle put dup (C) 0 get /BoldCircle put dup (u) 0 get /SolidTriangle put dup (t) 0 get /Triangle put dup (T) 0 get /BoldTriangle put dup (r) 0 get /SolidSquare put dup (s) 0 get /Square put dup (S) 0 get /BoldSquare put dup (q) 0 get /SolidPentagon put dup (p) 0 get /Pentagon put (P) 0 get /BoldPentagon put /Metrics 13 dict def Metrics begin /Bullet 1000 def /Circle 1000 def /BoldCircle 1000 def /SolidTriangle 1344 def /Triangle 1344 def /BoldTriangle 1344 def /SolidSquare 886 def /Square 886 def /BoldSquare 886 def /SolidPentagon 1093.2 def /Pentagon 1093.2 def /BoldPentagon 1093.2 def /.notdef 0 def end /BBoxes 13 dict def BBoxes begin /Circle { -550 -550 550 550 } def /BoldCircle /Circle load def /Bullet /Circle load def /Triangle { -571.5 -330 571.5 660 } def /BoldTriangle /Triangle load def /SolidTriangle /Triangle load def /Square { -450 -450 450 450 } def /BoldSquare /Square load def /SolidSquare /Square load def /Pentagon { -546.6 -465 546.6 574.7 } def /BoldPentagon /Pentagon load def /SolidPentagon /Pentagon load def /.notdef { 0 0 0 0 } def end /CharProcs 20 dict def CharProcs begin /Adjust { 2 copy dtransform floor .5 add exch floor .5 add exch idtransform 3 -1 roll div 3 1 roll exch div exch scale } def /CirclePath { 0 0 500 0 360 arc closepath } def /Bullet { 500 500 Adjust CirclePath fill } def /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath } def /SolidTriangle { TrianglePath fill } def /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath } def /SolidSquare { SquarePath fill } def /Square { SquarePath .89 .89 scale SquarePath eofill } def /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def /PentagonPath { -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto 0 574.7 lineto -546.6 177.6 lineto closepath } def /SolidPentagon { PentagonPath fill } def /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def /.notdef { } def end /BuildGlyph { exch begin Metrics 1 index get exec 0 BBoxes 3 index get exec setcachedevice CharProcs begin load exec end end } def /BuildChar { 1 index /Encoding get exch get 1 index /BuildGlyph get exec } bind defend/PSTricksDotFont exch definefont pop% END pst-dots.pro%%EndProcSet%%BeginProcSet: pst-node.pro%!% PostScript prologue for pst-node.tex.% Version 97 patch 1, 97/05/09.% For distribution, see pstricks.tex.%/tx@NodeDict 400 dict def tx@NodeDict begintx@Dict begin /T /translate load def end/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next endgrestore } def/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def} def/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exchSin mul } def } def/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def }ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dxdup Sin mul Cos Div } ifelse } def/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub/u ED /NodePos { GetRnodePos } def } def/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dupCos mul exch Sin mul } def/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w hmul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul} ifelse } def/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /dED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def dsub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atansin def /NodePos { TriNodePos } def } def/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Coshh mul Atan dup cos ww mul exch sin hh mul } def/GetCenter { begin X Y NodeMtrx transform CM itransform end } def/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { DistDist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg }{ 0 Dist Sin mul } ifelse } ifelse Do } def/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransformexch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrxdtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED popXYPos } ifelse } def/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1roll sin mul sub exch } ifelse } def/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleAAddOffset yA add /yA1 ED xA add /xA1 ED } def/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleBAddOffset yB add /yB1 ED xB add /xB1 ED } def/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmAAngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do EDArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED} ifelse } def/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmBAngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do EDArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED} ifelse } def/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict bknown and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yAED /xA ED NodeB GetCenter /yB ED /xB ED } if } def/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t submul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop} repeat LPutLine cleartomark } def/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bxsub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul muladd cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul addy0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mulmul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def} def/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd } def/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def} def/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomarkVPosEnd } def/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvxdef grestore exec /LPutVar /SaveLPutVar load def } def/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add defGetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {LPutVar VPutLine } def LPutVar } def/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop popend } def/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA subAtan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }ifelse } def/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmAGetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dictbegin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrxitransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate defxA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrxtransform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def }{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dictbegin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvxdef /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } ifxB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB EDGetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict beginfalse Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin falseLine end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def% DG/SR modification begin - May 9, 1997 - Patch 1%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp rr mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA addexch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED% DG/SR modification end} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a addAngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 rDiv def /y ED /x ED } def/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cosmul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dyadd xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVartx@Dict begin false Polygon end } def/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atandef /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r divdef /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add defGetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mulsub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn }{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 00 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat }ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le {r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC }{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul addadd AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t submul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 tsub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelsey0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos {LPutPos } def } def/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yBsub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xBw sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub negexch X sub neg exch moveto setmatrix CP grestore } def/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0def } ifelse LPutCoor } def/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg }if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED }def/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } ifr Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED }defend% END pst-node.pro%%EndProcSet%%BeginProcSet: pst-text.pro%!% PostScript header file pst-text.pro% Version 97, 94/04/20% For distribution, see pstricks.tex./tx@TextPathDict 40 dict deftx@TextPathDict begin% Syntax: <dist> PathPosition -% Function: Searches for position of currentpath distance <dist> from% beginning. Sets (X,Y)=position, and Angle=tangent./PathPosition{ /targetdist exch def /pathdist 0 def /continue true def /X { newx } def /Y { newy } def /Angle 0 def gsave flattenpath { movetoproc } { linetoproc } { } { firstx firsty linetoproc } /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if grestore} def/movetoproc { continue { @movetoproc } { pop pop } ifelse } def/@movetoproc{ /newy exch def /newx exch def /firstx newx def /firsty newy def} def/linetoproc { continue { @linetoproc } { pop pop } ifelse } def/@linetoproc{ /oldx newx def /oldy newy def /newy exch def /newx exch def /dx newx oldx sub def /dy newy oldy sub def /dist dx dup mul dy dup mul add sqrt def /pathdist pathdist dist add def pathdist targetdist ge { pathdist targetdist sub dist div dup dy mul neg newy add /Y exch def dx mul neg newx add /X exch def /Angle dy dx atan def /continue false def } if} def/TextPathShow{ /String exch def /CharCount 0 def String length { String CharCount 1 getinterval ShowChar 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c mul /e ED pop pop pop r a e d PtoC y add exch x addexch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div cmul neg d } def/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def/Rot { CP CP translate 3 -1 roll neg rotate NET } def/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngledup a add ] cvx def } def/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]cvx def } def/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b sabs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c bdiv w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {h1 abs h sub dup s mul abs } ifelse } def/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div smul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 addexch } def/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def} if } ifelse } def/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnitneg exch neg exch idtransform T moveto } def /BOL { BeginOL } def/IfVisible true def } defend% END pstricks.pro%%EndProcSet%%BeginProcSet: pst-dots.pro%!PS-Adobe-2.0%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07.%%Creator: Timothy Van Zandt <tvz@Princeton.EDU>%%Creation Date: May 7, 199310 dict dup begin /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /FontBBox [ 0 0 0 0 ] def /Encoding 256 array def 0 1 255 { Encoding exch /.notdef put } for Encoding dup (b) 0 get /Bullet put dup (c) 0 get /Circle put dup (C) 0 get /BoldCircle put dup (u) 0 get /SolidTriangle put dup (t) 0 get /Triangle put dup (T) 0 get /BoldTriangle put dup (r) 0 get /SolidSquare put dup (s) 0 get /Square put dup (S) 0 get /BoldSquare put dup (q) 0 get /SolidPentagon put dup (p) 0 get /Pentagon put (P) 0 get /BoldPentagon put /Metrics 13 dict def Metrics begin /Bullet 1000 def /Circle 1000 def /BoldCircle 1000 def /SolidTriangle 1344 def /Triangle 1344 def /BoldTriangle 1344 def /SolidSquare 886 def /Square 886 def /BoldSquare 886 def /SolidPentagon 1093.2 def /Pentagon 1093.2 def /BoldPentagon 1093.2 def /.notdef 0 def end /BBoxes 13 dict def BBoxes begin /Circle { -550 -550 550 550 } def /BoldCircle /Circle load def /Bullet /Circle load def /Triangle { -571.5 -330 571.5 660 } def /BoldTriangle /Triangle load def /SolidTriangle /Triangle load def /Square { -450 -450 450 450 } def /BoldSquare /Square load def /SolidSquare /Square load def /Pentagon { -546.6 -465 546.6 574.7 } def /BoldPentagon /Pentagon load def /SolidPentagon /Pentagon load def /.notdef { 0 0 0 0 } def end /CharProcs 20 dict def CharProcs begin /Adjust { 2 copy dtransform floor .5 add exch floor .5 add exch idtransform 3 -1 roll div 3 1 roll exch div exch scale } def /CirclePath { 0 0 500 0 360 arc closepath } def /Bullet { 500 500 Adjust CirclePath fill } def /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath } def /SolidTriangle { TrianglePath fill } def /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath } def /SolidSquare { SquarePath fill } def /Square { SquarePath .89 .89 scale SquarePath eofill } def /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def /PentagonPath { -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto 0 574.7 lineto -546.6 177.6 lineto closepath } def /SolidPentagon { PentagonPath fill } def /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def /.notdef { } def end /BuildGlyph { exch begin Metrics 1 index get exec 0 BBoxes 3 index get exec setcachedevice CharProcs begin load exec end end } def /BuildChar { 1 index /Encoding get exch get 1 index /BuildGlyph get exec } bind defend/PSTricksDotFont exch definefont pop% END pst-dots.pro%%EndProcSet%%BeginProcSet: pst-node.pro%!% PostScript prologue for pst-node.tex.% Version 97 patch 1, 97/05/09.% For distribution, see pstricks.tex.%/tx@NodeDict 400 dict def tx@NodeDict begintx@Dict begin /T /translate load def end/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next endgrestore } def/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def} def/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exchSin mul } def } def/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def }ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dxdup Sin mul Cos Div } ifelse } def/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub/u ED /NodePos { GetRnodePos } def } def/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dupCos mul exch Sin mul } def/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w hmul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul} ifelse } def/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /dED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def dsub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atansin def /NodePos { TriNodePos } def } def/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Coshh mul Atan dup cos ww mul exch sin hh mul } def/GetCenter { begin X Y NodeMtrx transform CM itransform end } def/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { DistDist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg }{ 0 Dist Sin mul } ifelse } ifelse Do } def/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransformexch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrxdtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED popXYPos } ifelse } def/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1roll sin mul sub exch } ifelse } def/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleAAddOffset yA add /yA1 ED xA add /xA1 ED } def/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleBAddOffset yB add /yB1 ED xB add /xB1 ED } def/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmAAngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do EDArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED} ifelse } def/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmBAngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do EDArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED} ifelse } def/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict bknown and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yAED /xA ED NodeB GetCenter /yB ED /xB ED } if } def/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t submul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop} repeat LPutLine cleartomark } def/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bxsub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul muladd cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul addy0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mulmul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def} def/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd } def/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def} def/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomarkVPosEnd } def/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvxdef grestore exec /LPutVar /SaveLPutVar load def } def/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add defGetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {LPutVar VPutLine } def LPutVar } def/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop popend } def/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA subAtan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }ifelse } def/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmAGetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dictbegin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrxitransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate defxA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrxtransform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def }{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dictbegin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvxdef /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } ifxB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB EDGetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict beginfalse Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin falseLine end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def% DG/SR modification begin - May 9, 1997 - Patch 1%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp rr mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA addexch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED% DG/SR modification end} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a addAngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 rDiv def /y ED /x ED } def/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cosmul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dyadd xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVartx@Dict begin false Polygon end } def/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atandef /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r divdef /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add defGetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mulsub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn }{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 00 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat }ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le {r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC }{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul addadd AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t submul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 tsub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelsey0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos {LPutPos } def } def/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yBsub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xBw sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub negexch X sub neg exch moveto setmatrix CP grestore } def/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0def } ifelse LPutCoor } def/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg }if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED }def/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } ifr Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED }defend% END pst-node.pro%%EndProcSet%%BeginProcSet: pst-text.pro%!% PostScript header file pst-text.pro% Version 97, 94/04/20% For distribution, see pstricks.tex./tx@TextPathDict 40 dict deftx@TextPathDict begin% Syntax: <dist> PathPosition -% Function: Searches for position of currentpath distance <dist> from% beginning. Sets (X,Y)=position, and Angle=tangent./PathPosition{ /targetdist exch def /pathdist 0 def /continue true def /X { newx } def /Y { newy } def /Angle 0 def gsave flattenpath { movetoproc } { linetoproc } { } { firstx firsty linetoproc } /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if grestore} def/movetoproc { continue { @movetoproc } { pop pop } ifelse } def/@movetoproc{ /newy exch def /newx exch def /firstx newx def /firsty newy def} def/linetoproc { continue { @linetoproc } { pop pop } ifelse } def/@linetoproc{ /oldx newx def /oldy newy def /newy exch def /newx exch def /dx newx oldx sub def /dy newy oldy sub def /dist dx dup mul dy dup mul add sqrt def /pathdist pathdist dist add def pathdist targetdist ge { pathdist targetdist sub dist div dup dy mul neg newy add /Y exch def dx mul neg newx add /X exch def /Angle dy dx atan def /continue false def } if} def/TextPathShow{ /String exch def /CharCount 0 def String length { String CharCount 1 getinterval ShowChar /CharCount CharCount 1 add def } repeat} def% Syntax: <pathlength> <position> InitTextPath -/InitTextPath{ gsave currentpoint /Y exch def /X exch def exch X Hoffset sub sub mul Voffset Hoffset sub add neg X add /Hoffset exch def /Voffset Y def grestore} def/Transform{ PathPosition dup Angle cos mul Y add exch Angle sin mul neg X add exch translate Angle rotate} def/ShowChar{ /Char exch def gsave Char end stringwidth tx@TextPathDict begin 2 div /Sy exch def 2 div /Sx exch def currentpoint Voffset sub Sy add exch Hoffset sub Sx add Transform Sx neg Sy neg moveto Char end tx@TextPathSavedShow tx@TextPathDict begin grestore Sx 2 mul Sy 2 mul rmoveto} defend% END pst-text.pro%%EndProcSet%%BeginProcSet: 8r.enc% @@psencodingfile@{% author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry",% version = "0.6",% date = "1 July 1998",% filename = "8r.enc",% email = "tex-fonts@@tug.org",% docstring = "Encoding for TrueType or Type 1 fonts% to be used with TeX."% @}% % Idea is to have all the characters normally included in Type 1 fonts% available for typesetting. This is effectively the characters in Adobe% Standard Encoding + ISO Latin 1 + extra characters from Lucida.% % Character code assignments were made as follows:% % (1) the Windows ANSI characters are almost all in their Windows ANSI% positions, because some Windows users cannot easily reencode the% fonts, and it makes no difference on other systems. The only Windows% ANSI characters not available are those that make no sense for% typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen% (173). quotesingle and grave are moved just because it's such an% irritation not having them in TeX positions.% % (2) Remaining characters are assigned arbitrarily to the lower part% of the range, avoiding 0, 10 and 13 in case we meet dumb software.% % (3) Y&Y Lucida Bright includes some extra text characters; in the% hopes that other PostScript fonts, perhaps created for public% consumption, will include them, they are included starting at 0x12.% % (4) Remaining positions left undefined are for use in (hopefully)% upward-compatible revisions, if someday more characters are generally% available.% % (5) hyphen appears twice for compatibility with both % ASCII and Windows.% /TeXBase1Encoding [% 0x00 (encoded characters from Adobe Standard not in Windows 3.1) /.notdef /dotaccent /fi /fl /fraction /hungarumlaut /Lslash /lslash /ogonek /ring /.notdef /breve /minus /.notdef % These are the only two remaining unencoded characters, so may as% well include them. /Zcaron /zcaron % 0x10 /caron /dotlessi % (unusual TeX characters available in, e.g., Lucida Bright) /dotlessj /ff /ffi /ffl /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef % very contentious; it's so painful not having quoteleft and quoteright % at 96 and 145 that we move the things normally found there to here. /grave /quotesingle % 0x20 (ASCII begins) /space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash% 0x30 /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question% 0x40 /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O% 0x50 /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore% 0x60 /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o% 0x70 /p /q /r /s 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Ga(c)26 b F4(:=)3267 1499 y F9(\()32941511 y Ga(y)3342 1499 y F9(\))3370 1511 y Ga(P)13 b F4(])pGa(;)i(c)p F4(\))q Ga(;)3621 1499 y F9(\()3649 1511 yGa(y)3697 1499 y F9(\))3724 1511 y Ga(P)e F4(\))552 1703y FL(And)707 1666 y Gc(i)707 1726 y(L)759 1703 y F4(\()7941691 y F9(\()822 1703 y Ga(x)874 1691 y F9(\))901 1703y Ga(M)d(;)15 b(y)s F4(\)[)p Ga(y)29 b F4(:=)1343 1691y FX(h)1370 1703 y Ga(c)1409 1691 y FX(i)1437 1703 yGa(P)13 b F4(])1580 1652 y F5(def)1587 1703 y F4(=)54b FL(Cut)p F4(\()1885 1691 y FX(h)1913 1703 y Ga(c)19521691 y FX(i)1980 1703 y Ga(P)13 b(;)2091 1691 y F9(\()21191703 y Ga(y)2167 1691 y F9(\))2194 1703 y FL(And)23491666 y Gc(i)2349 1726 y(L)2401 1703 y F4(\()2436 1691y F9(\()2463 1703 y Ga(x)2515 1691 y F9(\))2543 1703y Ga(M)d F4([)p Ga(y)28 b F4(:=)2861 1691 y FX(h)28881703 y Ga(c)2927 1691 y FX(i)2955 1703 y Ga(P)13 b F4(])pGa(;)i(y)s F4(\))q(\))615 1895 y FL(Or)714 1858 y Gc(i)7141918 y(R)772 1895 y F4(\()807 1883 y FX(h)834 1895 yGa(a)882 1883 y FX(i)910 1895 y Ga(M)10 b(;)15 b(c)pF4(\)[)p Ga(c)27 b F4(:=)1334 1883 y F9(\()1362 1895y Ga(y)1410 1883 y F9(\))1437 1895 y Ga(P)13 b F4(])15801844 y F5(def)1587 1895 y F4(=)54 b FL(Cut)p F4(\()18851883 y FX(h)1913 1895 y Ga(c)1952 1883 y FX(i)1980 1895y FL(Or)2079 1858 y Gc(i)2079 1918 y(R)2137 1895 y F4(\()21721883 y FX(h)2200 1895 y Ga(a)2248 1883 y FX(i)2275 1895y Ga(M)10 b F4([)p Ga(c)26 b F4(:=)2584 1883 y F9(\()26121895 y Ga(y)2660 1883 y F9(\))2687 1895 y Ga(P)13 b F4(])pGa(;)i(c)p F4(\))q Ga(;)2938 1883 y F9(\()2966 1895 yGa(y)3014 1883 y F9(\))3041 1895 y Ga(P)e F4(\))385 2087y FL(Or)484 2101 y Gc(L)536 2087 y F4(\()571 2075 y F9(\()5992087 y Ga(x)651 2075 y F9(\))678 2087 y Ga(M)e(;)8172075 y F9(\()844 2087 y Ga(y)892 2075 y F9(\))920 2087y Ga(N)f(;)15 b(z)t F4(\)[)p Ga(z)30 b F4(:=)1343 2075y FX(h)1370 2087 y Ga(c)1409 2075 y FX(i)1437 2087 yGa(P)13 b F4(])1580 2036 y F5(def)1587 2087 y F4(=)54b FL(Cut)p F4(\()1885 2075 y FX(h)1913 2087 y Ga(c)19522075 y FX(i)1980 2087 y Ga(P)13 b(;)2091 2075 y F9(\()21192087 y Ga(z)2165 2075 y F9(\))2192 2087 y FL(Or)22922101 y Gc(L)2344 2087 y F4(\()2379 2075 y F9(\()24072087 y Ga(x)2459 2075 y F9(\))2486 2087 y Ga(M)d F4([)pGa(z)30 b F4(:=)2802 2075 y FX(h)2830 2087 y Ga(c)28692075 y FX(i)2896 2087 y Ga(P)13 b F4(])q Ga(;)3033 2075y F9(\()3060 2087 y Ga(y)3108 2075 y F9(\))3136 2087y Ga(N)d F4([)p Ga(z)29 b F4(:=)3437 2075 y FX(h)34642087 y Ga(c)3503 2075 y FX(i)3531 2087 y Ga(P)13 b F4(])pGa(;)i(z)t F4(\))q(\))463 2279 y FL(Imp)608 2301 y Gc(R)6652279 y F4(\()700 2267 y F9(\()728 2279 y Ga(x)780 2267y F9(\))q FX(h)835 2279 y Ga(a)883 2267 y FX(i)911 2279y Ga(M)10 b(;)15 b(b)p F4(\)[)p Ga(b)26 b F4(:=)13342267 y F9(\()1362 2279 y Ga(y)1410 2267 y F9(\))14372279 y Ga(P)13 b F4(])1580 2228 y F5(def)1587 2279 yF4(=)54 b FL(Cut)p F4(\()1885 2267 y FX(h)1913 2279 yGa(b)1952 2267 y FX(i)1980 2279 y FL(Imp)2124 2301 yGc(R)2182 2279 y F4(\()2217 2267 y F9(\()2244 2279 yGa(x)2296 2267 y F9(\))q FX(h)2351 2279 y Ga(a)2399 2267y FX(i)2427 2279 y Ga(M)10 b F4([)p Ga(b)25 b F4(:=)27362267 y F9(\()2763 2279 y Ga(y)2811 2267 y F9(\))28382279 y Ga(P)13 b F4(])q Ga(;)i(b)p F4(\))p Ga(;)30892267 y F9(\()3117 2279 y Ga(y)3165 2267 y F9(\))31932279 y Ga(P)e F4(\))336 2471 y FL(Imp)481 2493 y Gc(L)5332471 y F4(\()568 2459 y FX(h)596 2471 y Ga(a)644 2459y FX(i)671 2471 y Ga(M)d(;)809 2459 y F9(\()837 2471y Ga(x)889 2459 y F9(\))917 2471 y Ga(N)f(;)15 b(y)sF4(\)[)p Ga(y)29 b F4(:=)1343 2459 y FX(h)1370 2471 yGa(c)1409 2459 y FX(i)1437 2471 y Ga(P)13 b F4(])15802420 y F5(def)1587 2471 y F4(=)54 b FL(Cut)p F4(\()18852459 y FX(h)1913 2471 y Ga(c)1952 2459 y FX(i)1980 2471y Ga(P)13 b(;)2091 2459 y F9(\()2119 2471 y Ga(y)21672459 y F9(\))2194 2471 y FL(Imp)2338 2493 y Gc(L)23912471 y F4(\()2426 2459 y FX(h)2453 2471 y Ga(a)2501 2459y FX(i)2529 2471 y Ga(M)d F4([)p Ga(y)28 b F4(:=)28472459 y FX(h)2874 2471 y Ga(c)2913 2459 y FX(i)2941 2471y Ga(P)13 b F4(])p Ga(;)3077 2459 y F9(\()3105 2471 yGa(x)3157 2459 y F9(\))3184 2471 y Ga(N)d F4([)p Ga(y)29b F4(:=)3487 2459 y FX(h)3514 2471 y Ga(c)3553 2459 yFX(i)3581 2471 y Ga(P)13 b F4(])p Ga(;)i(y)s F4(\))q(\))3152734 y Gb(Otherwise:)1114 2926 y FL(Ax)o F4(\()p Ga(x;)g(a)pF4(\)[)p Ga(\033)s F4(])1580 2874 y F5(def)1587 2926y F4(=)54 b FL(Ax)p F4(\()p Ga(x;)15 b(a)p F4(\))7883118 y FL(Cut)o F4(\()960 3106 y FX(h)988 3118 y Ga(a)10363106 y FX(i)1064 3118 y Ga(M)10 b(;)1202 3106 y F9(\()12303118 y Ga(x)1282 3106 y F9(\))1309 3118 y Ga(N)g F4(\)[)pGa(\033)s F4(])1580 3066 y F5(def)1587 3118 y F4(=)54b FL(Cut)p F4(\()1885 3106 y FX(h)1913 3118 y Ga(a)19613106 y FX(i)2014 3118 y Ga(M)10 b F4([)p Ga(\033)s F4(])qGa(;)2258 3106 y F9(\()2285 3118 y Ga(x)2337 3106 y F9(\))23903118 y Ga(N)g F4([)p Ga(\033)s F4(])q(\))863 3310 y FL(Not)10063324 y Gc(R)1063 3310 y F4(\()1098 3298 y F9(\()11263310 y Ga(x)1178 3298 y F9(\))1205 3310 y Ga(M)h(;)k(a)pF4(\)[)p Ga(\033)s F4(])1580 3258 y F5(def)1587 3310y F4(=)54 b FL(Not)1855 3324 y Gc(R)1913 3310 y F4(\()19483298 y F9(\()1976 3310 y Ga(x)2028 3298 y F9(\))20803310 y Ga(M)10 b F4([)p Ga(\033)s F4(])q Ga(;)15 b(a)pF4(\))868 3502 y FL(Not)1011 3516 y Gc(L)1063 3502 yF4(\()1098 3490 y FX(h)1126 3502 y Ga(a)1174 3490 y FX(i)12023502 y Ga(M)10 b(;)15 b(x)p F4(\)[)p Ga(\033)s F4(])15803450 y F5(def)1587 3502 y F4(=)54 b FL(Not)1855 3516y Gc(L)1907 3502 y F4(\()1942 3490 y FX(h)1970 3502 yGa(a)2018 3490 y FX(i)2071 3502 y Ga(M)10 b F4([)p Ga(\033)sF4(])q Ga(;)15 b(x)p F4(\))646 3694 y FL(And)801 3708y Gc(R)859 3694 y F4(\()894 3682 y FX(h)921 3694 y Ga(a)9693682 y FX(i)997 3694 y Ga(M)10 b(;)1135 3682 y FX(h)11633694 y Ga(b)1202 3682 y FX(i)1229 3694 y Ga(N)g(;)15b(c)p F4(\)[)p Ga(\033)s F4(])1580 3642 y F5(def)15873694 y F4(=)54 b FL(And)1867 3708 y Gc(R)1925 3694 yF4(\()1960 3682 y FX(h)1987 3694 y Ga(a)2035 3682 y FX(i)20883694 y Ga(M)10 b F4([)p Ga(\033)s F4(])q Ga(;)2332 3682y FX(h)2360 3694 y Ga(b)2399 3682 y FX(i)2452 3694 yGa(N)g F4([)p Ga(\033)s F4(])p Ga(;)15 b(c)p F4(\))8573886 y FL(And)1011 3849 y Gc(i)1011 3909 y(L)1063 3886y F4(\()1098 3874 y F9(\()1126 3886 y Ga(x)1178 3874y F9(\))1206 3886 y Ga(M)10 b(;)15 b(y)s F4(\)[)p Ga(\033)sF4(])1580 3834 y F5(def)1587 3886 y F4(=)54 b FL(And)18673849 y Gc(i)1867 3909 y(L)1919 3886 y F4(\()1954 3874y F9(\()1982 3886 y Ga(x)2034 3874 y F9(\))2087 3886y Ga(M)10 b F4([)p Ga(\033)s F4(])p Ga(;)15 b(y)s F4(\))9194077 y FL(Or)1018 4041 y Gc(i)1018 4101 y(R)1076 4077y F4(\()1111 4065 y FX(h)1139 4077 y Ga(a)1187 4065 yFX(i)1215 4077 y Ga(M)10 b(;)15 b(b)p F4(\)[)p Ga(\033)sF4(])1580 4026 y F5(def)1587 4077 y F4(=)54 b FL(Or)18124041 y Gc(i)1812 4101 y(R)1869 4077 y F4(\()1904 4065y FX(h)1932 4077 y Ga(a)1980 4065 y FX(i)2033 4077 yGa(M)10 b F4([)p Ga(\033)s F4(])q Ga(;)15 b(b)p F4(\))6884269 y FL(Or)787 4283 y Gc(L)839 4269 y F4(\()874 4257y F9(\()902 4269 y Ga(x)954 4257 y F9(\))981 4269 y Ga(M)10b(;)1119 4257 y F9(\()1147 4269 y Ga(y)1195 4257 y F9(\))12224269 y Ga(N)g(;)15 b(z)t F4(\)[)p Ga(\033)s F4(])15804218 y F5(def)1587 4269 y F4(=)54 b FL(Or)1812 4283 yGc(L)1864 4269 y F4(\()1899 4257 y F9(\()1927 4269 yGa(x)1979 4257 y F9(\))2031 4269 y Ga(M)10 b F4([)p Ga(\033)sF4(])q Ga(;)2275 4257 y F9(\()2303 4269 y Ga(y)2351 4257y F9(\))2403 4269 y Ga(N)g F4([)p Ga(\033)s F4(])q Ga(;)15b(z)t F4(\))767 4461 y FL(Imp)912 4483 y Gc(R)969 4461y F4(\()1004 4449 y F9(\()1032 4461 y Ga(x)1084 4449y F9(\))q FX(h)1139 4461 y Ga(a)1187 4449 y FX(i)12154461 y Ga(M)10 b(;)15 b(b)p F4(\)[)p Ga(\033)s F4(])15804410 y F5(def)1587 4461 y F4(=)54 b FL(Imp)1857 4483y Gc(R)1915 4461 y F4(\()1950 4449 y F9(\()1977 4461y Ga(x)2029 4449 y F9(\))q FX(h)2084 4461 y Ga(a)21324449 y FX(i)2185 4461 y Ga(M)10 b F4([)p Ga(\033)s F4(])qGa(;)15 b(b)p F4(\))641 4653 y FL(Imp)785 4675 y Gc(L)8374653 y F4(\()872 4641 y FX(h)900 4653 y Ga(a)948 4641y FX(i)975 4653 y Ga(M)c(;)1114 4641 y F9(\()1141 4653y Ga(x)1193 4641 y F9(\))1221 4653 y Ga(N)f(;)15 b(y)sF4(\)[)p Ga(\033)s F4(])1580 4602 y F5(def)1587 4653y F4(=)54 b FL(Imp)1857 4675 y Gc(L)1909 4653 y F4(\()19444641 y FX(h)1972 4653 y Ga(a)2020 4641 y FX(i)2073 4653y Ga(M)10 b F4([)p Ga(\033)s F4(])p Ga(;)2316 4641 yF9(\()2344 4653 y Ga(x)2396 4641 y F9(\))2449 4653 yGa(N)g F4([)p Ga(\033)s F4(])q Ga(;)15 b(y)s F4(\))p3965 4783 V 277 4786 3691 4 v Black 1340 4940 a Gg(Figure)24b(2.4:)29 b(Proof)24 b(substitution.)p Black Black BlackBlack eop end%%Page: 28 40TeXDict begin 28 39 bop Black -144 51 a Gb(28)2987 b(Sequent)22b(Calculi)p -144 88 3691 4 v Black 321 294 a Gg(original)31b(proof,)g(despite)f(\002rst)f(appearances,)k(is)28 bF7(not)h Gg(a)g(logical)h(cut,)g(b)n(ut)f(is)g(in)g(f)o(act)g(a)f(commuting)321 407 y(cut,)c(and)g(should)h(really)g(be)e(reduced)j(to)pBlack Black 1078 586 a FL(And)1233 600 y Gc(R)1290 586y F4(\()1325 574 y FX(h)1353 586 y Ga(a)1401 574 y FX(i)1429586 y Ga(M)10 b(;)1567 574 y FX(h)1595 586 y Ga(b)1634574 y FX(i)1661 586 y Ga(N)g(;)15 b(c)p F4(\)[)p Ga(c)27b F4(:=)2070 574 y F9(\()2098 586 y Ga(y)2146 574 y F9(\))2173586 y FL(And)2327 549 y F9(1)2327 609 y Gc(L)2380 586y 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1526 a F6(\017)p Black 46 w Gg(First,)37 b(there)f(are)g(tw)o(o)f(w)o(ays)g(to)g(reduce)i(a)d(cut-rule)k(ha)n(ving)f(an)e(implication)i(as)e(the)h(cut-)549 1639 y(formula.)29b(Consider)c(the)f(follo)n(wing)h(proof-fragment)p BlackBlack 989 1819 a FU(x)17 b FG(:)f FU(B)1182 1807 y FS(.)12351819 y FU(M)1348 1807 y FS(.)1401 1819 y FU(a)g FG(:)hFU(C)p 752 1839 1051 4 v 775 1906 a FS(.)828 1918 y FF(Imp)9601938 y FS(R)1015 1918 y FG(\()1047 1906 y FJ(\()10731918 y FU(x)1120 1906 y FJ(\))p FQ(h)1173 1918 y FU(a)12171906 y FQ(i)1244 1918 y FU(M)9 b(;)14 b(b)p FG(\))14611906 y FS(.)1514 1918 y FU(b)i FG(:)h FU(B)t FT(\033)oFU(C)1844 1855 y FT(\033)1909 1867 y FS(R)2128 1791 y(.)21811803 y FU(N)2280 1791 y FS(.)2333 1803 y FU(c)f FG(:)gFU(B)254 b(y)19 b FG(:)d FU(C)2928 1791 y FS(.)2981 1803y FU(P)3069 1791 y FS(.)p 2046 1839 1135 4 v 2046 1918a FU(z)k FG(:)c FU(B)t FT(\033)p FU(C)2364 1906 y FS(.)24171918 y FF(Imp)2549 1938 y FS(L)2599 1918 y FG(\()26311906 y FQ(h)2658 1918 y FU(c)2694 1906 y 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bop Black 277 51 a Gb(2.3)23 b(Pr)n(oof)i(of)e(Str)n(ong)h(Normalisation)2290 b(35)p 277 88 3691 4 v BlackBlack 277 492 V 277 4876 4 4384 v Black Black 708 834a F5(N)t(O)q(T)t(R)t(I)t(G)t(H)t(T)1075 849 y FQ(h:)pFS(B)s FQ(i)1231 834 y FG(\()p FU(X)7 b FG(\))1471 787y F5(def)1481 834 y FG(=)1655 664 y FI(8)1655 738 y(<)1655888 y(:)1771 721 y FQ(h)1798 733 y FU(a)r FG(:)r FT(:)pFU(B)1991 721 y FQ(i)2019 733 y FF(Not)2149 745 y FS(R)2204733 y FG(\()2236 721 y FJ(\()2262 733 y FU(x)r FG(:)rFU(B)2403 721 y FJ(\))2430 733 y FU(M)i(;)14 b(a)p FG(\))23b FT(j)1960 833 y FF(Not)2090 845 y FS(R)2144 833 y FG(\()2176821 y FJ(\()2203 833 y FU(x)r FG(:)r FU(B)2344 821 yFJ(\))2371 833 y FU(M)9 b(;)14 b(a)p FG(\))23 b Gd(freshly)c(introduces)i FU(a;)1960 920 y FJ(\()1986 932 y FU(x)rFG(:)r FU(B)2127 920 y FJ(\))2154 932 y FU(M)32 b FT(2)23b FU(X)3326 664 y FI(9)3326 738 y(=)3326 888 y(;)7591279 y F5(N)t(O)q(T)t(L)t(E)t(F)t(T)1079 1294 y FJ(\()pFQ(:)p FS(B)s FJ(\))1231 1279 y FG(\()p FU(X)7 b 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FU(M)c(;)8312016 y FJ(\()857 2028 y FU(x)904 2016 y FJ(\))931 2028y FU(N)g(;)14 b(y)s FG(\)\))1236 1993 y FS(x)1173 2028y FT(\000)-25 b(\000)g(!)22 b FF(Cut)p FG(\()1516 2016y FQ(h)1543 2028 y FU(c)1579 2016 y FQ(i)1606 2028 yFU(P)11 b(;)1707 2016 y FJ(\()1733 2028 y FU(y)1777 2016y FJ(\))1803 2028 y FF(Imp)1935 2049 y FS(L)1985 2028y FG(\()2017 2016 y FQ(h)2044 2028 y FU(a)2088 2016 yFQ(i)2114 2028 y FF(Cut)2181 1981 y FC(!)2242 2028 yFG(\()2274 2016 y FQ(h)2301 2028 y FU(c)2337 2016 y FQ(i)23642028 y FU(P)h(;)2466 2016 y FJ(\()2492 2028 y FU(y)25362016 y FJ(\))2561 2028 y FU(M)d FG(\))p FU(;)2720 2016y FJ(\()2746 2028 y FU(x)2793 2016 y FJ(\))2820 2028y FF(Cut)2886 1981 y FC(!)2947 2028 y FG(\()2979 2016y FQ(h)3006 2028 y FU(c)3042 2016 y FQ(i)3069 2028 yFU(P)j(;)3171 2016 y FJ(\()3197 2028 y FU(y)3241 2016y FJ(\))3267 2028 y FU(N)c FG(\))q FU(;)14 b(y)s FG(\))o(\))-1112212 y FR(Otherwise:)386 2324 y FF(Cut)453 2277 y FC( )5142324 y FG(\()546 2312 y FQ(h)573 2324 y FU(b)609 2312y FQ(i)636 2324 y FF(Ax)p FG(\()p FU(x;)g(a)p FG(\))qFU(;)959 2312 y FJ(\()985 2324 y FU(y)1029 2312 y FJ(\))10542324 y FU(P)e FG(\))1236 2288 y FS(x)1173 2324 y FT(\000)-25b(\000)g(!)22 b FF(Ax)p FG(\()p FU(x;)14 b(a)p FG(\))832460 y FF(Cut)150 2413 y FC( )211 2460 y FG(\()243 2448y FQ(h)270 2460 y FU(b)306 2448 y FQ(i)332 2460 y FF(Cut)pFG(\()490 2448 y FQ(h)517 2460 y FU(a)561 2448 y FQ(i)5882460 y FU(M)9 b(;)715 2448 y FJ(\()741 2460 y FU(x)7882448 y FJ(\))814 2460 y FU(N)g FG(\))p FU(;)959 2448y FJ(\()985 2460 y FU(y)1029 2448 y FJ(\))1054 2460 yFU(P)j FG(\))1236 2424 y FS(x)1173 2460 y FT(\000)-25b(\000)g(!)22 b FF(Cut)p FG(\()1516 2448 y FQ(h)15432460 y FU(a)1587 2448 y FQ(i)1614 2460 y FF(Cut)16802413 y FC( )1741 2460 y FG(\()1773 2448 y FQ(h)1800 2460y FU(b)1836 2448 y FQ(i)1863 2460 y FU(M)9 b(;)1990 2448y FJ(\()2015 2460 y FU(y)2059 2448 y FJ(\))2085 2460y FU(P)j FG(\))p FU(;)2219 2448 y FJ(\()2245 2460 y FU(x)22922448 y FJ(\))2318 2460 y FF(Cut)2385 2413 y FC( )24462460 y FG(\()2478 2448 y FQ(h)2505 2460 y FU(b)2541 2448y FQ(i)2568 2460 y FU(N)d(;)2681 2448 y FJ(\()2706 2460y FU(y)2750 2448 y FJ(\))2776 2460 y FU(P)j FG(\)\))1542596 y FF(Cut)220 2549 y FC( )281 2596 y FG(\()313 2584y FQ(h)340 2596 y FU(b)376 2584 y FQ(i)403 2596 y FF(Not)5332608 y FS(R)588 2596 y FG(\()620 2584 y FJ(\()646 2596y FU(x)693 2584 y FJ(\))719 2596 y FU(M)d(;)14 b(a)pFG(\))p FU(;)959 2584 y FJ(\()985 2596 y FU(y)1029 2584y FJ(\))1054 2596 y FU(P)e FG(\))1236 2560 y FS(x)11732596 y FT(\000)-25 b(\000)g(!)22 b FF(Not)1488 2608 yFS(R)1542 2596 y FG(\()1574 2584 y FJ(\()1601 2596 yFU(x)1648 2584 y FJ(\))1674 2596 y FF(Cut)1741 2549 yFC( )1802 2596 y FG(\()1834 2584 y FQ(h)1861 2596 y FU(b)18972584 y FQ(i)1924 2596 y FU(M)8 b(;)2050 2584 y FJ(\()20762596 y FU(y)2120 2584 y FJ(\))2146 2596 y FU(P)j FG(\))qFU(;)j(a)p FG(\))156 2732 y FF(Cut)223 2685 y FC( )2842732 y FG(\()316 2720 y FQ(h)343 2732 y FU(b)379 2720y FQ(i)406 2732 y FF(Not)536 2744 y FS(L)586 2732 y FG(\()6182720 y FQ(h)645 2732 y FU(a)689 2720 y FQ(i)716 2732y FU(M)8 b(;)14 b(x)p FG(\))q FU(;)959 2720 y FJ(\()9852732 y FU(y)1029 2720 y FJ(\))1054 2732 y FU(P)e FG(\))12362696 y FS(x)1173 2732 y FT(\000)-25 b(\000)g(!)22 b FF(Not)14882744 y FS(L)1538 2732 y FG(\()1570 2720 y FQ(h)1597 2732y FU(a)1641 2720 y FQ(i)1668 2732 y FF(Cut)1734 2685y FC( )1795 2732 y FG(\()1827 2720 y FQ(h)1855 2732 yFU(b)1891 2720 y FQ(i)1917 2732 y FU(M)9 b(;)2044 2720y FJ(\()2069 2732 y FU(y)2113 2720 y FJ(\))2139 2732y FU(P)j FG(\))p FU(;)i(x)p FG(\))-57 2868 y FF(Cut)102821 y FC( )70 2868 y FG(\()102 2856 y FQ(h)130 2868y FU(d)173 2856 y FQ(i)200 2868 y FF(And)341 2880 y FS(R)3952868 y FG(\()427 2856 y FQ(h)454 2868 y FU(a)498 2856y FQ(i)525 2868 y FU(M)9 b(;)652 2856 y FQ(h)679 2868y FU(b)715 2856 y FQ(i)741 2868 y FU(N)g(;)14 b(c)p FG(\))pFU(;)959 2856 y FJ(\()985 2868 y FU(y)1029 2856 y FJ(\))10542868 y FU(P)e FG(\))1236 2832 y FS(x)1173 2868 y FT(\000)-25b(\000)g(!)22 b FF(And)1499 2880 y FS(R)1553 2868 y FG(\()15852856 y FQ(h)1612 2868 y FU(a)1656 2856 y FQ(i)1683 2868y FF(Cut)1750 2821 y FC( )1811 2868 y FG(\()1843 2856y FQ(h)1870 2868 y FU(d)1913 2856 y FQ(i)1940 2868 yFU(M)9 b(;)2067 2856 y FJ(\()2093 2868 y FU(y)2137 2856y FJ(\))2162 2868 y FU(P)j FG(\))p FU(;)2296 2856 y FQ(h)23232868 y FU(b)2359 2856 y FQ(i)2386 2868 y FF(Cut)24532821 y FC( )2513 2868 y FG(\()2545 2856 y FQ(h)2573 2868y FU(d)2616 2856 y FQ(i)2643 2868 y FU(N)c(;)2755 2856y FJ(\()2781 2868 y FU(y)2825 2856 y FJ(\))2851 2868y FU(P)k FG(\))p FU(;)i(c)p FG(\))141 3004 y FF(Cut)2082957 y FC( )269 3004 y FG(\()301 2992 y FQ(h)328 3004y FU(a)372 2992 y FQ(i)398 3004 y FF(And)540 2967 y FS(i)5403024 y(L)589 3004 y FG(\()621 2992 y FJ(\()648 3004 yFU(x)695 2992 y FJ(\))721 3004 y FU(M)9 b(;)14 b(y)sFG(\))o FU(;)960 2992 y FJ(\()986 3004 y FU(z)1029 2992y FJ(\))1054 3004 y FU(P)e FG(\))1236 2968 y FS(x)11733004 y FT(\000)-25 b(\000)g(!)22 b FF(And)1499 2967 yFS(i)1499 3024 y(L)1549 3004 y FG(\()1581 2992 y FJ(\()16073004 y FU(x)1654 2992 y FJ(\))1680 3004 y FF(Cut)17472957 y FC( )1808 3004 y FG(\()1840 2992 y FQ(h)1867 3004y FU(a)1911 2992 y FQ(i)1938 3004 y FU(M)8 b(;)2064 2992y FJ(\()2090 3004 y FU(z)2133 2992 y FJ(\))2158 3004y FU(P)k FG(\))q FU(;)i(y)s FG(\))199 3140 y FF(Cut)2663093 y FC( )327 3140 y FG(\()359 3128 y FQ(h)386 3140y FU(c)422 3128 y FQ(i)449 3140 y FF(Or)539 3103 y FS(i)5393160 y(R)594 3140 y FG(\()626 3128 y FQ(h)653 3140 yFU(a)697 3128 y FQ(i)724 3140 y FU(M)8 b(;)14 b(b)p FG(\))pFU(;)955 3128 y FJ(\()981 3140 y FU(x)1028 3128 y FJ(\))10543140 y FU(P)e FG(\))1236 3104 y FS(x)1173 3140 y FT(\000)-25b(\000)g(!)22 b FF(Or)1448 3103 y FS(i)1448 3160 y(R)15033140 y FG(\()1535 3128 y FQ(h)1562 3140 y FU(a)1606 3128y FQ(i)1633 3140 y FF(Cut)1700 3093 y FC( )1760 3140y FG(\()1792 3128 y FQ(h)1820 3140 y FU(c)1856 3128 yFQ(i)1882 3140 y FU(M)9 b(;)2009 3128 y FJ(\()2035 3140y FU(x)2082 3128 y FJ(\))2108 3140 y FU(P)j FG(\))p FU(;)i(b)pFG(\))-16 3276 y FF(Cut)50 3229 y FC( )111 3276 y 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TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot}imagemask grestore}}ifelse B/QV{gsave newpath transform round exch roundexch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlinetofill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S pdelta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 Srmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end%%EndProcSet%%BeginProcSet: pstricks.pro%!% PostScript prologue for pstricks.tex.% Version 97 patch 3, 98/06/01% For distribution, see pstricks.tex.%/tx@Dict 200 dict def tx@Dict begin/ADict 25 dict def/CM { matrix currentmatrix } bind def/SLW /setlinewidth load def/CLW /currentlinewidth load def/CP /currentpoint load def/ED { exch def } bind def/L /lineto load def/T /translate load def/TMatrix { } def/RAngle { 0 } def/Atan { /atan load stopped { pop pop 0 } if } def/Div { dup 0 eq { pop } { div } ifelse } def/NET { neg exch neg exch T } def/Pyth { dup mul exch dup mul add sqrt } def/PtoC { 2 copy cos mul 3 1 roll sin mul } def/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def }def/PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def} { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ }/pathforall load stopped { pop pop pop pop } if z } def/STP { .996264 dup scale } def/STV { SDict begin normalscale end STP } def/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 defPathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul ymul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ]0 } ifelse setdash stroke } def/DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt{ /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y adddef } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1setlinecap stroke } def/LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25% DG/SR modification begin - Dec. 12, 1997 - Patch 2%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED aitransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a% DG/SR modification endDiv cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }% defa mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestorepop pop } def% DG/SR modification end/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub negexch 3 index sub exch Atan rotate newpath } def/EndArrow { @mtrx setmatrix CP grestore end } def/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fillgrestore } def/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0CLW moveto } def/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0CLW moveto } def/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto }def/SD { 0 360 arc fill } def/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DSCLW sub SD } if 0 DS z add CLW 4 div sub moveto } def/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {/closepath load } /pathforall load stopped { pop pop pop pop CP /movetoload } if ] cvx newpath 3 1 roll T exec } def/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exchcvi def } def/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } iff { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 subdef n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }ifelse { pop } repeat a } def/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eqand { pop pop /n n 1 sub def } if } def/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll LinetoLineto pop pop closepath } ifelse } def/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mulneg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w adddef } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrxsetmatrix } def% DG modification begin - Jan. 15, 1997%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx%setmatrix } def/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dupCLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)% setmatrix } defsetmatrix pop } def% DG/SR modification end/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pythdef } def/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pythdef } def/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c expmul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cosabs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mulm mul neg def } def/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }def/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def/NC { CC x1 y1 x2 y2 x y curveto } def/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def/NAC { x2 y2 x y curveto CC x1 y1 } def/EAC { x2 y2 x y ArrowB curveto pop pop } def/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub defn { NC } repeat EOC } ifelse } def/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { poppop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }repeat closepath pop pop } ifelse } def/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }def/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrixrotate matrix concatmatrix exch findfont exch makefont setfont } def/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 linetox1 y1 lineto closepath } def/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 divexch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arctox2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }ifelse } def/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {pop pop Rect } { OvalFrame } ifelse } def/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 62 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }ifelse } def/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }def/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowAx0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0y0 x0 2 mul x1 sub y1 ] def } def/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 }if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy divround cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx divround cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def }if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def }{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 addexch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy ndiv ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt {dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dupstringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i iw add def } repeat grestore gsave n 0 gt% DG/SR modification begin - Nov. 7, 1997 - Patch 1%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }% DG/SR modification end{ 2 setlinecap } ifelse /i y1 def /f x1 dx muln 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx ndiv 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvsdup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto gexch t L stroke /i i h add def } repeat grestore } def/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 01 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x addexch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div cmul neg d } def/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def/Rot { CP CP translate 3 -1 roll neg rotate NET } def/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngledup a add ] cvx def } def/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]cvx def } def/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b sabs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c bdiv w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {h1 abs h sub dup s mul abs } ifelse } def/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div smul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 addexch } def/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def} if } ifelse } def/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnitneg exch neg exch idtransform T moveto } def /BOL { BeginOL } def/IfVisible true def } defend% END pstricks.pro%%EndProcSet%%BeginProcSet: pst-dots.pro%!PS-Adobe-2.0%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07.%%Creator: Timothy Van Zandt <tvz@Princeton.EDU>%%Creation Date: May 7, 199310 dict dup begin /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /FontBBox [ 0 0 0 0 ] def /Encoding 256 array def 0 1 255 { Encoding exch /.notdef put } for Encoding dup (b) 0 get /Bullet put dup (c) 0 get /Circle put dup (C) 0 get /BoldCircle put dup (u) 0 get /SolidTriangle put dup (t) 0 get /Triangle put dup (T) 0 get /BoldTriangle put dup (r) 0 get /SolidSquare put dup (s) 0 get /Square put dup (S) 0 get /BoldSquare put dup (q) 0 get /SolidPentagon put dup (p) 0 get /Pentagon put (P) 0 get /BoldPentagon put /Metrics 13 dict def Metrics begin /Bullet 1000 def /Circle 1000 def /BoldCircle 1000 def /SolidTriangle 1344 def /Triangle 1344 def /BoldTriangle 1344 def /SolidSquare 886 def /Square 886 def /BoldSquare 886 def /SolidPentagon 1093.2 def /Pentagon 1093.2 def /BoldPentagon 1093.2 def /.notdef 0 def end /BBoxes 13 dict def BBoxes begin /Circle { -550 -550 550 550 } def /BoldCircle /Circle load def /Bullet /Circle load def /Triangle { -571.5 -330 571.5 660 } def /BoldTriangle /Triangle load def /SolidTriangle /Triangle load def /Square { -450 -450 450 450 } def /BoldSquare /Square load def /SolidSquare /Square load def /Pentagon { -546.6 -465 546.6 574.7 } def /BoldPentagon /Pentagon load def /SolidPentagon /Pentagon load def /.notdef { 0 0 0 0 } def end /CharProcs 20 dict def CharProcs begin /Adjust { 2 copy dtransform floor .5 add exch floor .5 add exch idtransform 3 -1 roll div 3 1 roll exch div exch scale } def /CirclePath { 0 0 500 0 360 arc closepath } def /Bullet { 500 500 Adjust CirclePath fill } def /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath } def /SolidTriangle { TrianglePath fill } def /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath } def /SolidSquare { SquarePath fill } def /Square { SquarePath .89 .89 scale SquarePath eofill } def /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def /PentagonPath { -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto 0 574.7 lineto -546.6 177.6 lineto closepath } def /SolidPentagon { PentagonPath fill } def /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def /.notdef { } def end /BuildGlyph { exch begin Metrics 1 index get exec 0 BBoxes 3 index get exec setcachedevice CharProcs begin load exec end end } def /BuildChar { 1 index /Encoding get exch get 1 index /BuildGlyph get exec } bind defend/PSTricksDotFont exch definefont pop% END pst-dots.pro%%EndProcSet%%BeginProcSet: pst-node.pro%!% PostScript prologue for pst-node.tex.% Version 97 patch 1, 97/05/09.% For distribution, see pstricks.tex.%/tx@NodeDict 400 dict def tx@NodeDict begintx@Dict begin /T /translate load def end/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next endgrestore } def/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def} def/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exchSin mul } def } def/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def }ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dxdup Sin mul Cos Div } ifelse } def/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub/u ED /NodePos { GetRnodePos } def } def/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dupCos mul exch Sin mul } def/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w hmul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul} ifelse } def/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /dED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def dsub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atansin def /NodePos { TriNodePos } def } def/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Coshh mul Atan dup cos ww mul exch sin hh mul } def/GetCenter { begin X Y NodeMtrx transform CM itransform end } def/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { DistDist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg }{ 0 Dist Sin mul } ifelse } ifelse Do } def/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransformexch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrxdtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED popXYPos } ifelse } def/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1roll sin mul sub exch } ifelse } def/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleAAddOffset yA add /yA1 ED xA add /xA1 ED } def/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleBAddOffset yB add /yB1 ED xB add /xB1 ED } def/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmAAngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do EDArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED} ifelse } def/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmBAngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do EDArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED} ifelse } def/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict bknown and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yAED /xA ED NodeB GetCenter /yB ED /xB ED } if } def/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t submul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop} repeat LPutLine cleartomark } def/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bxsub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul muladd cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul addy0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mulmul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def} def/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd } def/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def} def/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomarkVPosEnd } def/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvxdef grestore exec /LPutVar /SaveLPutVar load def } def/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add defGetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {LPutVar VPutLine } def LPutVar } def/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop popend } def/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA subAtan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }ifelse } def/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmAGetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dictbegin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrxitransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate defxA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrxtransform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def }{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dictbegin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvxdef /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } ifxB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB EDGetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict beginfalse Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin falseLine end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def% DG/SR modification begin - May 9, 1997 - Patch 1%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp rr mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA addexch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED% DG/SR modification end} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a addAngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 rDiv def /y ED /x ED } def/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cosmul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dyadd xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVartx@Dict begin false Polygon end } def/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atandef /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r divdef /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add defGetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mulsub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn }{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 00 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat }ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le {r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC }{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul addadd AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t submul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 tsub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelsey0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos {LPutPos } def } def/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yBsub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xBw sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub negexch X sub neg exch moveto setmatrix CP grestore } def/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0def } ifelse LPutCoor } def/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg }if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED }def/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } ifr Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED }defend% END pst-node.pro%%EndProcSet%%BeginProcSet: pst-text.pro%!% PostScript header file pst-text.pro% Version 97, 94/04/20% For distribution, see pstricks.tex./tx@TextPathDict 40 dict deftx@TextPathDict begin% Syntax: <dist> PathPosition -% Function: Searches for position of currentpath distance <dist> from% beginning. 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2254 yF6(j)p Ga(M)10 b F6(j)2274 2221 y Fu(S)2318 2254 y Ga(;)15b(a)p F4(\))-41 2451 y Gg(\(7\))430 b F6(j)p FL(And)6742414 y Gc(i)674 2474 y(E)734 2451 y F4(\()769 2439 yFX(h)797 2451 y Ga(a)845 2439 y FX(i)872 2451 y FL(Id)pF4(\()p Ga(z)t(;)15 b(a)p F4(\))r Ga(;)1190 2439 y F9(\()12182451 y Ga(x)1270 2439 y F9(\))1297 2451 y Ga(N)10 b F4(\))pF6(j)1440 2418 y Fu(S)1584 2399 y F5(def)1591 2451 yF4(=)106 b FL(And)1923 2414 y Gc(i)1923 2474 y(L)19752451 y F4(\()2010 2439 y F9(\()2038 2451 y Ga(x)20902439 y F9(\))2132 2451 y F6(j)p Ga(N)10 b F6(j)2265 2418y Fu(S)2309 2451 y Ga(;)15 b(z)t F4(\))-41 2601 y Gg(\(8\))272b F6(j)p FL(Or)460 2615 y Gc(E)520 2601 y F4(\()555 2589y FX(h)583 2601 y Ga(a)631 2589 y FX(i)658 2601 y FL(Id)pF4(\()p Ga(z)t(;)15 b(a)p F4(\))r Ga(;)976 2589 y F9(\()10042601 y Ga(x)1056 2589 y F9(\))1083 2601 y Ga(N)10 b(;)12062589 y F9(\()1234 2601 y Ga(y)1282 2589 y F9(\))13092601 y Ga(P)j F4(\))p F6(j)1440 2568 y Fu(S)1584 2549y F5(def)1591 2601 y F4(=)106 b FL(Or)1867 2615 y Gc(L)19192601 y F4(\()1954 2589 y F9(\()1982 2601 y Ga(x)20342589 y F9(\))2077 2601 y F6(j)p Ga(N)10 b F6(j)2210 2568y Fu(S)2254 2601 y Ga(;)2294 2589 y F9(\()2321 2601 yGa(y)2369 2589 y F9(\))2412 2601 y F6(j)p Ga(P)j F6(j)25332568 y Fu(S)2577 2601 y Ga(;)i(z)t F4(\))-41 2751 y Gg(\(9\))235b F6(j)p FL(Imp)469 2772 y Gc(E)529 2751 y F4(\()5642739 y FX(h)591 2751 y Ga(a)639 2739 y FX(i)667 2751y FL(Id)p F4(\()p Ga(z)t(;)15 b(a)p F4(\))q Ga(;)9842739 y FX(h)1012 2751 y Ga(b)1051 2739 y FX(i)1079 2751y Ga(N)10 b(;)1202 2739 y F9(\()1230 2751 y Ga(x)12822739 y F9(\))1309 2751 y Ga(P)j F4(\))p F6(j)1440 2718y Fu(S)1584 2699 y F5(def)1591 2751 y F4(=)106 b FL(Imp)19122772 y Gc(L)1965 2751 y F4(\()2000 2739 y FX(h)2027 2751y Ga(b)2066 2739 y FX(i)2109 2751 y F6(j)p Ga(N)10 bF6(j)2242 2718 y Fu(S)2286 2751 y Ga(;)2326 2739 y F9(\()23542751 y Ga(x)2406 2739 y F9(\))2448 2751 y F6(j)p Ga(P)jF6(j)2569 2718 y Fu(S)2613 2751 y Ga(;)i(z)t F4(\))-412901 y Gg(\(10\))410 b F6(j)p FL(Not)687 2915 y Gc(E)7472901 y F4(\()782 2889 y FX(h)810 2901 y Ga(a)858 2889y FX(i)885 2901 y FL(Id)p F4(\()p Ga(z)t(;)15 b(a)p F4(\))rGa(;)1203 2889 y FX(h)1231 2901 y Ga(b)1270 2889 y FX(i)12972901 y Ga(N)10 b F4(\))p F6(j)1440 2868 y Fu(S)1584 2849y F5(def)1591 2901 y F4(=)106 b FL(Not)1911 2915 y Gc(L)19632901 y F4(\()1998 2889 y FX(h)2026 2901 y Ga(b)2065 2889y FX(i)2107 2901 y F6(j)p Ga(N)10 b F6(j)2240 2868 yFu(S)2284 2901 y Ga(;)15 b(z)t F4(\))-41 3095 y Gb(Otherwise:)-413221 y Gg(\(11\))565 b F6(j)p FL(And)854 3184 y Gc(i)8543244 y(E)913 3221 y F4(\()948 3209 y FX(h)976 3221 yGa(a)1024 3209 y FX(i)1052 3221 y Ga(M)10 b(;)1190 3209y F9(\()1218 3221 y Ga(x)1270 3209 y F9(\))1297 3221y Ga(N)g F4(\))p F6(j)1440 3188 y Fu(S)1584 3169 y F5(def)15913221 y F4(=)106 b FL(Cut)p F4(\()1941 3209 y FX(h)19693221 y Ga(a)2017 3209 y FX(i)2059 3221 y F6(j)p Ga(M)10b F6(j)2207 3188 y Fu(S)2251 3221 y Ga(;)2291 3209 yF9(\()2319 3221 y Ga(y)2367 3209 y F9(\))2394 3221 yFL(And)2549 3184 y Gc(i)2549 3244 y(L)2601 3221 y F4(\()26363209 y F9(\()2664 3221 y Ga(x)2716 3209 y F9(\))27583221 y F6(j)p Ga(N)g F6(j)2891 3188 y Fu(S)2935 3221y Ga(;)15 b(y)s F4(\))q(\))-41 3371 y Gg(\(12\))406 bF6(j)p FL(Or)640 3385 y Gc(E)699 3371 y F4(\()734 3359y FX(h)762 3371 y Ga(a)810 3359 y FX(i)838 3371 y Ga(M)10b(;)976 3359 y F9(\()1004 3371 y Ga(x)1056 3359 y F9(\))10833371 y Ga(N)g(;)1206 3359 y F9(\()1234 3371 y Ga(y)12823359 y F9(\))1309 3371 y Ga(P)j F4(\))p F6(j)1440 3338y Fu(S)1584 3319 y F5(def)1591 3371 y F4(=)106 b FL(Cut)pF4(\()1941 3359 y FX(h)1969 3371 y Ga(a)2017 3359 y FX(i)20593371 y F6(j)p Ga(M)10 b F6(j)2207 3338 y Fu(S)2251 3371y Ga(;)2291 3359 y F9(\()2319 3371 y Ga(z)2365 3359 yF9(\))2393 3371 y FL(Or)2492 3385 y Gc(L)2544 3371 yF4(\()2579 3359 y F9(\()2607 3371 y Ga(x)2659 3359 yF9(\))2702 3371 y F6(j)p Ga(N)g F6(j)2835 3338 y Fu(S)28783371 y Ga(;)2918 3359 y F9(\()2946 3371 y Ga(y)2994 3359y F9(\))3037 3371 y F6(j)p Ga(P)j F6(j)3158 3338 y Fu(S)32023371 y Ga(;)i(z)t F4(\))q(\))-41 3521 y Gg(\(13\))370b F6(j)p FL(Imp)648 3543 y Gc(E)708 3521 y F4(\()7433509 y FX(h)771 3521 y Ga(a)819 3509 y FX(i)846 3521y Ga(M)10 b(;)984 3509 y FX(h)1012 3521 y Ga(b)1051 3509y FX(i)1079 3521 y Ga(N)g(;)1202 3509 y F9(\()1230 3521y Ga(x)1282 3509 y F9(\))1309 3521 y Ga(P)j F4(\))p F6(j)14403488 y Fu(S)1584 3469 y F5(def)1591 3521 y F4(=)106 bFL(Cut)p F4(\()1941 3509 y FX(h)1969 3521 y Ga(a)20173509 y FX(i)2059 3521 y F6(j)p Ga(M)10 b F6(j)2207 3488y Fu(S)2251 3521 y Ga(;)2291 3509 y F9(\()2319 3521 yGa(y)2367 3509 y F9(\))2394 3521 y FL(Imp)2539 3543 yGc(L)2591 3521 y F4(\()2626 3509 y FX(h)2654 3521 y Ga(b)26933509 y FX(i)2735 3521 y F6(j)p Ga(N)g F6(j)2868 3488y Fu(S)2912 3521 y Ga(;)2952 3509 y F9(\()2980 3521 yGa(x)3032 3509 y F9(\))3075 3521 y F6(j)p Ga(P)j F6(j)31963488 y Fu(S)3239 3521 y Ga(;)i(y)s F4(\))q(\))-41 3671y Gg(\(14\))590 b F6(j)p FL(Not)867 3685 y Gc(E)926 3671y F4(\()961 3659 y FX(h)989 3671 y Ga(a)1037 3659 y FX(i)10653671 y Ga(M)10 b(;)1203 3659 y FX(h)1231 3671 y Ga(b)12703659 y FX(i)1297 3671 y Ga(N)g F4(\))p F6(j)1440 3638y Fu(S)1584 3619 y F5(def)1591 3671 y F4(=)106 b FL(Cut)pF4(\()1941 3659 y FX(h)1969 3671 y Ga(a)2017 3659 y FX(i)20593671 y F6(j)p Ga(M)10 b F6(j)2207 3638 y Fu(S)2251 3671y Ga(;)2291 3659 y F9(\()2319 3671 y Ga(y)2367 3659 yF9(\))2394 3671 y FL(Not)2537 3685 y Gc(L)2589 3671 yF4(\()2624 3659 y FX(h)2652 3671 y Ga(b)2691 3659 y FX(i)27343671 y F6(j)p Ga(N)g F6(j)2867 3638 y Fu(S)2910 3671y Ga(;)15 b(y)s F4(\))q(\))268 3912 y Gg(where)24 b(in)48b(\(11\))h Ga(y)28 b F6(62)c Ga(F)13 b(N)d F4(\()11773900 y F9(\()1205 3912 y Ga(x)1257 3900 y F9(\))12853912 y F6(j)p Ga(N)g F6(j)1418 3879 y Fu(S)1462 3912y F4(\))464 b Gg(\(12\))49 b Ga(z)30 b F6(62)24 b Ga(F)13b(N)d F4(\()2506 3900 y F9(\()2534 3912 y Ga(x)2586 3900y F9(\))2614 3912 y F6(j)p Ga(N)g F6(j)2747 3879 y Fu(S)27913912 y Ga(;)2831 3900 y F9(\()2858 3912 y Ga(y)2906 3900y F9(\))2934 3912 y F6(j)p Ga(P)j F6(j)3055 3879 y Fu(S)30993912 y F4(\))631 4059 y Gg(\(13\))49 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FL(And)1490 1655 y Gc(R)1548 1641 y F4(\()15831629 y FX(h)1611 1641 y Ga(a)1659 1629 y FX(i)1686 1641y Ga(M)10 b(;)1824 1629 y FX(h)1852 1641 y Ga(b)18911629 y FX(i)1919 1641 y Ga(N)f(;)15 b(c)p F4(\))p F6(j)21401608 y Fu(N)2295 1590 y F5(def)2302 1641 y F4(=)107 bFL(And)2634 1655 y Gc(I)2674 1641 y F4(\()2709 1629 yFX(h)2737 1641 y Ga(a)2785 1629 y FX(i)2828 1641 y F6(j)pGa(M)10 b F6(j)2976 1608 y Fu(N)3030 1641 y Ga(;)30701629 y FX(h)3098 1641 y Ga(b)3137 1629 y FX(i)3180 1641y F6(j)p Ga(N)g F6(j)3313 1608 y Fu(N)3367 1641 y Ga(;)15b(c)p F4(\))442 1791 y Gg(\(3\))1036 b F6(j)p FL(Or)17081754 y Gc(i)1708 1814 y(R)1765 1791 y F4(\()1800 1779y FX(h)1828 1791 y Ga(a)1876 1779 y FX(i)1904 1791 yGa(M)10 b(;)15 b(b)p F4(\))p F6(j)2141 1758 y Fu(N)22951740 y F5(def)2302 1791 y F4(=)107 b FL(Or)2579 1754y Gc(i)2579 1814 y(I)2619 1791 y F4(\()2654 1779 y FX(h)26821791 y Ga(a)2730 1779 y FX(i)2772 1791 y F6(j)p Ga(M)10b F6(j)2920 1758 y Fu(N)2975 1791 y Ga(;)15 b(b)p F4(\))4421941 y Gg(\(4\))884 b F6(j)p FL(Imp)1601 1963 y Gc(R)16591941 y F4(\()1694 1929 y F9(\()1721 1941 y Ga(x)17731929 y F9(\))q FX(h)1828 1941 y Ga(a)1876 1929 y FX(i)19041941 y Ga(M)10 b(;)15 b(b)p F4(\))p F6(j)2141 1908 yFu(N)2295 1890 y F5(def)2302 1941 y F4(=)107 b FL(Imp)26241963 y Gc(I)2664 1941 y F4(\()2699 1929 y F9(\()27271941 y Ga(x)2779 1929 y F9(\))p FX(h)2834 1941 y Ga(a)28821929 y FX(i)2925 1941 y F6(j)p Ga(M)10 b F6(j)3073 1908y Fu(N)3127 1941 y Ga(;)15 b(b)p F4(\))442 2091 y Gg(\(5\))980b F6(j)p FL(Not)1695 2105 y Gc(R)1752 2091 y F4(\()17872079 y F9(\()1815 2091 y Ga(x)1867 2079 y F9(\))18952091 y Ga(M)10 b(;)15 b(a)p F4(\))p F6(j)2141 2058 yFu(N)2295 2040 y F5(def)2302 2091 y F4(=)107 b FL(Not)26232105 y Gc(I)2662 2091 y F4(\()2697 2079 y F9(\()27252091 y Ga(x)2777 2079 y F9(\))2820 2091 y F6(j)p Ga(M)10b F6(j)2968 2058 y Fu(N)3022 2091 y Ga(;)15 b(a)p F4(\))4422288 y Gg(\(6\))974 b F6(j)p FL(And)1701 2252 y Gc(i)17012311 y(L)1753 2288 y F4(\()1788 2276 y F9(\()1815 2288y 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CP 4 2 roll ArrowB L pop pop } if } def/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }ifelse { pop } repeat a } def/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eqand { pop pop /n n 1 sub def } if } def/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll LinetoLineto pop pop closepath } ifelse } def/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mulneg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w adddef } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrxsetmatrix } def% DG modification begin - Jan. 15, 1997%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx%setmatrix } def/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dupCLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)% setmatrix } defsetmatrix pop } def% DG/SR modification end/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pythdef } def/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pythdef } def/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c expmul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cosabs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mulm mul neg def } def/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }def/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def/NC { CC x1 y1 x2 y2 x y curveto } def/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def/NAC { x2 y2 x y curveto CC x1 y1 } def/EAC { x2 y2 x y ArrowB curveto pop pop } def/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub defn { NC } repeat EOC } ifelse } def/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { poppop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }repeat closepath pop pop } ifelse } def/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }def/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrixrotate matrix concatmatrix exch findfont exch makefont setfont } def/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 linetox1 y1 lineto closepath } def/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 divexch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arctox2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }ifelse } def/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {pop pop Rect } { OvalFrame } ifelse } def/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 62 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }ifelse } def/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }def/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowAx0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0y0 x0 2 mul x1 sub y1 ] def } def/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 }if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy divround cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx divround cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def }if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def }{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 addexch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy ndiv ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt {dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dupstringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i iw add def } repeat grestore gsave n 0 gt% DG/SR modification begin - Nov. 7, 1997 - Patch 1%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }% DG/SR modification end{ 2 setlinecap } ifelse /i y1 def /f x1 dx muln 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx ndiv 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvsdup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto gexch t L stroke /i i h add def } repeat grestore } def/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 01 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x addexch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div cmul neg d } def/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def/Rot { CP CP translate 3 -1 roll neg rotate NET } def/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngledup a add ] cvx def } def/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]cvx def } def/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b sabs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c bdiv w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {h1 abs h sub dup s mul abs } ifelse } def/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div smul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 addexch } def/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def} if } ifelse } def/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnitneg exch neg exch idtransform T moveto } def /BOL { BeginOL } def/IfVisible true def } defend% END pstricks.pro%%EndProcSet%%BeginProcSet: pst-dots.pro%!PS-Adobe-2.0%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07.%%Creator: Timothy Van Zandt <tvz@Princeton.EDU>%%Creation Date: May 7, 199310 dict dup begin /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /FontBBox [ 0 0 0 0 ] def /Encoding 256 array def 0 1 255 { Encoding exch /.notdef put } for Encoding dup (b) 0 get /Bullet put dup (c) 0 get /Circle put dup (C) 0 get /BoldCircle put dup (u) 0 get /SolidTriangle put dup (t) 0 get /Triangle put dup (T) 0 get /BoldTriangle put dup (r) 0 get /SolidSquare put dup (s) 0 get /Square put dup (S) 0 get /BoldSquare put dup (q) 0 get /SolidPentagon put dup (p) 0 get /Pentagon put (P) 0 get /BoldPentagon put /Metrics 13 dict def Metrics begin /Bullet 1000 def /Circle 1000 def /BoldCircle 1000 def /SolidTriangle 1344 def /Triangle 1344 def /BoldTriangle 1344 def /SolidSquare 886 def /Square 886 def /BoldSquare 886 def /SolidPentagon 1093.2 def /Pentagon 1093.2 def /BoldPentagon 1093.2 def /.notdef 0 def end /BBoxes 13 dict def BBoxes begin /Circle { -550 -550 550 550 } def /BoldCircle /Circle load def /Bullet /Circle load def /Triangle { -571.5 -330 571.5 660 } def /BoldTriangle /Triangle load def /SolidTriangle /Triangle load def /Square { -450 -450 450 450 } def /BoldSquare /Square load def /SolidSquare /Square load def /Pentagon { -546.6 -465 546.6 574.7 } def /BoldPentagon /Pentagon load def /SolidPentagon /Pentagon load def /.notdef { 0 0 0 0 } def end /CharProcs 20 dict def CharProcs begin /Adjust { 2 copy dtransform floor .5 add exch floor .5 add exch idtransform 3 -1 roll div 3 1 roll exch div exch scale } def /CirclePath { 0 0 500 0 360 arc closepath } def /Bullet { 500 500 Adjust CirclePath fill } def /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath } def /SolidTriangle { TrianglePath fill } def /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath } def /SolidSquare { SquarePath fill } def /Square { SquarePath .89 .89 scale SquarePath eofill } def /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def /PentagonPath { -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto 0 574.7 lineto -546.6 177.6 lineto closepath } def /SolidPentagon { PentagonPath fill } def /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def /.notdef { } def end /BuildGlyph { exch begin Metrics 1 index get exec 0 BBoxes 3 index get exec setcachedevice CharProcs begin load exec end end } def /BuildChar { 1 index /Encoding get exch get 1 index /BuildGlyph get exec } bind defend/PSTricksDotFont exch definefont pop% END pst-dots.pro%%EndProcSet%%BeginProcSet: pst-node.pro%!% PostScript prologue for pst-node.tex.% Version 97 patch 1, 97/05/09.% For copying restrictions, see pstricks.tex.%/tx@NodeDict 400 dict def tx@NodeDict begintx@Dict begin /T /translate load def end/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next endgrestore } def/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def} def/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exchSin mul } def } def/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def }ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dxdup Sin mul Cos Div } ifelse } def/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub/u ED /NodePos { GetRnodePos } def } def/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dupCos mul exch Sin mul } def/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w hmul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul} ifelse } def/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /dED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def dsub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atansin def /NodePos { TriNodePos } def } def/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Coshh mul Atan dup cos ww mul exch sin hh mul } def/GetCenter { begin X Y NodeMtrx transform CM itransform end } def/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { DistDist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg }{ 0 Dist Sin mul } ifelse } ifelse Do } def/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransformexch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrxdtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED popXYPos } ifelse } def/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1roll sin mul sub exch } ifelse } def/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleAAddOffset yA add /yA1 ED xA add /xA1 ED } def/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleBAddOffset yB add /yB1 ED xB add /xB1 ED } def/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmAAngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do EDArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED} ifelse } def/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmBAngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do EDArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED} ifelse } def/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict bknown and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yAED /xA ED NodeB GetCenter /yB ED /xB ED } if } def/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t submul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop} repeat LPutLine cleartomark } def/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bxsub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul muladd cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul addy0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mulmul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def} def/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd } def/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def} def/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomarkVPosEnd } def/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvxdef grestore exec /LPutVar /SaveLPutVar load def } def/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add defGetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {LPutVar VPutLine } def LPutVar } def/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop popend } def/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA subAtan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }ifelse } def/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmAGetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dictbegin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrxitransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate defxA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrxtransform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def }{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dictbegin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvxdef /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } ifxB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB EDGetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict beginfalse Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin falseLine end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def% DG/SR modification begin - May 9, 1997 - Patch 1%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp rr mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA addexch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED% DG/SR modification end} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a addAngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 rDiv def /y ED /x ED } def/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cosmul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dyadd xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVartx@Dict begin false Polygon end } def/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atandef /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r divdef /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add defGetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mulsub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn }{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 00 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat }ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le {r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC }{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul addadd AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t submul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 tsub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelsey0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos {LPutPos } def } def/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yBsub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xBw sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub negexch X sub neg exch moveto setmatrix CP grestore } def/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0def } ifelse LPutCoor } def/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg }if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED }def/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } ifr Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED }defend% END pst-node.pro%%EndProcSet%%BeginProcSet: pst-text.pro%!% PostScript header file pst-text.pro% Version 97, 94/04/20% For copying restrictions, see pstricks.tex./tx@TextPathDict 40 dict deftx@TextPathDict begin% Syntax: <dist> PathPosition -% Function: Searches for position of currentpath distance <dist> from% beginning. 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M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 Srmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end%%EndProcSet%%BeginProcSet: pstricks.pro%!% PostScript prologue for pstricks.tex.% Version 97 patch 3, 98/06/01% For distribution, see pstricks.tex.%/tx@Dict 200 dict def tx@Dict begin/ADict 25 dict def/CM { matrix currentmatrix } bind def/SLW /setlinewidth load def/CLW /currentlinewidth load def/CP /currentpoint load def/ED { exch def } bind def/L /lineto load def/T /translate load def/TMatrix { } def/RAngle { 0 } def/Atan { /atan load stopped { pop pop 0 } if } def/Div { dup 0 eq { pop } { div } ifelse } def/NET { neg exch neg exch T } def/Pyth { dup mul exch dup mul add sqrt } def/PtoC { 2 copy cos mul 3 1 roll sin mul } def/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def }def/PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def} { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ }/pathforall load stopped { pop pop pop pop } if z } def/STP { .996264 dup scale } def/STV { SDict begin normalscale end STP } def/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 defPathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul ymul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ]0 } ifelse setdash stroke } def/DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt{ /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y adddef } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1setlinecap stroke } def/LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25% DG/SR modification begin - Dec. 12, 1997 - Patch 2%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED aitransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a% DG/SR modification endDiv cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }% defa mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestorepop pop } def% DG/SR modification end/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub negexch 3 index sub exch Atan rotate newpath } def/EndArrow { @mtrx setmatrix CP grestore end } def/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fillgrestore } def/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0CLW moveto } def/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0CLW moveto } def/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto }def/SD { 0 360 arc fill } def/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DSCLW sub SD } if 0 DS z add CLW 4 div sub moveto } def/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {/closepath load } /pathforall load stopped { pop pop pop pop CP /movetoload } if ] cvx newpath 3 1 roll T exec } def/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exchcvi def } def/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } iff { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 subdef n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }ifelse { pop } repeat a } def/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eqand { pop pop /n n 1 sub def } if } def/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll LinetoLineto pop pop closepath } ifelse } def/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mulneg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w adddef } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrxsetmatrix } def% DG modification begin - Jan. 15, 1997%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx%setmatrix } def/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dupCLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)% setmatrix } defsetmatrix pop } def% DG/SR modification end/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pythdef } def/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pythdef } def/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c expmul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cosabs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mulm mul neg def } def/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }def/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def/NC { CC x1 y1 x2 y2 x y curveto } def/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def/NAC { x2 y2 x y curveto CC x1 y1 } def/EAC { x2 y2 x y ArrowB curveto pop pop } def/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub defn { NC } repeat EOC } ifelse } def/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { poppop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }repeat closepath pop pop } ifelse } def/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }def/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrixrotate matrix concatmatrix exch findfont exch makefont setfont } def/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 linetox1 y1 lineto closepath } def/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 divexch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arctox2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }ifelse } def/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {pop pop Rect } { OvalFrame } ifelse } def/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 62 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }ifelse } def/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }def/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowAx0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0y0 x0 2 mul x1 sub y1 ] def } def/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 }if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy divround cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx divround cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def }if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def }{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 addexch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy ndiv ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt {dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dupstringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i iw add def } repeat grestore gsave n 0 gt% DG/SR modification begin - Nov. 7, 1997 - Patch 1%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }% DG/SR modification end{ 2 setlinecap } ifelse /i y1 def /f x1 dx muln 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx ndiv 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvsdup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto gexch t L stroke /i i h add def } repeat grestore } def/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 01 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x addexch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div cmul neg d } def/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def/Rot { CP CP translate 3 -1 roll neg rotate NET } def/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngledup a add ] cvx def } def/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]cvx def } def/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b sabs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c bdiv w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {h1 abs h sub dup s mul abs } ifelse } def/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div smul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 addexch } def/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def} if } ifelse } def/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnitneg exch neg exch idtransform T moveto } def /BOL { BeginOL } def/IfVisible true def } defend% END pstricks.pro%%EndProcSet%%BeginProcSet: pst-dots.pro%!PS-Adobe-2.0%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07.%%Creator: Timothy Van Zandt <tvz@Princeton.EDU>%%Creation Date: May 7, 199310 dict dup begin /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /FontBBox [ 0 0 0 0 ] def /Encoding 256 array def 0 1 255 { Encoding exch /.notdef put } for Encoding dup (b) 0 get /Bullet put dup (c) 0 get /Circle put dup (C) 0 get /BoldCircle put dup (u) 0 get /SolidTriangle put dup (t) 0 get /Triangle put dup (T) 0 get /BoldTriangle put dup (r) 0 get /SolidSquare put dup (s) 0 get /Square put dup (S) 0 get /BoldSquare put dup (q) 0 get /SolidPentagon put dup (p) 0 get /Pentagon put (P) 0 get /BoldPentagon put /Metrics 13 dict def Metrics begin /Bullet 1000 def /Circle 1000 def /BoldCircle 1000 def /SolidTriangle 1344 def /Triangle 1344 def /BoldTriangle 1344 def /SolidSquare 886 def /Square 886 def /BoldSquare 886 def /SolidPentagon 1093.2 def /Pentagon 1093.2 def /BoldPentagon 1093.2 def /.notdef 0 def end /BBoxes 13 dict def BBoxes begin /Circle { -550 -550 550 550 } def /BoldCircle /Circle load def /Bullet /Circle load def /Triangle { -571.5 -330 571.5 660 } def /BoldTriangle /Triangle load def /SolidTriangle /Triangle load def /Square { -450 -450 450 450 } def /BoldSquare /Square load def /SolidSquare /Square load def /Pentagon { -546.6 -465 546.6 574.7 } def /BoldPentagon /Pentagon load def /SolidPentagon /Pentagon load def /.notdef { 0 0 0 0 } def end /CharProcs 20 dict def CharProcs begin /Adjust { 2 copy dtransform floor .5 add exch floor .5 add exch idtransform 3 -1 roll div 3 1 roll exch div exch scale } def /CirclePath { 0 0 500 0 360 arc closepath } def /Bullet { 500 500 Adjust CirclePath fill } def /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath } def /SolidTriangle { TrianglePath fill } def /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath } def /SolidSquare { SquarePath fill } def /Square { SquarePath .89 .89 scale SquarePath eofill } def /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def /PentagonPath { -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto 0 574.7 lineto -546.6 177.6 lineto closepath } def /SolidPentagon { PentagonPath fill } def /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def /.notdef { } def end /BuildGlyph { exch begin Metrics 1 index get exec 0 BBoxes 3 index get exec setcachedevice CharProcs begin load exec end end } def /BuildChar { 1 index /Encoding get exch get 1 index /BuildGlyph get exec } bind defend/PSTricksDotFont exch definefont pop% END pst-dots.pro%%EndProcSet%%BeginProcSet: pst-node.pro%!% PostScript prologue for pst-node.tex.% Version 97 patch 1, 97/05/09.% For distribution, see pstricks.tex.%/tx@NodeDict 400 dict def tx@NodeDict begintx@Dict begin /T /translate load def end/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next endgrestore } def/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def} def/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exchSin mul } def } def/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def }ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dxdup Sin mul Cos Div } ifelse } def/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub/u ED /NodePos { GetRnodePos } def } def/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dupCos mul exch Sin mul } def/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w hmul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul} ifelse } def/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /dED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def dsub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atansin def /NodePos { TriNodePos } def } def/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Coshh mul Atan dup cos ww mul exch sin hh mul } def/GetCenter { begin X Y NodeMtrx transform CM itransform end } def/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { DistDist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg }{ 0 Dist Sin mul } ifelse } ifelse Do } def/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransformexch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrxdtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED popXYPos } ifelse } def/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1roll sin mul sub exch } ifelse } def/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleAAddOffset yA add /yA1 ED xA add /xA1 ED } def/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleBAddOffset yB add /yB1 ED xB add /xB1 ED } def/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmAAngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do EDArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED} ifelse } def/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmBAngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do EDArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED} ifelse } def/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict bknown and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yAED /xA ED NodeB GetCenter /yB ED /xB ED } if } def/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t submul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop} repeat LPutLine cleartomark } def/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bxsub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul muladd cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul addy0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mulmul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def} def/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd } def/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def} def/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomarkVPosEnd } def/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvxdef grestore exec /LPutVar /SaveLPutVar load def } def/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add defGetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {LPutVar VPutLine } def LPutVar } def/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop popend } def/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA subAtan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }ifelse } def/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmAGetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dictbegin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrxitransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate defxA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrxtransform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def }{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dictbegin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvxdef /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } ifxB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB EDGetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict beginfalse Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin falseLine end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def% DG/SR modification begin - May 9, 1997 - Patch 1%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp rr mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA addexch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED% DG/SR modification end} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a addAngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 rDiv def /y ED /x ED } def/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cosmul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dyadd xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVartx@Dict begin false Polygon end } def/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atandef /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r divdef /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add defGetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mulsub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn }{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 00 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat }ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le {r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC }{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul addadd AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t submul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 tsub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelsey0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos {LPutPos } def } def/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yBsub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xBw sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub negexch X sub neg exch moveto setmatrix CP grestore } def/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0def } ifelse LPutCoor } def/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg }if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED }def/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } ifr Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED }defend% END pst-node.pro%%EndProcSet%%BeginProcSet: pst-text.pro%!% PostScript header file pst-text.pro% Version 97, 94/04/20% For distribution, see pstricks.tex./tx@TextPathDict 40 dict deftx@TextPathDict begin% Syntax: <dist> PathPosition -% Function: Searches for position of currentpath distance <dist> from% beginning. Sets (X,Y)=position, and Angle=tangent./PathPosition{ /targetdist exch def /pathdist 0 def /continue true def /X { newx } def /Y { newy } def /Angle 0 def gsave flattenpath { movetoproc } { linetoproc } { } { firstx firsty linetoproc } /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if grestore} def/movetoproc { continue { @movetoproc } { pop pop } ifelse } def/@movetoproc{ /newy exch def /newx exch def /firstx newx def /firsty newy def} def/linetoproc { continue { @linetoproc } { pop pop } ifelse } def/@linetoproc{ /oldx newx def /oldy newy def /newy exch def /newx exch def /dx newx oldx sub def /dy newy oldy sub def /dist dx dup mul dy dup mul add sqrt def /pathdist pathdist dist add def pathdist targetdist ge { pathdist targetdist sub dist div dup dy mul neg newy add /Y exch def dx mul neg newx add /X exch def /Angle dy dx atan def /continue false def } if} def/TextPathShow{ /String exch def /CharCount 0 def String length { String CharCount 1 getinterval ShowChar /CharCount CharCount 1 add def } repeat} def% Syntax: <pathlength> <position> InitTextPath -/InitTextPath{ gsave currentpoint /Y exch def /X exch def exch X Hoffset sub sub mul Voffset Hoffset sub add neg X add /Hoffset exch def /Voffset Y def grestore} def/Transform{ PathPosition dup Angle cos mul Y add exch Angle sin mul neg X add exch translate Angle rotate} def/ShowChar{ /Char exch def gsave Char end stringwidth tx@TextPathDict begin 2 div /Sy exch def 2 div /Sx exch def currentpoint Voffset sub Sy add exch Hoffset sub Sx add Transform Sx neg Sy neg moveto Char end tx@TextPathSavedShow tx@TextPathDict begin grestore Sx 2 mul Sy 2 mul rmoveto} defend% END pst-text.pro%%EndProcSet%%BeginProcSet: special.pro%!TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc 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mul sub } if def /g y2 dy mul n 0 gt {dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dupstringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i iw add def } repeat grestore gsave n 0 gt% DG/SR modification begin - Nov. 7, 1997 - Patch 1%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }% DG/SR modification end{ 2 setlinecap } ifelse /i y1 def /f x1 dx muln 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx ndiv 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvsdup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto gexch t L stroke /i i h add def } repeat grestore } def/ArcArrow { /d 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abs } {h1 abs h sub dup s mul abs } ifelse } def/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div smul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 addexch } def/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def} if } ifelse } def/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnitneg exch neg exch idtransform T moveto } def /BOL { BeginOL } def/IfVisible true def } defend% END pstricks.pro%%EndProcSet%%BeginProcSet: pst-dots.pro%!PS-Adobe-2.0%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07.%%Creator: Timothy Van Zandt <tvz@Princeton.EDU>%%Creation Date: May 7, 199310 dict dup begin /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /FontBBox [ 0 0 0 0 ] def /Encoding 256 array def 0 1 255 { Encoding exch /.notdef put } for Encoding dup (b) 0 get /Bullet put dup (c) 0 get /Circle put dup (C) 0 get /BoldCircle put dup (u) 0 get /SolidTriangle put dup (t) 0 get /Triangle put dup (T) 0 get /BoldTriangle put dup (r) 0 get /SolidSquare put dup (s) 0 get /Square put dup (S) 0 get /BoldSquare put dup (q) 0 get /SolidPentagon put dup (p) 0 get /Pentagon put (P) 0 get /BoldPentagon put /Metrics 13 dict def Metrics begin /Bullet 1000 def /Circle 1000 def /BoldCircle 1000 def /SolidTriangle 1344 def /Triangle 1344 def /BoldTriangle 1344 def /SolidSquare 886 def /Square 886 def /BoldSquare 886 def /SolidPentagon 1093.2 def /Pentagon 1093.2 def /BoldPentagon 1093.2 def /.notdef 0 def end /BBoxes 13 dict def BBoxes begin /Circle { -550 -550 550 550 } def /BoldCircle /Circle load def /Bullet /Circle load def /Triangle { -571.5 -330 571.5 660 } def /BoldTriangle /Triangle load def /SolidTriangle /Triangle load def /Square { -450 -450 450 450 } def /BoldSquare /Square load def /SolidSquare /Square load def /Pentagon { -546.6 -465 546.6 574.7 } def /BoldPentagon /Pentagon load def /SolidPentagon /Pentagon load def /.notdef { 0 0 0 0 } def end /CharProcs 20 dict def CharProcs begin /Adjust { 2 copy dtransform floor .5 add exch floor .5 add exch idtransform 3 -1 roll div 3 1 roll exch div exch scale } def /CirclePath { 0 0 500 0 360 arc closepath } def /Bullet { 500 500 Adjust CirclePath fill } def /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath } def /SolidTriangle { TrianglePath fill } def /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath } def /SolidSquare { SquarePath fill } def /Square { SquarePath .89 .89 scale SquarePath eofill } def /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def /PentagonPath { -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto 0 574.7 lineto -546.6 177.6 lineto closepath } def /SolidPentagon { PentagonPath fill } def /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def /.notdef { } def end /BuildGlyph { exch begin Metrics 1 index get exec 0 BBoxes 3 index get exec setcachedevice CharProcs begin load exec end end } def /BuildChar { 1 index /Encoding get exch get 1 index /BuildGlyph get exec } bind defend/PSTricksDotFont exch definefont pop% END pst-dots.pro%%EndProcSet%%BeginProcSet: pst-node.pro%!% PostScript prologue for pst-node.tex.% Version 97 patch 1, 97/05/09.% For distribution, see pstricks.tex.%/tx@NodeDict 400 dict def tx@NodeDict begintx@Dict begin /T /translate load def end/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next endgrestore } def/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def} def/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exchSin mul } def } def/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def }ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dxdup Sin mul Cos Div } ifelse } def/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub/u ED /NodePos { GetRnodePos } def } def/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dupCos mul exch Sin mul } def/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w hmul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul} ifelse } def/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /dED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def dsub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atansin def /NodePos { TriNodePos } def } def/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Coshh mul Atan dup cos ww mul exch sin hh mul } def/GetCenter { begin X Y NodeMtrx transform CM itransform end } def/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { DistDist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg }{ 0 Dist Sin mul } ifelse } ifelse Do } def/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransformexch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrxdtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED popXYPos } ifelse } def/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1roll sin mul sub exch } ifelse } def/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleAAddOffset yA add /yA1 ED xA add /xA1 ED } def/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleBAddOffset yB add /yB1 ED xB add /xB1 ED } def/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmAAngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do EDArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED} ifelse } def/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmBAngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do EDArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED} ifelse } def/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict bknown and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yAED /xA ED NodeB GetCenter /yB ED /xB ED } if } def/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t submul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop} repeat LPutLine cleartomark } def/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bxsub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul muladd cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul addy0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mulmul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def} def/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd } def/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def} def/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomarkVPosEnd } def/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvxdef grestore exec /LPutVar /SaveLPutVar load def } def/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add defGetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {LPutVar VPutLine } def LPutVar } def/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop popend } def/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA subAtan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }ifelse } def/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmAGetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dictbegin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrxitransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate defxA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrxtransform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def }{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dictbegin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvxdef /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } ifxB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB EDGetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict beginfalse Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin falseLine end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def% DG/SR modification begin - May 9, 1997 - Patch 1%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp rr mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA addexch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED% DG/SR modification end} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a addAngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 rDiv def /y ED /x ED } def/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cosmul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dyadd xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVartx@Dict begin false Polygon end } def/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atandef /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r divdef /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add defGetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mulsub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn }{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 00 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat }ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le {r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC }{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul addadd AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t submul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 tsub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelsey0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos {LPutPos } def } def/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yBsub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xBw sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub negexch X sub neg exch moveto setmatrix CP grestore } def/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0def } ifelse LPutCoor } def/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg }if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED }def/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } ifr Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED }defend% END pst-node.pro%%EndProcSet%%BeginProcSet: pst-text.pro%!% PostScript header file pst-text.pro% Version 97, 94/04/20% For distribution, see pstricks.tex./tx@TextPathDict 40 dict deftx@TextPathDict begin% Syntax: <dist> PathPosition -% Function: Searches for position of currentpath distance <dist> from% beginning. Sets (X,Y)=position, and Angle=tangent./PathPosition{ /targetdist exch def /pathdist 0 def /continue true def /X { newx } def /Y { newy } def /Angle 0 def gsave flattenpath { movetoproc } { linetoproc } { } { firstx firsty linetoproc } /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if grestore} def/movetoproc { continue { @movetoproc } { pop pop } ifelse } def/@movetoproc{ /newy exch def /newx exch def /firstx newx def /firsty newy def} def/linetoproc { continue { @linetoproc } { pop pop } ifelse } def/@linetoproc{ /oldx newx def /oldy newy def /newy exch def /newx exch def /dx newx oldx sub def /dy newy oldy sub def /dist dx dup mul dy dup mul add sqrt def /pathdist pathdist dist add def pathdist targetdist ge { pathdist targetdist sub dist div dup dy mul neg newy add /Y exch def dx mul neg newx add /X exch def /Angle dy dx atan def /continue false def } if} def/TextPathShow{ /String exch def /CharCount 0 def String length { String CharCount 1 getinterval ShowChar /CharCount CharCount 1 add def } repeat} def% Syntax: <pathlength> <position> InitTextPath -/InitTextPath{ gsave currentpoint /Y exch def /X exch def exch X Hoffset sub sub mul Voffset Hoffset sub add neg X add /Hoffset exch def /Voffset Y def grestore} def/Transform{ PathPosition dup Angle cos mul Y add exch Angle sin mul neg X add exch translate Angle rotate} def/ShowChar{ /Char exch def gsave Char end stringwidth tx@TextPathDict begin 2 div /Sy exch def 2 div /Sx exch def currentpoint Voffset sub Sy add exch Hoffset sub Sx add Transform Sx neg Sy neg moveto Char end tx@TextPathSavedShow tx@TextPathDict begin grestore Sx 2 mul Sy 2 mul rmoveto} defend% END pst-text.pro%%EndProcSet%%BeginProcSet: special.pro%!TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/hoX}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known{userdict/md get type/dicttype eq{userdict begin md length 10 add mdmaxlength ge{/md md dup length 20 add dict copy def}if end md begin/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform Satan/pa X newpath clippath mark{transform{itransform moveto}}{transform{itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 rolltransform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 rollcurveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdfpop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1-1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflipyflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg subneg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 getneg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4-1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg STR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale}if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedStatesave N userdict maxlength dict begin/magscale true def normalscalecurrentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts/psf$y psfts/psf$x psfts 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/dx 0 def /dy 0 def }def/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def/NC { CC x1 y1 x2 y2 x y curveto } def/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def/NAC { x2 y2 x y curveto CC x1 y1 } def/EAC { x2 y2 x y ArrowB curveto pop pop } def/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub defn { NC } repeat EOC } ifelse } def/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { poppop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }repeat closepath pop pop } ifelse } def/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }def/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrixrotate matrix concatmatrix exch findfont exch makefont setfont } def/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 linetox1 y1 lineto closepath } def/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 divexch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arctox2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }ifelse } def/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {pop pop Rect } { OvalFrame } ifelse } def/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 62 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }ifelse } def/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }def/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowAx0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0y0 x0 2 mul x1 sub y1 ] def } def/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 }if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy divround cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx divround cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def }if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def }{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 addexch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy ndiv ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt {dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dupstringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i iw add def } repeat grestore gsave n 0 gt% DG/SR modification begin - Nov. 7, 1997 - Patch 1%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }% DG/SR modification end{ 2 setlinecap } ifelse /i y1 def /f x1 dx muln 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx ndiv 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvsdup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto gexch t L stroke /i i h add def } repeat grestore } def/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 01 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x addexch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div cmul neg d } def/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def/Rot { CP CP translate 3 -1 roll neg rotate NET } def/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngledup a add ] cvx def } def/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]cvx def } def/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b sabs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c bdiv w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {h1 abs h sub dup s mul abs } ifelse } def/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div smul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 addexch } def/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def} if } ifelse } def/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnitneg exch neg exch idtransform T moveto } def /BOL { BeginOL } def/IfVisible true def } defend% END pstricks.pro%%EndProcSet%%BeginProcSet: pst-dots.pro%!PS-Adobe-2.0%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07.%%Creator: Timothy Van Zandt <tvz@Princeton.EDU>%%Creation Date: May 7, 199310 dict dup begin /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /FontBBox [ 0 0 0 0 ] def /Encoding 256 array def 0 1 255 { Encoding exch /.notdef put } for Encoding dup (b) 0 get /Bullet put dup (c) 0 get /Circle put dup (C) 0 get /BoldCircle put dup (u) 0 get /SolidTriangle put dup (t) 0 get /Triangle put dup (T) 0 get /BoldTriangle put dup (r) 0 get /SolidSquare put dup (s) 0 get /Square put dup (S) 0 get /BoldSquare put dup (q) 0 get /SolidPentagon put dup (p) 0 get /Pentagon put (P) 0 get /BoldPentagon put /Metrics 13 dict def Metrics begin /Bullet 1000 def /Circle 1000 def /BoldCircle 1000 def /SolidTriangle 1344 def /Triangle 1344 def /BoldTriangle 1344 def /SolidSquare 886 def /Square 886 def /BoldSquare 886 def /SolidPentagon 1093.2 def /Pentagon 1093.2 def /BoldPentagon 1093.2 def /.notdef 0 def end /BBoxes 13 dict def BBoxes begin /Circle { -550 -550 550 550 } def /BoldCircle /Circle load def /Bullet /Circle load def /Triangle { -571.5 -330 571.5 660 } def /BoldTriangle /Triangle load def /SolidTriangle /Triangle load def /Square { -450 -450 450 450 } def /BoldSquare /Square load def /SolidSquare /Square load def /Pentagon { -546.6 -465 546.6 574.7 } def /BoldPentagon /Pentagon load def /SolidPentagon /Pentagon load def /.notdef { 0 0 0 0 } def end /CharProcs 20 dict def CharProcs begin /Adjust { 2 copy dtransform floor .5 add exch floor .5 add exch idtransform 3 -1 roll div 3 1 roll exch div exch scale } def /CirclePath { 0 0 500 0 360 arc closepath } def /Bullet { 500 500 Adjust CirclePath fill } def /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath } def /SolidTriangle { TrianglePath fill } def /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath } def /SolidSquare { SquarePath fill } def /Square { SquarePath .89 .89 scale SquarePath eofill } def /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def /PentagonPath { -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto 0 574.7 lineto -546.6 177.6 lineto closepath } def /SolidPentagon { PentagonPath fill } def /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def /.notdef { } def end /BuildGlyph { exch begin Metrics 1 index get exec 0 BBoxes 3 index get exec setcachedevice CharProcs begin load exec end end } def /BuildChar { 1 index /Encoding get exch get 1 index /BuildGlyph get exec } bind defend/PSTricksDotFont exch definefont pop% END pst-dots.pro%%EndProcSet%%BeginProcSet: pst-node.pro%!% PostScript prologue for pst-node.tex.% Version 97 patch 1, 97/05/09.% For distribution, see pstricks.tex.%/tx@NodeDict 400 dict def tx@NodeDict begintx@Dict begin /T /translate load def end/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next endgrestore } def/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def} def/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exchSin mul } def } def/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def }ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dxdup Sin mul Cos Div } ifelse } def/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub/u ED /NodePos { GetRnodePos } def } def/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dupCos mul exch Sin mul } def/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w hmul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul} ifelse } def/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /dED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def dsub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atansin def /NodePos { TriNodePos } def } def/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Coshh mul Atan dup cos ww mul exch sin hh mul } def/GetCenter { begin X Y NodeMtrx transform CM itransform end } def/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { DistDist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg }{ 0 Dist Sin mul } ifelse } ifelse Do } def/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransformexch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrxdtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED popXYPos } ifelse } def/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1roll sin mul sub exch } ifelse } def/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleAAddOffset yA add /yA1 ED xA add /xA1 ED } def/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleBAddOffset yB add /yB1 ED xB add /xB1 ED } def/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmAAngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do EDArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED} ifelse } def/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmBAngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do EDArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED} ifelse } def/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict bknown and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yAED /xA ED NodeB GetCenter /yB ED /xB ED } if } def/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t submul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop} repeat LPutLine cleartomark } def/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bxsub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul muladd cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul addy0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mulmul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def} def/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd } def/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def} def/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomarkVPosEnd } def/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvxdef grestore exec /LPutVar /SaveLPutVar load def } def/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add defGetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {LPutVar VPutLine } def LPutVar } def/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop popend } def/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA subAtan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }ifelse } def/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmAGetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dictbegin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrxitransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate defxA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrxtransform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def }{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dictbegin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvxdef /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } ifxB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB EDGetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict beginfalse Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin falseLine end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def% DG/SR modification begin - May 9, 1997 - Patch 1%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp rr mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA addexch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED% DG/SR modification end} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a addAngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 rDiv def /y ED /x ED } def/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cosmul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dyadd xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVartx@Dict begin false Polygon end } def/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atandef /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r divdef /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add defGetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mulsub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn }{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 00 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat }ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le {r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC }{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul addadd AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t submul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 tsub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelsey0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos {LPutPos } def } def/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yBsub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xBw sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }def /HPutPos { VPutPos@ HPutLine } def mark 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1 index 0 eq {pop pop Rect } { OvalFrame } ifelse } def/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 62 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }ifelse } def/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }def/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowAx0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0y0 x0 2 mul x1 sub y1 ] def } def/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 }if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy divround cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx divround cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def }if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def }{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 addexch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy ndiv ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt {dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dupstringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i iw add def } repeat grestore gsave n 0 gt% DG/SR modification begin - Nov. 7, 1997 - Patch 1%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }% DG/SR modification end{ 2 setlinecap } ifelse /i y1 def /f x1 dx muln 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx ndiv 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvsdup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto gexch t L stroke /i i h add def } repeat grestore } def/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 01 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x addexch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div cmul neg d } def/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def/Rot { CP CP translate 3 -1 roll neg rotate NET } def/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngledup a add ] cvx def } def/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]cvx def } def/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b sabs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c bdiv w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {h1 abs h sub dup s mul abs } ifelse } def/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div smul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 addexch } def/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def} if } ifelse } def/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnitneg exch neg exch idtransform T moveto } def /BOL { BeginOL } def/IfVisible true def } defend% END pstricks.pro%%EndProcSet%%BeginProcSet: pst-dots.pro%!PS-Adobe-2.0%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07.%%Creator: Timothy Van Zandt <tvz@Princeton.EDU>%%Creation Date: May 7, 199310 dict dup begin /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /FontBBox [ 0 0 0 0 ] def /Encoding 256 array def 0 1 255 { Encoding exch /.notdef put } for Encoding dup (b) 0 get /Bullet put dup (c) 0 get /Circle put dup (C) 0 get /BoldCircle put dup (u) 0 get /SolidTriangle put dup (t) 0 get /Triangle put dup (T) 0 get /BoldTriangle put dup (r) 0 get /SolidSquare put dup (s) 0 get /Square put dup (S) 0 get /BoldSquare put dup (q) 0 get /SolidPentagon put dup (p) 0 get /Pentagon put (P) 0 get /BoldPentagon put /Metrics 13 dict def Metrics begin /Bullet 1000 def /Circle 1000 def /BoldCircle 1000 def /SolidTriangle 1344 def /Triangle 1344 def /BoldTriangle 1344 def /SolidSquare 886 def /Square 886 def /BoldSquare 886 def /SolidPentagon 1093.2 def /Pentagon 1093.2 def /BoldPentagon 1093.2 def /.notdef 0 def end /BBoxes 13 dict def BBoxes begin /Circle { -550 -550 550 550 } def /BoldCircle /Circle load def /Bullet /Circle load def /Triangle { -571.5 -330 571.5 660 } def /BoldTriangle /Triangle load def /SolidTriangle /Triangle load def /Square { -450 -450 450 450 } def /BoldSquare /Square load def /SolidSquare /Square load def /Pentagon { -546.6 -465 546.6 574.7 } def /BoldPentagon /Pentagon load def /SolidPentagon /Pentagon load def /.notdef { 0 0 0 0 } def end /CharProcs 20 dict def CharProcs begin /Adjust { 2 copy dtransform floor .5 add exch floor .5 add exch idtransform 3 -1 roll div 3 1 roll exch div exch scale } def /CirclePath { 0 0 500 0 360 arc closepath } def /Bullet { 500 500 Adjust CirclePath fill } def /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath } def /SolidTriangle { TrianglePath fill } def /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath } def /SolidSquare { SquarePath fill } def /Square { SquarePath .89 .89 scale SquarePath eofill } def /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def /PentagonPath { -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto 0 574.7 lineto -546.6 177.6 lineto closepath } def /SolidPentagon { PentagonPath fill } def /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def /.notdef { } def end /BuildGlyph { exch begin Metrics 1 index get exec 0 BBoxes 3 index get exec setcachedevice CharProcs begin load exec end end } def /BuildChar { 1 index /Encoding get exch get 1 index /BuildGlyph get exec } bind defend/PSTricksDotFont exch definefont pop% END pst-dots.pro%%EndProcSet%%BeginProcSet: pst-node.pro%!% PostScript prologue for pst-node.tex.% Version 97 patch 1, 97/05/09.% For distribution, see pstricks.tex.%/tx@NodeDict 400 dict def tx@NodeDict begintx@Dict begin /T /translate load def end/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next endgrestore } def/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def} def/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exchSin mul } def } def/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def }ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dxdup Sin mul Cos Div } ifelse } def/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub/u ED /NodePos { GetRnodePos } def } def/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dupCos mul exch Sin mul } def/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w hmul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul} ifelse } def/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /dED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def dsub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atansin def /NodePos { TriNodePos } def } def/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Coshh mul Atan dup cos ww mul exch sin hh mul } def/GetCenter { begin X Y NodeMtrx transform CM itransform end } def/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { DistDist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg }{ 0 Dist Sin mul } ifelse } ifelse Do } def/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransformexch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrxdtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED popXYPos } ifelse } def/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1roll sin mul sub exch } ifelse } def/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleAAddOffset yA add /yA1 ED xA add /xA1 ED } def/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleBAddOffset yB add /yB1 ED xB add /xB1 ED } def/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmAAngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do EDArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED} ifelse } def/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmBAngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do EDArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED} ifelse } def/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict bknown and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yAED /xA ED NodeB GetCenter /yB ED /xB ED } if } def/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t submul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop} repeat LPutLine cleartomark } def/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bxsub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul muladd cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul addy0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mulmul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def} def/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd } def/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def} def/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomarkVPosEnd } def/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvxdef grestore exec /LPutVar /SaveLPutVar load def } def/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add defGetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {LPutVar VPutLine } def LPutVar } def/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop popend } def/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA subAtan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }ifelse } def/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmAGetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dictbegin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrxitransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate defxA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrxtransform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def }{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dictbegin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvxdef /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } ifxB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB EDGetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict beginfalse Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin falseLine end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def% DG/SR modification begin - May 9, 1997 - Patch 1%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp rr mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA addexch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED% DG/SR modification end} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a addAngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 rDiv def /y ED /x ED } def/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cosmul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dyadd xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVartx@Dict begin false Polygon end } def/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atandef /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r divdef /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add defGetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mulsub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn }{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 00 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat }ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le {r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC }{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul addadd AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t submul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 tsub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelsey0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos {LPutPos } def } def/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yBsub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xBw sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub negexch X sub neg exch moveto setmatrix CP grestore } def/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0def } ifelse LPutCoor } def/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg }if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED }def/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } ifr Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED }defend% END pst-node.pro%%EndProcSet%%BeginProcSet: pst-text.pro%!% PostScript header file pst-text.pro% Version 97, 94/04/20% For distribution, see pstricks.tex./tx@TextPathDict 40 dict deftx@TextPathDict begin% Syntax: <dist> PathPosition -% Function: Searches for position of currentpath distance <dist> from% beginning. Sets (X,Y)=position, and Angle=tangent./PathPosition{ /targetdist exch def /pathdist 0 def /continue true def /X { newx } def /Y { newy } def /Angle 0 def gsave flattenpath { movetoproc } { linetoproc } { } { firstx firsty linetoproc } /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if grestore} def/movetoproc { continue { @movetoproc } { pop pop } ifelse } def/@movetoproc{ /newy exch def /newx exch def /firstx newx def /firsty newy def} def/linetoproc { continue { @linetoproc } { pop pop } ifelse } def/@linetoproc{ /oldx newx def /oldy newy def /newy exch def /newx exch def /dx newx oldx sub def /dy newy oldy sub def /dist dx dup mul dy dup mul add sqrt def /pathdist pathdist dist add def pathdist targetdist ge { pathdist targetdist sub dist div dup dy mul neg newy add /Y exch def dx mul neg newx add /X exch def /Angle dy dx atan def /continue false def } if} def/TextPathShow{ /String exch def /CharCount 0 def String length { String CharCount 1 getinterval ShowChar 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B/QV{gsave newpath transform round exch roundexch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlinetofill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S pdelta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 Srmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end%%EndProcSet%%BeginProcSet: pstricks.pro%!% PostScript prologue for pstricks.tex.% Version 97 patch 3, 98/06/01% For distribution, see pstricks.tex.%/tx@Dict 200 dict def tx@Dict begin/ADict 25 dict def/CM { matrix currentmatrix } bind def/SLW /setlinewidth load def/CLW /currentlinewidth load def/CP /currentpoint load def/ED { exch def } bind def/L /lineto load def/T /translate load def/TMatrix { } def/RAngle { 0 } def/Atan { /atan load stopped { pop pop 0 } if } def/Div { dup 0 eq { pop } { div } ifelse } def/NET { neg exch neg exch T } def/Pyth { dup mul exch dup mul add sqrt } def/PtoC { 2 copy cos mul 3 1 roll sin mul } def/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def }def/PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def} { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ }/pathforall load stopped { pop pop pop pop } if z } def/STP { .996264 dup scale } def/STV { SDict begin normalscale end STP } def/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 defPathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul ymul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ]0 } ifelse setdash stroke } def/DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt{ /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y adddef } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1setlinecap stroke } def/LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25% DG/SR modification begin - Dec. 12, 1997 - Patch 2%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED aitransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a% DG/SR modification endDiv cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }% defa mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestorepop pop } def% DG/SR modification end/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub negexch 3 index sub exch Atan rotate newpath } def/EndArrow { @mtrx setmatrix CP grestore end } def/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fillgrestore } def/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0CLW moveto } def/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0CLW moveto } def/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto }def/SD { 0 360 arc fill } def/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DSCLW sub SD } if 0 DS z add CLW 4 div sub moveto } def/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {/closepath load } /pathforall load stopped { pop pop pop pop CP /movetoload } if ] cvx newpath 3 1 roll T exec } def/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exchcvi def } def/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } iff { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 subdef n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }ifelse { pop } repeat a } def/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eqand { pop pop /n n 1 sub def } if } def/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll LinetoLineto pop pop closepath } ifelse } def/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mulneg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w adddef } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrxsetmatrix } def% DG modification begin - Jan. 15, 1997%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx%setmatrix } def/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dupCLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)% setmatrix } defsetmatrix pop } def% DG/SR modification end/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pythdef } def/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pythdef } def/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c expmul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cosabs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mulm mul neg def } def/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }def/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def/NC { CC x1 y1 x2 y2 x y curveto } def/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def/NAC { x2 y2 x y curveto CC x1 y1 } def/EAC { x2 y2 x y ArrowB curveto pop pop } def/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub defn { NC } repeat EOC } ifelse } def/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { poppop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }repeat closepath pop pop } ifelse } def/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }def/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrixrotate matrix concatmatrix exch findfont exch makefont setfont } def/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 linetox1 y1 lineto closepath } def/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 divexch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arctox2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }ifelse } def/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {pop pop Rect } { OvalFrame } ifelse } def/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 62 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }ifelse } def/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }def/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowAx0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0y0 x0 2 mul x1 sub y1 ] def } def/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 }if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy divround cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx divround cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def }if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def }{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 addexch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy ndiv ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt {dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dupstringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i iw add def } repeat grestore gsave n 0 gt% DG/SR modification begin - Nov. 7, 1997 - Patch 1%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }% DG/SR modification end{ 2 setlinecap } ifelse /i y1 def /f x1 dx muln 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx ndiv 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvsdup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto gexch t L stroke /i i h add def } repeat grestore } def/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 01 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x addexch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div cmul neg d } def/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def/Rot { CP CP translate 3 -1 roll neg rotate NET } def/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngledup a add ] cvx def } def/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]cvx def } def/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b sabs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c bdiv w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {h1 abs h sub dup s mul abs } ifelse } def/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div smul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 addexch } def/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def} if } ifelse } def/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnitneg exch neg exch idtransform T moveto } def /BOL { BeginOL } def/IfVisible true def } defend% END pstricks.pro%%EndProcSet%%BeginProcSet: pst-dots.pro%!PS-Adobe-2.0%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07.%%Creator: Timothy Van Zandt <tvz@Princeton.EDU>%%Creation Date: May 7, 199310 dict dup begin /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /FontBBox [ 0 0 0 0 ] def /Encoding 256 array def 0 1 255 { Encoding exch /.notdef put } for Encoding dup (b) 0 get /Bullet put dup (c) 0 get /Circle put dup (C) 0 get /BoldCircle put dup (u) 0 get /SolidTriangle put dup (t) 0 get /Triangle put dup (T) 0 get /BoldTriangle put dup (r) 0 get /SolidSquare put dup (s) 0 get /Square put dup (S) 0 get /BoldSquare put dup (q) 0 get /SolidPentagon put dup (p) 0 get /Pentagon put (P) 0 get /BoldPentagon put /Metrics 13 dict def Metrics begin /Bullet 1000 def /Circle 1000 def /BoldCircle 1000 def /SolidTriangle 1344 def /Triangle 1344 def /BoldTriangle 1344 def /SolidSquare 886 def /Square 886 def /BoldSquare 886 def /SolidPentagon 1093.2 def /Pentagon 1093.2 def /BoldPentagon 1093.2 def /.notdef 0 def end /BBoxes 13 dict def BBoxes begin /Circle { -550 -550 550 550 } def /BoldCircle /Circle load def /Bullet /Circle load def /Triangle { -571.5 -330 571.5 660 } def /BoldTriangle /Triangle load def /SolidTriangle /Triangle load def /Square { -450 -450 450 450 } def /BoldSquare /Square load def /SolidSquare /Square load def /Pentagon { -546.6 -465 546.6 574.7 } def /BoldPentagon /Pentagon load def /SolidPentagon /Pentagon load def /.notdef { 0 0 0 0 } def end /CharProcs 20 dict def CharProcs begin /Adjust { 2 copy dtransform floor .5 add exch floor .5 add exch idtransform 3 -1 roll div 3 1 roll exch div exch scale } def /CirclePath { 0 0 500 0 360 arc closepath } def /Bullet { 500 500 Adjust CirclePath fill } def /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath } def /SolidTriangle { TrianglePath fill } def /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath } def /SolidSquare { SquarePath fill } def /Square { SquarePath .89 .89 scale SquarePath eofill } def /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def /PentagonPath { -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto 0 574.7 lineto -546.6 177.6 lineto closepath } def /SolidPentagon { PentagonPath fill } def /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def /.notdef { } def end /BuildGlyph { exch begin Metrics 1 index get exec 0 BBoxes 3 index get exec setcachedevice CharProcs begin load exec end end } def /BuildChar { 1 index /Encoding get exch get 1 index /BuildGlyph get exec } bind defend/PSTricksDotFont exch definefont pop% END pst-dots.pro%%EndProcSet%%BeginProcSet: pst-node.pro%!% PostScript prologue for pst-node.tex.% Version 97 patch 1, 97/05/09.% For distribution, see pstricks.tex.%/tx@NodeDict 400 dict def tx@NodeDict begintx@Dict begin /T /translate load def end/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next endgrestore } def/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def} def/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exchSin mul } def } def/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def }ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dxdup Sin mul Cos Div } ifelse } def/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub/u ED /NodePos { GetRnodePos } def } def/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dupCos mul exch Sin mul } def/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w hmul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul} ifelse } def/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /dED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def dsub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atansin def /NodePos { TriNodePos } def } def/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Coshh mul Atan dup cos ww mul exch sin hh mul } def/GetCenter { begin X Y NodeMtrx transform CM itransform end } def/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { DistDist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg }{ 0 Dist Sin mul } ifelse } ifelse Do } def/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransformexch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrxdtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED popXYPos } ifelse } def/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1roll sin mul sub exch } ifelse } def/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleAAddOffset yA add /yA1 ED xA add /xA1 ED } def/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleBAddOffset yB add /yB1 ED xB add /xB1 ED } def/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmAAngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do EDArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED} ifelse } def/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmBAngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do EDArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED} ifelse } def/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict bknown and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yAED /xA ED NodeB GetCenter /yB ED /xB ED } if } def/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t submul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop} repeat LPutLine cleartomark } def/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bxsub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul muladd cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul addy0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mulmul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def} def/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd } def/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def} def/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomarkVPosEnd } def/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvxdef grestore exec /LPutVar /SaveLPutVar load def } def/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add defGetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {LPutVar VPutLine } def LPutVar } def/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop popend } def/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA subAtan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }ifelse } def/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmAGetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dictbegin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrxitransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate defxA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrxtransform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def }{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dictbegin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvxdef /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } ifxB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB EDGetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict beginfalse Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin falseLine end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def% DG/SR modification begin - May 9, 1997 - Patch 1%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp rr mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA addexch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED% DG/SR modification end} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a addAngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 rDiv def /y ED /x ED } def/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cosmul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dyadd xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVartx@Dict begin false Polygon end } def/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atandef /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r divdef /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add defGetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mulsub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn }{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 00 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat }ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le {r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC }{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul addadd AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t submul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 tsub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelsey0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos {LPutPos } def } def/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yBsub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xBw sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub negexch X sub neg exch moveto setmatrix CP grestore } def/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0def } ifelse LPutCoor } def/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg }if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED }def/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } ifr Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED }defend% END pst-node.pro%%EndProcSet%%BeginProcSet: pst-text.pro%!% PostScript header file pst-text.pro% Version 97, 94/04/20% For distribution, see pstricks.tex./tx@TextPathDict 40 dict deftx@TextPathDict begin% Syntax: <dist> PathPosition -% Function: Searches for position of currentpath distance <dist> from% beginning. Sets (X,Y)=position, and Angle=tangent./PathPosition{ /targetdist exch def /pathdist 0 def /continue true def /X { newx } def /Y { newy } def /Angle 0 def gsave flattenpath { movetoproc } { linetoproc } { } { firstx firsty linetoproc } /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if grestore} def/movetoproc { continue { @movetoproc } { pop pop } ifelse } def/@movetoproc{ /newy exch def /newx exch def /firstx newx def /firsty newy def} def/linetoproc { continue { @linetoproc } { pop pop } ifelse } def/@linetoproc{ /oldx newx def /oldy newy def /newy exch def /newx exch def /dx newx oldx sub def /dy newy oldy sub def /dist dx dup mul dy dup mul add sqrt def /pathdist pathdist dist add def pathdist targetdist ge { pathdist targetdist sub dist div dup dy mul neg newy add /Y exch def dx mul neg newx add /X exch def /Angle dy dx atan def /continue false def } if} def/TextPathShow{ /String exch def /CharCount 0 def String length { String CharCount 1 getinterval ShowChar 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y2 x2 y1 b arctox2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }ifelse } def/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {pop pop Rect } { OvalFrame } ifelse } def/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 62 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }ifelse } def/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }def/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1sub 3 div def 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0 gt {dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dupstringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i iw add def } repeat grestore gsave n 0 gt% DG/SR modification begin - Nov. 7, 1997 - Patch 1%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }% DG/SR modification end{ 2 setlinecap } ifelse /i y1 def /f x1 dx muln 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx ndiv 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvsdup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto gexch t L stroke /i i h add def } repeat grestore } def/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 01 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x addexch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div cmul neg d } def/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def/Rot { CP CP translate 3 -1 roll neg rotate NET } def/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngledup a add ] cvx def } def/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]cvx def } def/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b sabs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c bdiv w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {h1 abs h sub dup s mul abs } ifelse } def/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div smul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 addexch } def/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def} if } ifelse } def/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnitneg exch neg exch idtransform T moveto } def /BOL { BeginOL } def/IfVisible true def } defend% END pstricks.pro%%EndProcSet%%BeginProcSet: pst-dots.pro%!PS-Adobe-2.0%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07.%%Creator: Timothy Van Zandt <tvz@Princeton.EDU>%%Creation Date: May 7, 199310 dict dup begin /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /FontBBox [ 0 0 0 0 ] def /Encoding 256 array def 0 1 255 { Encoding exch /.notdef put } for Encoding dup (b) 0 get /Bullet put dup (c) 0 get /Circle put dup (C) 0 get /BoldCircle put dup (u) 0 get /SolidTriangle put dup (t) 0 get /Triangle put dup (T) 0 get /BoldTriangle put dup (r) 0 get /SolidSquare put dup (s) 0 get /Square put dup (S) 0 get /BoldSquare put dup (q) 0 get /SolidPentagon put dup (p) 0 get /Pentagon put (P) 0 get /BoldPentagon put /Metrics 13 dict def Metrics begin /Bullet 1000 def /Circle 1000 def /BoldCircle 1000 def /SolidTriangle 1344 def /Triangle 1344 def /BoldTriangle 1344 def /SolidSquare 886 def /Square 886 def /BoldSquare 886 def /SolidPentagon 1093.2 def /Pentagon 1093.2 def /BoldPentagon 1093.2 def /.notdef 0 def end /BBoxes 13 dict def BBoxes begin /Circle { -550 -550 550 550 } def /BoldCircle /Circle load def /Bullet /Circle load def /Triangle { -571.5 -330 571.5 660 } def /BoldTriangle /Triangle load def /SolidTriangle /Triangle load def /Square { -450 -450 450 450 } def /BoldSquare /Square load def /SolidSquare /Square load def /Pentagon { -546.6 -465 546.6 574.7 } def /BoldPentagon /Pentagon load def /SolidPentagon /Pentagon load def /.notdef { 0 0 0 0 } def end /CharProcs 20 dict def CharProcs begin /Adjust { 2 copy dtransform floor .5 add exch floor .5 add exch idtransform 3 -1 roll div 3 1 roll exch div exch scale } def /CirclePath { 0 0 500 0 360 arc closepath } def /Bullet { 500 500 Adjust CirclePath fill } def /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath } def /SolidTriangle { TrianglePath fill } def /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath } def /SolidSquare { SquarePath fill } def /Square { SquarePath .89 .89 scale SquarePath eofill } def /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def /PentagonPath { -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto 0 574.7 lineto -546.6 177.6 lineto closepath } def /SolidPentagon { PentagonPath fill } def /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def /.notdef { } def end /BuildGlyph { exch begin Metrics 1 index get exec 0 BBoxes 3 index get exec setcachedevice CharProcs begin load exec end end } def /BuildChar { 1 index /Encoding get exch get 1 index /BuildGlyph get exec } bind defend/PSTricksDotFont exch definefont pop% END pst-dots.pro%%EndProcSet%%BeginProcSet: pst-node.pro%!% PostScript prologue for pst-node.tex.% Version 97 patch 1, 97/05/09.% For distribution, see pstricks.tex.%/tx@NodeDict 400 dict def tx@NodeDict begintx@Dict begin /T /translate load def end/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next endgrestore } def/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def} def/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exchSin mul } def } def/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def }ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dxdup Sin mul Cos Div } ifelse } def/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub/u ED /NodePos { GetRnodePos } def } def/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dupCos mul exch Sin mul } def/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w hmul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul} ifelse } def/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /dED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def dsub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atansin def /NodePos { TriNodePos } def } def/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Coshh mul Atan dup cos ww mul exch sin hh mul } def/GetCenter { begin X Y NodeMtrx transform CM itransform end } def/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { DistDist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg }{ 0 Dist Sin mul } ifelse } ifelse Do } def/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransformexch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrxdtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED popXYPos } ifelse } def/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1roll sin mul sub exch } ifelse } def/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleAAddOffset yA add /yA1 ED xA add /xA1 ED } def/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleBAddOffset yB add /yB1 ED xB add /xB1 ED } def/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmAAngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do EDArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED} ifelse } def/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmBAngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do EDArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED} ifelse } def/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict bknown and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yAED /xA ED NodeB GetCenter /yB ED /xB ED } if } def/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t submul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop} repeat LPutLine cleartomark } def/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bxsub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul muladd cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul addy0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mulmul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def} def/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd } def/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def} def/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomarkVPosEnd } def/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvxdef grestore exec /LPutVar /SaveLPutVar load def } def/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add defGetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {LPutVar VPutLine } def LPutVar } def/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop popend } def/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA subAtan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }ifelse } def/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmAGetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dictbegin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrxitransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate defxA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrxtransform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def }{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dictbegin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvxdef /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } ifxB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB EDGetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict beginfalse Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin falseLine end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def% DG/SR modification begin - May 9, 1997 - Patch 1%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp rr mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA addexch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED% DG/SR modification end} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a addAngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 rDiv def /y ED /x ED } def/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cosmul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dyadd xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVartx@Dict begin false Polygon end } def/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atandef /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r divdef /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add defGetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mulsub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn }{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 00 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat }ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le {r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC }{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul addadd AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t submul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 tsub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelsey0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos {LPutPos } def } def/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yBsub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xBw sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub negexch X sub neg exch moveto setmatrix CP grestore } def/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0def } ifelse LPutCoor } def/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg }if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED }def/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } ifr Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop }ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED }defend% END pst-node.pro%%EndProcSet%%BeginProcSet: pst-text.pro%!% PostScript header file pst-text.pro% Version 97, 94/04/20% For distribution, see pstricks.tex./tx@TextPathDict 40 dict deftx@TextPathDict begin% Syntax: <dist> PathPosition -% Function: Searches for position of currentpath distance <dist> from% beginning. Sets (X,Y)=position, and Angle=tangent./PathPosition{ /targetdist exch def /pathdist 0 def /continue true def /X { newx } def /Y { newy } def /Angle 0 def gsave flattenpath { movetoproc } { linetoproc } { } { firstx firsty linetoproc } /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if grestore} def/movetoproc { continue { @movetoproc } { pop pop } ifelse } def/@movetoproc{ /newy exch def /newx exch def /firstx newx def /firsty newy def} def/linetoproc { continue { @linetoproc } { pop pop } ifelse } def/@linetoproc{ /oldx newx def /oldy newy def /newy exch def /newx exch def /dx newx oldx sub def /dy newy oldy sub def /dist dx dup mul dy dup mul add sqrt def /pathdist pathdist dist add def pathdist targetdist ge { pathdist targetdist sub dist div dup dy mul neg newy add /Y exch def dx mul neg newx add /X exch def /Angle dy dx atan def /continue false def } if} def/TextPathShow{ /String exch def /CharCount 0 def String length { String CharCount 1 getinterval ShowChar 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4 roll LinetoLineto pop pop closepath } ifelse } def/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mulneg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w adddef } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrxsetmatrix } def% DG modification begin - Jan. 15, 1997%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx%setmatrix } def/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dupCLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)% setmatrix } defsetmatrix pop } def% DG/SR modification end/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pythdef } def/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pythdef } def/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c expmul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cosabs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mulm mul neg def } def/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }def/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def/NC { CC x1 y1 x2 y2 x y curveto } def/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def/NAC { x2 y2 x y curveto CC x1 y1 } def/EAC { x2 y2 x y ArrowB curveto pop pop } def/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub defn { NC } repeat EOC } ifelse } def/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { poppop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }repeat closepath pop pop } ifelse } def/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }def/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrixrotate matrix concatmatrix exch findfont exch makefont setfont } def/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 linetox1 y1 lineto closepath } def/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 divexch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arctox2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }ifelse } def/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {pop pop Rect } { OvalFrame } ifelse } def/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 62 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }ifelse } def/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }def/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowAx0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0y0 x0 2 mul x1 sub y1 ] def } def/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 }if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy divround cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx divround cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def }if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def }{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 addexch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy ndiv ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt {dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dupstringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i iw add def } repeat grestore gsave n 0 gt% DG/SR modification begin - Nov. 7, 1997 - Patch 1%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }% DG/SR modification end{ 2 setlinecap } ifelse /i y1 def /f x1 dx muln 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx ndiv 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvsdup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto gexch t L stroke /i i h add def } repeat grestore } def/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 01 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x addexch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div cmul neg d } def/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def/Rot { CP CP translate 3 -1 roll neg rotate NET } def/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngledup a add ] cvx def } def/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]cvx def } def/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b sabs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c bdiv w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {h1 abs h sub dup s mul abs } ifelse } def/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div smul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 addexch } def/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def} if } ifelse } def/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnitneg exch neg exch idtransform T moveto } def /BOL { BeginOL } def/IfVisible true def } defend% END pstricks.pro%%EndProcSet%%BeginProcSet: pst-dots.pro%!PS-Adobe-2.0%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07.%%Creator: Timothy Van Zandt <tvz@Princeton.EDU>%%Creation Date: May 7, 199310 dict dup begin /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /FontBBox [ 0 0 0 0 ] def /Encoding 256 array def 0 1 255 { Encoding exch /.notdef put } for Encoding dup (b) 0 get /Bullet put dup (c) 0 get /Circle put dup (C) 0 get /BoldCircle put dup (u) 0 get /SolidTriangle put dup (t) 0 get /Triangle put dup (T) 0 get /BoldTriangle put dup (r) 0 get /SolidSquare put dup (s) 0 get /Square put dup (S) 0 get /BoldSquare put dup (q) 0 get /SolidPentagon put dup (p) 0 get /Pentagon put (P) 0 get /BoldPentagon put /Metrics 13 dict def Metrics begin /Bullet 1000 def /Circle 1000 def /BoldCircle 1000 def /SolidTriangle 1344 def /Triangle 1344 def /BoldTriangle 1344 def /SolidSquare 886 def /Square 886 def /BoldSquare 886 def /SolidPentagon 1093.2 def /Pentagon 1093.2 def /BoldPentagon 1093.2 def /.notdef 0 def end /BBoxes 13 dict def BBoxes begin /Circle { -550 -550 550 550 } def /BoldCircle /Circle load def /Bullet /Circle load def /Triangle { -571.5 -330 571.5 660 } def /BoldTriangle /Triangle load def /SolidTriangle /Triangle load def /Square { -450 -450 450 450 } def /BoldSquare /Square load def /SolidSquare /Square load def /Pentagon { -546.6 -465 546.6 574.7 } def /BoldPentagon /Pentagon load def /SolidPentagon /Pentagon load def /.notdef { 0 0 0 0 } def end /CharProcs 20 dict def CharProcs begin /Adjust { 2 copy dtransform floor .5 add exch floor .5 add exch idtransform 3 -1 roll div 3 1 roll exch div exch scale } def /CirclePath { 0 0 500 0 360 arc closepath } def /Bullet { 500 500 Adjust CirclePath fill } def /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath } def /SolidTriangle { TrianglePath fill } def /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath } def /SolidSquare { SquarePath fill } def /Square { SquarePath .89 .89 scale SquarePath eofill } def /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def /PentagonPath { -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto 0 574.7 lineto -546.6 177.6 lineto closepath } def /SolidPentagon { PentagonPath fill } def /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def /.notdef { } def end /BuildGlyph { exch begin Metrics 1 index get exec 0 BBoxes 3 index get exec setcachedevice CharProcs begin load exec end end } def /BuildChar { 1 index /Encoding get exch get 1 index /BuildGlyph get exec } bind defend/PSTricksDotFont exch definefont pop% END pst-dots.pro%%EndProcSet%%BeginProcSet: pst-node.pro%!% PostScript prologue for pst-node.tex.% Version 97 patch 1, 97/05/09.% For distribution, see pstricks.tex.%/tx@NodeDict 400 dict def tx@NodeDict begintx@Dict begin /T /translate load def end/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next endgrestore } def/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def} def/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exchSin mul } def } def/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def }ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dxdup Sin mul Cos Div } ifelse } def/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub/u ED /NodePos { GetRnodePos } def } def/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dupCos mul exch Sin mul } def/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w hmul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul} ifelse } def/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /dED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def dsub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atansin def /NodePos { TriNodePos } def } def/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Coshh mul Atan dup cos ww mul exch sin hh mul } def/GetCenter { begin X Y NodeMtrx transform CM itransform end } def/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { DistDist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg }{ 0 Dist Sin mul } ifelse } ifelse Do } def/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransformexch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrxdtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED popXYPos } ifelse } def/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1roll sin mul sub exch } ifelse } def/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleAAddOffset yA add /yA1 ED xA add /xA1 ED } def/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleBAddOffset yB add /yB1 ED xB add /xB1 ED } def/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmAAngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do EDArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED} ifelse } def/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmBAngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do EDArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED} ifelse } def/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict bknown and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yAED /xA ED NodeB GetCenter /yB ED /xB ED } if } def/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t submul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop} repeat LPutLine cleartomark } def/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bxsub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul muladd cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul addy0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mulmul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def} def/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd } def/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def} def/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def/NAngle yyB yyA sub xxB xxA sub Atan def } def/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomarkVPosEnd } def/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvxdef grestore exec /LPutVar /SaveLPutVar load def } def/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add defGetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {LPutVar VPutLine } def LPutVar } def/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop popend } def/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA subAtan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }ifelse } def/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmAGetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dictbegin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrxitransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate defxA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrxtransform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def }{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dictbegin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvxdef /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } ifxB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB EDGetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict beginfalse Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }def/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotatedef xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin falseLine end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {VPutLines } def } def% DG/SR modification begin - May 9, 1997 - Patch 1%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp rr mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA addexch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED% DG/SR modification end} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a addAngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 rDiv def /y ED /x ED } def/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cosmul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dyadd xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVartx@Dict begin false Polygon end } def/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atandef /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def/x0 xA r tA cos mul add def /y0 yA 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FV(=)f Ff(f2)p FZ(;)j Ff(0)l FZ(<)lFf(1)p FC(^)r Ff(f0)d FV(=)g Ff(f1)q FZ(;)j Ff(1)l FZ(<)lFf(2)p FC(^)r Ff(f1)d FV(=)g Ff(f2)q FZ(;)j Ff(f0)e FV(=)fFf(1)5535 1168 y FC(^)5577 1179 y Fd(R)p 3159 1246 20794 v 3159 1300 a FZ(M)3217 1310 y FP(1)3250 1300 y FZ(;)j(M)33371310 y FP(2)3369 1300 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()pFf(fx)e FV(=)f Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))pFZ(;)j(S)o(;)h(T)p 3966 1288 6 23 v 3972 1278 25 3 v57 w FC(9)p Ff(m)p FZ(:)p FV(\()p Ff(0)l FZ(<)l Ff(m)pFC(^)q Ff(f0)c FV(=)g Ff(fm)p FV(\))p FZ(;)k Ff(0)l FZ(<)lFf(1)p FC(^)q Ff(f0)d FV(=)f Ff(f1)p FZ(;)j Ff(1)l FZ(<)lFf(2)p FC(^)r Ff(f1)e FV(=)f Ff(f2)p FZ(;)j Ff(f0)e FV(=)fFf(1)5237 1257 y FC(9)5272 1268 y Fd(R)p 3135 1332 21274 v 3135 1386 a FZ(M)3193 1396 y FP(1)3226 1386 y FZ(;)j(M)33131396 y FP(2)3345 1386 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()pFf(fx)e FV(=)f Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))pFZ(;)j(S)o(;)h(T)p 3943 1374 6 23 v 3948 1364 25 3 v67 w Ff(0)l FZ(<)l Ff(1)p FC(^)r Ff(f0)c FV(=)g 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FZ(;)k(S)o(;)f(T)p 4098 1547 623 v 4104 1537 25 3 v 68 w Ff(1)l FZ(<)l Ff(2)p FC(^)qFf(f1)e FV(=)f Ff(f2)p FZ(;)k Ff(f0)c FV(=)g Ff(1)p FZ(;)pFC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)lFf(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p FV(\))5343 1516y FC(9)5378 1527 y Fd(R)p 3209 1591 1981 4 v 3209 1645a FZ(M)3267 1655 y FP(1)3299 1645 y FZ(;)j(M)3386 1655y FP(2)3419 1645 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()pFf(fx)e FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))pFZ(;)j(S)o(;)h(T)p 4016 1633 6 23 v 4021 1623 25 3 v57 w FC(9)p Ff(m)p FZ(:)p FV(\()p Ff(1)l FZ(<)l Ff(m)pFC(^)q Ff(f1)c FV(=)g Ff(fm)p FV(\))p FZ(;)k Ff(f0)dFV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)pFV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)g FV(=)g Ff(fm)pFV(\))5188 1603 y FC(9)5223 1614 y Fd(R)p 3209 1677 19814 v 3446 1731 a FZ(M)3504 1741 y FP(1)3537 1731 y FZ(;)j(M)36241741 y FP(2)3656 1731 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()pFf(fx)e FV(=)f Ff(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))pFZ(;)k(S)o(;)g(T)p 4253 1719 6 23 v 4259 1709 25 3 v67 w Ff(f0)d FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)pFf(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)gFV(=)g Ff(fm)p FV(\))5188 1689 y FC(9)5223 1700 y Fd(R)25671776 y Fc(|)p 2591 1776 1658 8 v 1658 w({z)p 4297 1776V 1658 w(})4233 1838 y Fd(X)4279 1850 y FP(5)2259 1970y Gc(M)2327 1979 y FV(1)2381 1970 y F9(=)19 b FX(8)pFu(y)q Gc(:)p Fu(x)p Gc(:)n F9(\()p Fu(x)8 b FX(\024)gFu(m)2788 1947 y Ff(x)p FZ(;)p Ff(y)2859 1970 y F9(\))101b Gc(T)30 b F9(=)19 b FX(8)p Fu(i)p Gc(:)p Fu(x)p Gc(:)pFu(y)q Gc(:)m F9(\(\()p Fu(fy)h F9(=)g Fu(i)p FX(^)pFu(fx)f F9(=)g Fu(i)p F9(\))12 b FX(\033)g Fu(fx)18 bF9(=)i Fu(fy)p F9(\))2259 2097 y Gc(M)2327 2106 y FV(2)23812097 y F9(=)f FX(8)p Fu(y)q Gc(:)p Fu(x)p Gc(:)n F9(\()pFu(y)9 b FX(\024)f Fu(m)2789 2073 y Ff(x)p FZ(;)p Ff(y)28602097 y F9(\))100 b Gc(S)23 b F9(=)d FX(8)p Fu(x)p Gc(:)pFu(y)q Gc(:)m F9(\()p Fu(sx)8 b FX(\024)g Fu(y)k FX(\033)gFu(x)c Gc(<)g Fu(y)q F9(\))6739 408 y currentpoint grestore moveto 6739 408 a 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-55 y FP(2)3483 -65 y FZ(;)p FC(8)pFf(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f Ff(0)p FC(_)p Ff(fx)gFV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p 4080 -77 6 23v 4086 -87 25 3 v 68 w Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)eFV(=)f Ff(f1)p FZ(;)k Ff(1)l FZ(<)l Ff(2)p FC(^)q Ff(f1)dFV(=)f Ff(f2)p FZ(;)k Ff(f0)c FV(=)g Ff(1)p FZ(;)p FC(9)pFf(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)pFC(^)q Ff(fn)h FV(=)f Ff(fm)p FV(\))5552 -108 y FC(8)5587-97 y Fd(L)2887 -21 y Fc(|)p 2911 -21 1365 8 v 1365 w({z)p4324 -21 V 1365 w(})4266 41 y Fd(Y)4300 53 y FP(6)p 2180995 247 4 v 2180 1047 a Ff(1)l FC(\024)l Ff(2)p 22881035 6 23 v 2294 1025 25 3 v 61 w(1)l FC(\024)l Ff(2)p2476 996 247 4 v 51 w(0)l FZ(<)l Ff(2)p 2584 1035 6 23v 2590 1025 25 3 v 61 w(0)l FZ(<)l Ff(2)p 2180 1077 5434 v 2196 1128 a(1)l FC(\024)l Ff(2)p FC(\033)q Ff(0)lFZ(<)l Ff(2)p FZ(;)13 b Ff(1)l FC(\024)l Ff(2)p 25691116 6 23 v 2574 1106 25 3 v 60 w(0)l FZ(<)l Ff(2)27221086 y FC(\033)2770 1097 y Fd(L)p 2139 1158 626 4 v 21281212 a FC(8)p Ff(y)q FZ(:)p FV(\()p Ff(1)l FC(\024)lFf(y)q FC(\033)r Ff(0)l FZ(<)l Ff(y)q FV(\))p FZ(;)fFf(1)l FC(\024)l Ff(2)p 2626 1200 6 23 v 2631 1190 253 v 60 w(0)l FZ(<)l Ff(2)2763 1170 y FC(8)2798 1181 yFd(L)p 2139 1244 626 4 v 2293 1296 a Ff(1)l FC(\024)lFf(2)p FZ(;)h(S)p 2471 1284 6 23 v 2477 1274 25 3 v 61w Ff(0)l FZ(<)l Ff(2)2763 1256 y FC(8)2798 1267 y Fd(L)p2892 813 319 4 v 2892 864 a Ff(f2)8 b FV(=)f Ff(1)p 3036852 6 23 v 3042 842 25 3 v 59 w(f2)g FV(=)g Ff(1)4299198 y F3(.)4299 231 y(.)4299 265 y(.)4299 298 y(.)4270349 y FZ(Y)4306 359 y FP(6)p 4407 298 319 4 v 4407 349a Ff(f0)g FV(=)g Ff(1)p 4551 337 6 23 v 4556 327 25 3v 59 w(f0)h FV(=)f Ff(1)p 3260 379 2458 4 v 3260 433a(f0)h FV(=)f Ff(0)p FC(_)p Ff(f0)g FV(=)g Ff(1)p FZ(;)k(M)3649443 y FP(1)3681 433 y FZ(;)g(M)3769 443 y FP(2)3801 433y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)fFf(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p4398 421 6 23 v 4404 411 25 3 v 68 w Ff(0)l FZ(<)l Ff(1)pFC(^)q Ff(f0)e FV(=)f Ff(f1)p FZ(;)k Ff(1)l FZ(<)l Ff(2)pFC(^)q Ff(f1)d FV(=)f Ff(f2)p FZ(;)k Ff(f0)c FV(=)g Ff(1)pFZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)lFZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p FV(\))5717387 y FC(_)5758 398 y Fd(L)p 3260 465 2458 4 v 3426 519a FZ(M)3484 529 y FP(1)3516 519 y FZ(;)j(M)3603 529 yFP(2)3636 519 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)eFV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p4233 507 6 23 v 4238 497 25 3 v 67 w Ff(0)l FZ(<)l Ff(1)pFC(^)r Ff(f0)d FV(=)f Ff(f1)p FZ(;)j Ff(1)l FZ(<)l Ff(2)pFC(^)r Ff(f1)d FV(=)g Ff(f2)q FZ(;)j Ff(f0)e FV(=)f Ff(1)pFZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)lFZ(<)l Ff(m)p FC(^)q Ff(fn)g FV(=)g Ff(fm)p FV(\))5717477 y FC(8)5752 488 y Fd(L)p 3343 551 2292 4 v 3343 605a FZ(M)3401 615 y FP(1)3434 605 y FZ(;)j(M)3521 615 yFP(2)3553 605 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)eFV(=)f Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p4150 593 6 23 v 4156 583 25 3 v 57 w FC(9)p Ff(m)p FZ(:)pFV(\()p Ff(0)l FZ(<)l Ff(m)p FC(^)q Ff(f0)c FV(=)g Ff(fm)pFV(\))p FZ(;)k Ff(1)l FZ(<)l Ff(2)p FC(^)q Ff(f1)d FV(=)fFf(f2)p FZ(;)j Ff(f0)e FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)pFZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)qFf(fn)h FV(=)f Ff(fm)p FV(\))5634 563 y FC(9)5669 574y Fd(R)p 3343 638 2292 4 v 3581 692 a FZ(M)3639 702 yFP(1)3671 692 y FZ(;)k(M)3759 702 y FP(2)3791 692 y FZ(;)pFC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f Ff(0)p FC(_)pFf(fx)g FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p 4388680 6 23 v 4394 670 25 3 v 68 w Ff(1)l FZ(<)l Ff(2)pFC(^)q Ff(f1)e FV(=)f Ff(f2)p FZ(;)k Ff(f0)c FV(=)g Ff(1)pFZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)lFZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p FV(\))5634649 y FC(9)5669 660 y Fd(R)p 3499 724 1981 4 v 3499 778a FZ(M)3557 788 y FP(1)3589 778 y FZ(;)k(M)3677 788 yFP(2)3709 778 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)dFV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p4306 766 6 23 v 4312 756 25 3 v 57 w FC(9)p Ff(m)p FZ(:)pFV(\()p Ff(1)l FZ(<)l Ff(m)p FC(^)q Ff(f1)e FV(=)f Ff(fm)pFV(\))p FZ(;)j Ff(f0)e FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)pFZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)qFf(fn)g FV(=)g Ff(fm)p FV(\))5478 736 y FC(9)5513 747y Fd(R)p 3499 810 1981 4 v 3736 864 a FZ(M)3794 874 yFP(1)3827 864 y FZ(;)j(M)3914 874 y FP(2)3947 864 y FZ(;)pFC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)g Ff(0)p FC(_)pFf(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p 4544852 6 23 v 4549 842 25 3 v 67 w Ff(f0)d FV(=)f Ff(1)pFZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)lFZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)o FV(\))5478822 y FC(9)5513 833 y Fd(R)p 2892 897 2350 4 v 3149 951a Ff(f2)h FV(=)f Ff(1)p FZ(;)j(M)3366 961 y FP(1)3398951 y FZ(;)h(M)3486 961 y FP(2)3518 951 y FZ(;)p FC(8)pFf(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f Ff(0)p FC(_)p Ff(fx)gFV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)g(T)p 4115 939 6 23v 4121 929 25 3 v 67 w Ff(f2)d FV(=)f Ff(1)p FC(^)o Ff(f0)hFV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)pFV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)pFV(\))5241 905 y FC(^)5282 916 y Fd(R)p 5852 899 3514 v 5852 951 a Ff(f0)h FV(=)f Ff(f2)p 6012 939 6 23 v6018 929 25 3 v 59 w(f0)h FV(=)f Ff(f2)p 3149 983 30544 v 3549 1037 a FV(\()p Ff(f2)h FV(=)f Ff(1)p FC(^)pFf(f0)g FV(=)g Ff(1)p FV(\))p FC(\033)p Ff(f0)h FV(=)fFf(f2)p FZ(;)k Ff(f2)d FV(=)f Ff(1)p FZ(;)j(M)4339 1047y FP(1)4371 1037 y FZ(;)h(M)4459 1047 y FP(2)4491 1037y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)fFf(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)g(T)p5088 1025 6 23 v 5094 1015 25 3 v 67 w Ff(f0)d FV(=)fFf(f2)p FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()pFf(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)o FV(\))6202992 y FC(\033)6250 1003 y Fd(L)p 3492 1069 2367 4 v 34821123 a FC(8)p Ff(y)q FZ(:)p FV(\(\()p Ff(fy)h FV(=)fFf(1)p FC(^)p Ff(f0)h FV(=)f Ff(1)p FV(\))p FC(\033)pFf(f0)g FV(=)g Ff(fy)q FV(\))p FZ(;)k Ff(f2)c FV(=)gFf(1)p FZ(;)k(M)4396 1133 y FP(1)4428 1123 y FZ(;)g(M)45161133 y FP(2)4548 1123 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()pFf(fx)d FV(=)f Ff(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))pFZ(;)k(S)o(;)g(T)p 5145 1111 6 23 v 5151 1101 25 3 v67 w Ff(f0)d FV(=)f Ff(f2)p FZ(;)p FC(9)p Ff(n)p FZ(:)pFf(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)gFV(=)g Ff(fm)p FV(\))5858 1081 y FC(8)5893 1092 y Fd(L)p3473 1156 2407 4 v 3462 1210 a FC(8)p Ff(x)p FZ(:)p Ff(y)qFZ(:)p FV(\(\()p Ff(fy)i FV(=)e Ff(1)p FC(^)p Ff(fx)gFV(=)g Ff(1)p FV(\))p FC(\033)p Ff(fx)h FV(=)f Ff(fy)qFV(\))p FZ(;)j Ff(f2)e FV(=)f Ff(1)p FZ(;)k(M)4416 1220y FP(1)4448 1210 y FZ(;)f(M)4535 1220 y FP(2)4568 1210y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)fFf(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p5165 1198 6 23 v 5170 1188 25 3 v 68 w Ff(f0)c FV(=)gFf(f2)q FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()pFf(n)l FZ(<)l Ff(m)p FC(^)p Ff(fn)h FV(=)f Ff(fm)p FV(\))58781167 y FC(8)5913 1178 y Fd(L)p 3473 1242 2407 4 v 38361296 a Ff(f2)g FV(=)g Ff(1)p 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Gc(M)2094 1747 yFV(1)2148 1738 y F9(=)20 b FX(8)p Fu(y)q Gc(:)p Fu(x)pGc(:)m F9(\()p Fu(x)8 b FX(\024)g Fu(m)2555 1714 y Ff(x)pFZ(;)p Ff(y)2626 1738 y F9(\))101 b Gc(T)30 b F9(=)19b FX(8)p Fu(i)p Gc(:)p Fu(x)p Gc(:)p Fu(y)q Gc(:)m F9(\(\()pFu(fy)i F9(=)e Fu(i)p FX(^)p Fu(fx)g F9(=)g Fu(i)p F9(\))12b FX(\033)g Fu(fx)19 b F9(=)g Fu(fy)p F9(\))2026 1864y Gc(M)2094 1873 y FV(2)2148 1864 y F9(=)h FX(8)p Fu(y)qGc(:)p Fu(x)p Gc(:)m F9(\()p Fu(y)9 b FX(\024)f Fu(m)25561840 y Ff(x)p FZ(;)p Ff(y)2627 1864 y F9(\))100 b Gc(S)23b F9(=)d FX(8)p Fu(x)p Gc(:)p Fu(y)q Gc(:)m F9(\()p Fu(sx)8b FX(\024)g Fu(y)k FX(\033)g Fu(x)c Gc(<)g Fu(y)q F9(\))6506465 y currentpoint grestore moveto 6506 465 a 3543 5116 4 4724 v 321 5119 3226 4 vBlack 1364 5273 a Gg(Figure)24 b(5:)29 b(Subproofs)dGa(Y)2173 5287 y F9(6)2235 5273 y Gg(and)e Ga(Y)24425287 y F9(7)2481 5273 y Gg(.)p Black Black eop end%%Page: 137 149TeXDict begin 137 148 bop Black 3831 51 a Gb(137)p 27788 3691 4 v Black Black 277 393 3226 4 v 277 5116 4 4724v 1882 465 a gsave currentpoint currentpoint translate -90 neg rotate neg exchneg exch translate 1882 465 a 2724 -693 247 4 v 2724 -641 aFf(1)l FC(\024)l Ff(1)p 2832 -653 6 23 v 2837 -663 253 v 60 w(1)l FC(\024)l Ff(1)p 3020 -692 247 4 v 52 w(0)lFZ(<)l Ff(1)p 3128 -653 6 23 v 3134 -663 25 3 v 61 w(0)lFZ(<)l Ff(1)p 2724 -611 543 4 v 2739 -559 a(1)l FC(\024)lFf(1)p FC(\033)r Ff(0)l FZ(<)l Ff(1)p FZ(;)12 b Ff(1)lFC(\024)l Ff(1)p 3112 -571 6 23 v 3118 -581 25 3 v 61w(0)l FZ(<)l Ff(1)3266 -602 y FC(\033)3314 -591 y Fd(L)p2682 -529 626 4 v 2672 -475 a FC(8)p Ff(y)q FZ(:)p FV(\()pFf(1)l FC(\024)l Ff(y)q FC(\033)q Ff(0)l FZ(<)l Ff(y)qFV(\))p FZ(;)g Ff(1)l FC(\024)l Ff(1)p 3169 -487 6 23v 3175 -497 25 3 v 61 w(0)l FZ(<)l Ff(1)3307 -518 y FC(8)3342-507 y Fd(L)p 2682 -443 626 4 v 2837 -392 a Ff(1)l FC(\024)lFf(1)p FZ(;)g(S)p 3015 -404 6 23 v 3020 -413 25 3 v 61w Ff(0)l FZ(<)l Ff(1)3307 -431 y FC(8)3342 -420 y Fd(L)p3448 -854 319 4 v 3448 -802 a Ff(f1)c FV(=)f Ff(0)p 3592-814 6 23 v 3598 -824 25 3 v 59 w(f1)h FV(=)f Ff(0)p3817 -854 319 4 v 50 w(f0)g FV(=)g Ff(0)p 3961 -814 623 v 3966 -824 25 3 v 59 w(f0)h FV(=)f Ff(0)p 3448 -783687 4 v 3467 -731 a(f1)h FV(=)f Ff(0)p FZ(;)k Ff(f0)cFV(=)g Ff(0)p 3770 -743 6 23 v 3776 -753 25 3 v 59 w(f1)hFV(=)f Ff(0)p FC(^)p Ff(f0)g FV(=)g Ff(0)4134 -774 yFC(^)4176 -763 y Fd(R)p 4273 -783 351 4 v 4273 -731 aFf(f0)g FV(=)g Ff(f1)p 4433 -743 6 23 v 4439 -753 253 v 60 w(f0)g FV(=)g Ff(f1)p 3467 -702 1157 4 v 3512-648 a FV(\()p Ff(f1)h FV(=)f Ff(0)p FC(^)o Ff(f0)h FV(=)fFf(0)p FV(\))p FC(\033)p Ff(f0)h FV(=)f Ff(f1)p FZ(;)kFf(f1)c FV(=)g Ff(0)p FZ(;)k Ff(f0)d FV(=)f Ff(0)p 4388-660 6 23 v 4394 -670 25 3 v 59 w(f0)g FV(=)g Ff(f1)4623-693 y FC(\033)4671 -681 y Fd(L)p 3455 -615 1181 4 v3445 -561 a FC(8)p Ff(y)q FZ(:)p FV(\(\()p Ff(fy)h FV(=)fFf(0)p FC(^)p Ff(f0)g FV(=)g Ff(0)p FV(\))p FC(\033)pFf(f0)h FV(=)f Ff(fy)q FV(\))p FZ(;)k Ff(f1)c FV(=)gFf(0)p FZ(;)k Ff(f0)d FV(=)f Ff(0)p 4445 -573 6 23 v4451 -583 25 3 v 59 w(f0)g FV(=)g Ff(f1)4635 -604 y FC(8)4670-593 y Fd(L)p 3436 -529 1220 4 v 3425 -475 a FC(8)p Ff(x)pFZ(:)p Ff(y)q FZ(:)p FV(\(\()p Ff(fy)i FV(=)e Ff(0)pFC(^)o Ff(fx)h FV(=)f Ff(0)p FV(\))p FC(\033)p Ff(fx)hFV(=)f Ff(fy)q FV(\))p FZ(;)j Ff(f1)e FV(=)f Ff(0)p FZ(;)jFf(f0)e FV(=)f Ff(0)p 4464 -487 6 23 v 4470 -497 25 3v 59 w(f0)h FV(=)f Ff(f1)4654 -517 y FC(8)4689 -506 yFd(L)p 3436 -443 1220 4 v 3761 -392 a Ff(f1)h FV(=)fFf(0)p FZ(;)k Ff(f0)c FV(=)g Ff(0)p FZ(;)k(T)p 4139 -4046 23 v 4144 -413 25 3 v 67 w Ff(f0)d FV(=)f Ff(f1)4654-431 y FC(8)4689 -420 y Fd(L)p 2837 -362 1493 4 v 3136-310 a Ff(f1)h FV(=)f Ff(0)p FZ(;)k Ff(1)l FC(\024)lFf(1)p FZ(;)h Ff(f0)c FV(=)f Ff(0)p FZ(;)j(S)o(;)h(T)p3704 -322 6 23 v 3709 -332 25 3 v 68 w Ff(0)l FZ(<)lFf(1)p FC(^)q Ff(f0)d FV(=)f Ff(f1)4329 -353 y FC(^)4370-342 y Fd(R)4829 -461 y F3(.)4829 -428 y(.)4829 -394y(.)4829 -361 y(.)4801 -310 y FZ(Y)4837 -300 y FP(3)p2425 -280 3175 4 v 2425 -226 a Ff(f1)g FV(=)g Ff(0)pFC(_)p Ff(f1)h FV(=)f Ff(1)p FZ(;)j Ff(1)l FC(\024)lFf(1)p FZ(;)j Ff(f0)7 b FV(=)g Ff(0)p FZ(;)k Ff(2)l FC(\024)lFf(2)p FZ(;)h Ff(f1)c FV(=)f Ff(1)p FZ(;)k(M)3379 -216y FP(1)3411 -226 y FZ(;)f(M)3498 -216 y FP(2)3531 -226y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)fFf(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p4128 -238 6 23 v 4133 -248 25 3 v 67 w Ff(0)l FZ(<)lFf(1)p FC(^)r Ff(f0)d FV(=)f Ff(f1)p FZ(;)j Ff(1)l FZ(<)lFf(3)p FC(^)r Ff(f1)d FV(=)g Ff(f3)q FZ(;)j Ff(1)l FZ(<)lFf(2)p FC(^)r Ff(f1)d FV(=)g Ff(f2)q FZ(;)p FC(9)p Ff(n)pFZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)pFf(fn)h FV(=)f Ff(fm)p FV(\))5598 -272 y FC(_)5639 -261y Fd(L)p 2425 -194 3175 4 v 2590 -140 a Ff(1)l FC(\024)lFf(1)p FZ(;)12 b Ff(f0)c FV(=)f Ff(0)p FZ(;)k Ff(2)lFC(\024)l Ff(2)p FZ(;)h Ff(f1)c FV(=)f Ff(1)p FZ(;)j(M)3213-130 y FP(1)3246 -140 y FZ(;)g(M)3333 -130 y FP(2)3365-140 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)fFf(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)g(T)p3962 -152 6 23 v 3968 -162 25 3 v 67 w Ff(0)l FZ(<)lFf(1)p FC(^)q Ff(f0)d FV(=)f Ff(f1)p FZ(;)k Ff(1)l FZ(<)lFf(3)p FC(^)q Ff(f1)d FV(=)f Ff(f3)p FZ(;)k Ff(1)l FZ(<)lFf(2)p FC(^)q Ff(f1)d FV(=)f Ff(f2)p FZ(;)p FC(9)p Ff(n)pFZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)qFf(fn)h FV(=)f Ff(fm)o FV(\))5598 -182 y FC(8)5633 -171y Fd(L)p 2498 -107 3028 4 v 2487 -43 a FC(8)p Ff(x)pFZ(:)p FV(\()p Ff(x)l FC(\024)l Ff(m)2695 -63 y Fe(x)pFd(;)p Fe(0)2752 -43 y FV(\))p FZ(;)j Ff(f0)e FV(=)fFf(0)p FZ(;)k Ff(2)l FC(\024)l Ff(2)p FZ(;)h Ff(f1)cFV(=)f Ff(1)p FZ(;)j(M)3305 -33 y FP(1)3338 -43 y FZ(;)g(M)3425-33 y FP(2)3457 -43 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()pFf(fx)e FV(=)f Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))pFZ(;)j(S)o(;)h(T)p 4054 -55 6 23 v 4060 -64 25 3 v 67w Ff(0)l FZ(<)l Ff(1)p FC(^)r Ff(f0)c FV(=)g Ff(f1)qFZ(;)j Ff(1)l FZ(<)l Ff(3)p FC(^)q Ff(f1)e FV(=)f Ff(f3)pFZ(;)k Ff(1)l FZ(<)l Ff(2)p FC(^)q Ff(f1)d FV(=)f Ff(f2)pFZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)lFZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p FV(\))5525-96 y FC(8)5560 -85 y Fd(L)p 2498 -10 3028 4 v 2652 44a Ff(f0)g FV(=)g Ff(0)p FZ(;)k Ff(2)l FC(\024)l Ff(2)pFZ(;)h Ff(f1)c FV(=)f Ff(1)p FZ(;)k(M)3152 54 y FP(1)318444 y FZ(;)f(M)3271 54 y FP(2)3304 44 y FZ(;)p FC(8)pFf(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)f Ff(0)p FC(_)o Ff(fx)hFV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p 3901 32 6 23v 3906 22 25 3 v 67 w Ff(0)l FZ(<)l Ff(1)p FC(^)r Ff(f0)cFV(=)g Ff(f1)q FZ(;)j Ff(1)l FZ(<)l Ff(3)p FC(^)r Ff(f1)dFV(=)g Ff(f3)q FZ(;)j Ff(1)l FZ(<)l Ff(2)p FC(^)q Ff(f1)eFV(=)f Ff(f2)p FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)pFV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)pFV(\))5525 2 y FC(8)5560 13 y Fd(L)2425 88 y Fc(|)p 244988 1582 8 v 1582 w({z)p 4079 88 V 1582 w(})4021 150 yFd(Y)4055 162 y FP(4)4057 424 y F3(.)4057 457 y(.)4057490 y(.)4057 523 y(.)4029 575 y FZ(Y)4065 585 y FP(4)p4165 523 319 4 v 4165 575 a Ff(f0)h FV(=)f Ff(1)p 4309563 6 23 v 4315 553 25 3 v 59 w(f0)h FV(=)f Ff(1)p 2722604 3051 4 v 2722 658 a(f0)h FV(=)f Ff(0)p FC(_)p Ff(f0)gFV(=)g Ff(1)p FZ(;)k Ff(2)l FC(\024)l Ff(2)p FZ(;)h Ff(f1)cFV(=)f Ff(1)p FZ(;)k(M)3394 668 y FP(1)3426 658 y FZ(;)g(M)3514668 y FP(2)3546 658 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()pFf(fx)d FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))pFZ(;)k(S)o(;)f(T)p 4143 646 6 23 v 4149 636 25 3 v 68w Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)e FV(=)f Ff(f1)pFZ(;)k Ff(1)l FZ(<)l Ff(3)p FC(^)q Ff(f1)d FV(=)f Ff(f3)pFZ(;)j Ff(1)l FZ(<)l Ff(2)p FC(^)r Ff(f1)d FV(=)g Ff(f2)qFZ(;)j Ff(f0)e FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)pFf(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)hFV(=)f Ff(fm)o FV(\))5772 612 y FC(_)5814 623 y Fd(L)p2722 690 3051 4 v 2888 744 a Ff(2)l FC(\024)l Ff(2)pFZ(;)12 b Ff(f1)c FV(=)f Ff(1)p FZ(;)j(M)3228 754 y FP(1)3261744 y FZ(;)g(M)3348 754 y FP(2)3381 744 y FZ(;)p FC(8)pFf(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)g Ff(0)p FC(_)p Ff(fx)hFV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p 3978 732 6 23v 3983 722 25 3 v 67 w Ff(0)l FZ(<)l Ff(1)p FC(^)r Ff(f0)cFV(=)g Ff(f1)q FZ(;)j Ff(1)l FZ(<)l Ff(3)p FC(^)r Ff(f1)dFV(=)g Ff(f3)q FZ(;)j Ff(1)l FZ(<)l Ff(2)p FC(^)q Ff(f1)eFV(=)f Ff(f2)p FZ(;)k Ff(f0)d FV(=)f Ff(1)p FZ(;)p FC(9)pFf(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)pFC(^)q Ff(fn)g FV(=)g Ff(fm)p FV(\))5772 702 y FC(8)5807713 y Fd(L)p 2806 777 2885 4 v 2806 831 a Ff(2)l FC(\024)lFf(2)p FZ(;)12 b Ff(f1)c FV(=)f Ff(1)p FZ(;)j(M)3146841 y FP(1)3178 831 y FZ(;)h(M)3266 841 y FP(2)3298 831y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)fFf(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)g(T)p3895 819 6 23 v 3901 809 25 3 v 56 w FC(9)p Ff(m)p FZ(:)pFV(\()p Ff(0)l FZ(<)l Ff(m)p FC(^)q Ff(f0)d FV(=)f Ff(fm)pFV(\))p FZ(;)j Ff(1)l FZ(<)l Ff(3)p FC(^)r Ff(f1)d FV(=)gFf(f3)q FZ(;)j Ff(1)l FZ(<)l Ff(2)p FC(^)r Ff(f1)d FV(=)gFf(f2)q FZ(;)j Ff(f0)e FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)pFZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)qFf(fn)g FV(=)g Ff(fm)p FV(\))5689 788 y FC(9)5724 799y Fd(R)p 2806 863 2885 4 v 3043 917 a Ff(2)l FC(\024)lFf(2)p FZ(;)13 b Ff(f1)7 b FV(=)g Ff(1)p FZ(;)k(M)3384927 y FP(1)3416 917 y FZ(;)g(M)3504 927 y FP(2)3536 917y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)fFf(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p4133 905 6 23 v 4139 895 25 3 v 68 w Ff(1)l FZ(<)l Ff(3)pFC(^)q Ff(f1)e FV(=)f Ff(f3)p FZ(;)k Ff(1)l FZ(<)l Ff(2)pFC(^)q Ff(f1)d FV(=)f Ff(f2)p FZ(;)j Ff(f0)e FV(=)f Ff(1)pFZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)lFZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p FV(\))5689875 y FC(9)5724 886 y Fd(R)p 2961 949 2574 4 v 2961 1003a Ff(2)l FC(\024)l Ff(2)p FZ(;)12 b Ff(f1)c FV(=)f Ff(1)pFZ(;)k(M)3302 1013 y FP(1)3334 1003 y FZ(;)f(M)3421 1013y FP(2)3454 1003 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()pFf(fx)e FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))pFZ(;)j(S)o(;)h(T)p 4051 991 6 23 v 4056 981 25 3 v 57w FC(9)p Ff(m)p FZ(:)p FV(\()p Ff(1)l FZ(<)l Ff(m)p FC(^)qFf(f1)c FV(=)g Ff(fm)p FV(\))p FZ(;)k Ff(1)l FZ(<)l Ff(2)pFC(^)q Ff(f1)d FV(=)f Ff(f2)p FZ(;)k Ff(f0)c FV(=)g Ff(1)pFZ(;)p FC(9)p Ff(n)p 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F9(\))11981641 y Ga(P)s F6(g)g(2)f Ga(S)5 b(N)1550 1655 y Gc(aux)16951641 y Gg(for)23 b(all)1937 1629 y F9(\()1965 1641 yGa(v)5 b F4(:)r Ga(C)i F6(\033)o Ga(D)2261 1629 y F9(\))22891641 y Ga(P)38 b F6(2)25 b FB(J)p F4(\()p Ga(C)7 b F6(\033)oGa(D)s F4(\))p FB(K)190 b Gg(by)24 b(Def.)e(2.3.3)5041765 y(\(2.3\))101 b Ga(M)5 b F6(f)-7 b Ga(b)26 b F4(:=)10951753 y F9(\()1123 1765 y Ga(z)1169 1753 y F9(\))11971765 y Ga(N)p F6(g)g(2)f Ga(S)5 b(N)1561 1779 y Gc(aux)24081765 y Gg(by)23 b(\(1\),)h(\(2.2\))g(and)3024 1753 yF9(\()3051 1765 y Ga(v)3098 1753 y F9(\))3126 1765 yGa(P)38 b F6(\021)3318 1753 y F9(\()3345 1765 y Ga(z)33911753 y F9(\))3419 1765 y Ga(N)504 1889 y Gg(\(2.4\))101b(The)23 b(follo)n(wing)i(calculation)i(sho)n(ws)d(that)gFL(Cut)p F4(\()2318 1877 y FX(h)2345 1889 y Ga(c)23841877 y FX(i)2412 1889 y Ga(M)10 b(;)2550 1877 y F9(\()25781889 y Ga(z)2624 1877 y F9(\))2652 1889 y Ga(N)g F4(\))25b F6(2)g Ga(S)5 b(N)3015 1903 y Gc(aux)3138 1889 y Gg(.)pBlack Black 874 2104 a Ga(M)g F6(f)-7 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b(;)1774 3006 y F9(\()1802 3018 y Ga(x)18543006 y F9(\))1882 3018 y Ga(S)5 b F4(\))p Ga(;)2018 3006y F9(\()2046 3018 y Ga(y)2094 3006 y F9(\))2121 3018y Ga(U)10 b F4(\))24 b Gg(must)g(be)g(strongly)j(normalising,)f(too.)504 3130 y(In)34 b(f)o(act)h(both)g(reducts)g(must)f(be)g(strongly)j(normalising.)62 b(The)34 b(case)g(where)3069 3118 yF9(\()3096 3130 y Ga(z)6 b F4(:)r Ga(C)h F6(\033)p Ga(D)33923118 y F9(\))3419 3130 y Ga(N)504 3243 y Gg(belongs)26b(to)f FW(B)t(I)t(N)t(D)t(I)t(N)t(G)1240 3262 y F9(\()pGc(C)5 b FX(\033)r Gc(D)r F9(\))1471 3243 y F4(\()p FB(J)pF6(h)p Ga(C)i F6(\033)o Ga(D)s F6(i)p FB(K)p F4(\))23b Gg(is)g(similar)-5 b(.)504 3401 y(W)e(e)34 b(no)n(w)f(ha)n(v)o(e)i(to)f(sho)n(w)g(that)h(the)g(reduct)g(is)f(strongly)j(normalising)g(in)d(the)g(case)h(where)504 3502 y FX(h)532 3514 y Ga(b)17b F4(:)g Ga(C)7 b F6(\033)p Ga(D)851 3502 y FX(i)8783514 y Ga(M)45 b Gg(and)1178 3502 y F9(\()1205 3514 yGa(z)22 b F4(:)17 b Ga(C)7 b F6(\033)o Ga(D)1531 3502y F9(\))1558 3514 y Ga(N)46 b Gg(belong)37 b(to)h FW(I)t(M)t(P)t(R)t(I)t(G)t(H)t(T)2449 3533 y FX(h)p Gc(C)5 b FX(\033)t Gc(D)rFX(i)2681 3514 y F4(\()p FB(J)p F4(\()p Ga(C)i F4(\))qFB(K)o Ga(;)15 b FB(J)p F6(h)p Ga(D)s F6(i)q FB(K)o F4(\))36b Gg(and)g(to)506 3627 y FW(I)t(M)t(P)t(L)t(E)t(F)t(T)8333646 y F9(\()p Gc(C)6 b FX(\033)f Gc(D)r F9(\))1068 3627y F4(\()p FB(J)p F6(h)p Ga(C)i F6(i)p FB(K)o Ga(;)15b FB(J)p F4(\()p Ga(D)s F4(\))q FB(K)p F4(\))p Gg(,)22b(respecti)n(v)o(ely)-6 b(.)504 3785 y(W)f(e)23 b(\002rst)g(sho)n(w)h(that)g(the)f(inner)i(cut)f(of)f(the)h(reduct)h(is)e(strongly)j(normalising.)504 3945 y(\(3.1\))778 3933 y FX(h)8063945 y Ga(b)17 b F4(:)g Ga(C)7 b F6(\033)o Ga(D)11243933 y FX(i)1152 3945 y Ga(M)35 b F6(2)27 b FW(I)t(M)t(P)t(R)t(I)t(G)t(H)t(T)1745 3964 y FX(h)p Gc(C)5 b FX(\033)t Gc(D)r FX(i)19773945 y F4(\()p FB(J)p F4(\()p Ga(C)i F4(\))p FB(K)p Ga(;)15b FB(J)p F6(h)p Ga(D)s F6(i)p FB(K)p F4(\))p Gg(,)7784058 y F9(\()806 4070 y Ga(z)21 b F4(:)d Ga(C)7 b F6(\033)oGa(D)1132 4058 y F9(\))1159 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b(;)27641237 y F9(\()2792 1249 y Ga(y)2840 1237 y F9(\))28671249 y Ga(U)10 b F4(\)\))26 b Ga(:)321 1492 y Gg(W)-7b(e)23 b(ha)n(v)o(e)h(sho)n(wn)f(that)h(all)f(immediate)i(reducts)g(of)e FL(Cut)p F4(\()2146 1480 y FX(h)2174 1492 y Ga(a)22221480 y FX(i)2249 1492 y Ga(M)10 b(;)2387 1480 y F9(\()24151492 y Ga(x)2467 1480 y F9(\))2494 1492 y Ga(N)g F4(\))23b Gg(are)h(strongly)h(normalising.)321 1605 y(Consequently)-6b(,)27 b FL(Cut)p F4(\()1034 1593 y FX(h)1062 1605 yGa(a)1110 1593 y FX(i)1137 1605 y Ga(M)10 b(;)1275 1593y F9(\()1303 1605 y Ga(x)1355 1593 y F9(\))1382 1605y Ga(N)g F4(\))23 b Gg(must)h(be)g(strongly)h(normalising.)31b(Thus)24 b(we)f(are)g(done.)p 3480 1605 4 62 v 34841547 55 4 v 3484 1605 V 3538 1605 4 62 v Black 321 1818a Gb(Pr)n(oof)h(of)f(Lemma)e(2.3.18.)p Black 35 w Gg(W)-7b(e)22 b(shall)h(gi)n(v)o(e)g(\002)n(v)o(e)f(representati)n(v)o(e)k(cases,)e(in)f(which)g(the)g(e)o(xpression)326 1931 yF4(^)-50 b Ga(\033)t(;)15 b F6(f)p Ga(\033)s F6(g)24b Gg(will)f(stand)i(for)e(the)h(set)29 b F4(^)-50 b Ga(\033)23b F6([)d(f)p Ga(\033)s F6(g)k Gg(with)f F6(f)p Ga(\033)sF6(g)k(62)i F4(^)-50 b Ga(\033)t Gg(.)p Black 321 2162a Gb(Case)24 b FL(Ax)o F4(\()p Ga(x;)15 b(a)p F4(\))pGb(:)p Black 47 w Gg(W)-7 b(e)27 b(ha)n(v)o(e)h(to)f(pro)o(v)o(e)h(that)g FL(Ax)o F4(\()p Ga(x;)15 b(a)p F4(\))39 b(^)-50b Ga(\033)s(;)10 b F6(f)-7 b Ga(x)34 b F4(:=)2440 2150y FX(h)2468 2162 y Ga(b)2507 2150 y FX(i)2534 2162 yGa(P)t F6(g)p Ga(;)10 b F6(f)-7 b Ga(a)34 b F4(:=)29242150 y F9(\()2951 2162 y Ga(y)2999 2150 y F9(\))30272162 y Ga(Q)-10 b F6(g)27 b Gg(is)g(strongly)549 2275y(normalising)f(for)d(arbitrary)j(\(co-\)named)g(terms)21372263 y FX(h)2164 2275 y Ga(b)r F4(:)r Ga(B)2306 2263y FX(i)2333 2275 y Ga(P)39 b F6(2)24 b FB(J)p F6(h)pGa(B)5 b F6(i)p FB(K)23 b Gg(and)2910 2263 y F9(\()29372275 y Ga(y)5 b F4(:)r Ga(B)3088 2263 y F9(\))3115 2275y Ga(Q)25 b F6(2)g FB(J)p F4(\()p Ga(B)5 b F4(\))p FB(K)pGg(.)549 2428 y(\(1\))48 b FL(Ax)o F4(\()p Ga(x;)15 b(a)pF4(\))32 b(^)-50 b Ga(\033)s(;)10 b F6(f)-7 b Ga(x)26b F4(:=)1368 2416 y FX(h)1396 2428 y Ga(b)1435 2416 yFX(i)1462 2428 y Ga(P)t F6(g)p Ga(;)10 b F6(f)-7 b Ga(a)27b F4(:=)1838 2416 y F9(\()1865 2428 y Ga(y)1913 2416y F9(\))1941 2428 y Ga(Q)-10 b F6(g)26 b F4(=)f FL(Cut)pF4(\()2343 2416 y FX(h)2370 2428 y Ga(b)2409 2416 y FX(i)24372428 y Ga(P)13 b(;)2548 2416 y F9(\()2576 2428 y Ga(y)26242416 y F9(\))2651 2428 y Ga(Q)p F4(\))239 b Gg(by)24b(Def.)e(of)i F6(f)p 3438 2428 28 4 v 3456 2428 V 34742428 V 65 w(g)549 2549 y Gg(\(2\))702 2537 y FX(h)7292549 y Ga(b)r F4(:)r Ga(B)871 2537 y FX(i)899 2549 yGa(P)38 b F6(2)25 b FB(J)p F6(h)p Ga(B)5 b F6(i)p FB(K)22b Gg(and)1475 2537 y F9(\()1502 2549 y Ga(y)5 b F4(:)rGa(B)1653 2537 y F9(\))1680 2549 y Ga(Q)26 b F6(2)e FB(J)pF4(\()p Ga(B)5 b F4(\))p FB(K)938 b Gg(by)23 b(assumption)5492670 y(\(3\))48 b Ga(P)38 b F6(2)25 b Ga(S)5 b(N)10182684 y Gc(aux)1163 2670 y Gg(and)24 b Ga(Q)h F6(2)g Ga(S)5b(N)1634 2684 y Gc(aux)2905 2670 y Gg(by)24 b(Lemma)e(2.3.13)5492791 y(\(4\))48 b FL(Cut)p F4(\()875 2779 y FX(h)9032791 y Ga(b)942 2779 y FX(i)969 2791 y Ga(P)13 b(;)10802779 y F9(\()1108 2791 y Ga(y)1156 2779 y F9(\))11832791 y Ga(Q)p F4(\))26 b F6(2)e Ga(S)5 b(N)1535 2805y Gc(aux)2905 2791 y Gg(by)24 b(Lemma)e(2.3.14)549 2912y(\(5\))48 b FL(Ax)o F4(\()p Ga(x;)15 b(a)p F4(\))32b(^)-50 b Ga(\033)s(;)10 b F6(f)-7 b Ga(x)26 b F4(:=)13682900 y FX(h)1396 2912 y Ga(b)1435 2900 y FX(i)1462 2912y Ga(P)t F6(g)p Ga(;)10 b F6(f)-7 b Ga(a)27 b F4(:=)18382900 y F9(\()1865 2912 y Ga(y)1913 2900 y F9(\))19412912 y Ga(Q)-10 b F6(g)26 b(2)f Ga(S)5 b(N)2294 2926y Gc(aux)3044 2912 y Gg(by)24 b(\(1\))f(and)h(\(4\))pBlack 321 3148 a Gb(Case)g FL(And)685 3162 y Gc(R)7433148 y F4(\()778 3136 y FX(h)806 3148 y Ga(a)854 3136y FX(i)881 3148 y Ga(M)11 b(;)1020 3136 y FX(h)1047 3148y Ga(b)1086 3136 y FX(i)1114 3148 y Ga(N)f(;)15 b(c)pF4(\))p Gb(:)p Black 47 w Gg(W)-7 b(e)24 b(ha)n(v)o(e)i(to)f(pro)o(v)o(e)h(that)g FL(And)2363 3162 y Gc(R)2421 3148 y F4(\()24563136 y FX(h)2484 3148 y Ga(a)2532 3136 y FX(i)2559 3148y Ga(M)10 b(;)2697 3136 y FX(h)2725 3148 y Ga(b)27643136 y FX(i)2792 3148 y Ga(N)f(;)15 b(c)p F4(\))35 b(^)-50b Ga(\033)s(;)10 b F6(f)-7 b Ga(c)30 b F4(:=)3339 3136y F9(\()3367 3148 y Ga(z)3413 3136 y F9(\))3441 3148y Ga(R)-9 b F6(g)549 3261 y Gg(is)23 b(strongly)j(normalising)g(for)d(an)h(arbitrary)i(named)e(term)2437 3249 y F9(\()24653261 y Ga(z)6 b F4(:)r Ga(B)f F6(^)o Ga(C)2746 3249 yF9(\))2773 3261 y Ga(R)26 b F6(2)f FB(J)p F4(\()p Ga(B)5b F6(^)o Ga(C)i F4(\))p FB(K)p Gg(.)549 3414 y(\(1\))48b FL(And)856 3428 y Gc(R)914 3414 y F4(\()949 3402 yFX(h)977 3414 y Ga(a)1025 3402 y FX(i)1052 3414 y Ga(M)10b(;)1190 3402 y FX(h)1218 3414 y Ga(b)1257 3402 y FX(i)12853414 y Ga(N)g(;)15 b(c)p F4(\))21 b(^)-51 b Ga(\033)t(;)10b F6(f)-7 b Ga(c)10 b F4(:=)1781 3402 y F9(\()1810 3414y Ga(z)1856 3402 y F9(\))1884 3414 y Ga(R)-9 b F6(g)26b F4(=)702 3535 y FL(Cut)p F4(\()875 3523 y FX(h)9033535 y Ga(c)942 3523 y FX(i)969 3535 y FL(And)1124 3549y Gc(R)1182 3535 y F4(\()1217 3523 y FX(h)1244 3535 yGa(a)1292 3523 y FX(i)1345 3535 y Ga(M)15 b F4(^)-50b Ga(\033)s(;)10 b F6(f)-7 b Ga(c)27 b F4(:=)1758 3523y F9(\()1786 3535 y Ga(z)1832 3523 y F9(\))1859 3535y Ga(R)-8 b F6(g)p Ga(;)2005 3523 y FX(h)2033 3535 yGa(b)2072 3523 y FX(i)2125 3535 y Ga(N)15 b F4(^)-50b Ga(\033)s(;)10 b F6(f)-7 b Ga(c)27 b F4(:=)2523 3523y F9(\()2550 3535 y Ga(z)2596 3523 y F9(\))2624 3535y Ga(R)-9 b F6(g)q Ga(;)15 b(c)p F4(\))q Ga(;)2885 3523y F9(\()2913 3535 y Ga(z)2959 3523 y F9(\))2986 3535y Ga(R)q F4(\))35 b Gg(Def.)23 b(of)8 b F6(f)p 3438 3535V 3456 3535 V 3474 3535 V 65 w(g)549 3656 y Gg(\(2\))48b Ga(M)40 b F4(^)-50 b Ga(\033)s(;)10 b F6(f)-7 b Ga(c)27b F4(:=)1140 3644 y F9(\()1168 3656 y Ga(z)1214 3644y F9(\))1241 3656 y Ga(R)-8 b F6(g)p Ga(;)10 b F6(f)-7b Ga(a)26 b F4(:=)1616 3644 y F9(\()1643 3656 y Ga(y)16913644 y F9(\))1718 3656 y Ga(P)t F6(g)g(2)f Ga(S)5 b(N)20713670 y Gc(aux)2216 3656 y Gg(for)23 b(arbitrary)26803644 y F9(\()2707 3656 y Ga(y)5 b F4(:)r Ga(B)2858 3644y F9(\))2886 3656 y Ga(P)38 b F6(2)25 b FB(J)p F4(\()pGa(B)5 b F4(\))o FB(K)p Gg(,)702 3777 y Ga(N)40 b F4(^)-50b Ga(\033)s(;)10 b F6(f)-7 b Ga(c)27 b F4(:=)1125 3765y F9(\()1153 3777 y Ga(z)1199 3765 y F9(\))1226 3777y Ga(R)-8 b F6(g)p Ga(;)10 b F6(f)-7 b Ga(b)26 b F4(:=)15923765 y F9(\()1619 3777 y Ga(x)1671 3765 y F9(\))16983777 y Ga(Q)-9 b F6(g)25 b(2)g Ga(S)5 b(N)2051 3791 yGc(aux)2196 3777 y Gg(for)24 b(arbitrary)2661 3765 yF9(\()2688 3777 y Ga(x)r F4(:)r Ga(C)2841 3765 y F9(\))28683777 y Ga(Q)i F6(2)e FB(J)p F4(\()p Ga(C)7 b F4(\))pFB(K)3089 3898 y Gg(by)24 b(induction)549 4018 y(\(3\))48b F4(\()p Ga(M)15 b F4(^)-50 b Ga(\033)s(;)10 b F6(f)-7b Ga(c)27 b F4(:=)1150 4006 y F9(\()1178 4018 y Ga(z)12244006 y F9(\))1252 4018 y Ga(R)-9 b F6(g)p F4(\))k F6(f)eGa(a)27 b F4(:=)1621 4006 y F9(\()1648 4018 y Ga(y)16964006 y F9(\))1723 4018 y Ga(P)t F6(g)f(2)f Ga(S)5 b(N)20764032 y Gc(aux)2198 4018 y Gg(,)702 4139 y F4(\()p Ga(N)15b F4(^)-50 b Ga(\033)s(;)10 b F6(f)-7 b Ga(c)27 b F4(:=)11354127 y F9(\()1163 4139 y Ga(z)1209 4127 y F9(\))12364139 y Ga(R)-8 b F6(g)p F4(\))j F6(f)e Ga(b)26 b F4(:=)15974127 y F9(\()1624 4139 y Ga(x)1676 4127 y F9(\))17034139 y Ga(Q)-9 b F6(g)26 b(2)e Ga(S)5 b(N)2056 4153 yGc(aux)3044 4139 y Gg(by)24 b(\(2\))f(and)h(sss)549 4260y(\(4\))702 4248 y FX(h)729 4260 y Ga(a)r F4(:)r Ga(B)8804248 y FX(i)908 4260 y F4(\()p Ga(M)15 b F4(^)-50 b Ga(\033)s(;)10b F6(f)-7 b Ga(c)27 b F4(:=)1356 4248 y F9(\()1384 4260y Ga(z)1430 4248 y F9(\))1457 4260 y Ga(R)-8 b F6(g)pF4(\))26 b F6(2)e FB(J)p F6(h)p Ga(B)5 b F6(i)p FB(K)pGg(,)702 4369 y FX(h)729 4381 y Ga(b)r F4(:)r Ga(C)8694369 y FX(i)897 4381 y F4(\()p Ga(N)15 b F4(^)-50 b Ga(\033)s(;)10b F6(f)-7 b Ga(c)27 b F4(:=)1330 4369 y F9(\()1357 4381y Ga(z)1403 4369 y F9(\))1431 4381 y Ga(R)-9 b F6(g)pF4(\))26 b F6(2)f FB(J)p F6(h)p Ga(C)7 b F6(i)p FB(K)960b Gg(by)24 b(De\002nition)h(2.3.3)549 4502 y(\(5\))48b FL(And)856 4516 y Gc(R)914 4502 y F4(\()949 4490 yFX(h)977 4502 y Ga(a)1025 4490 y FX(i)1052 4502 y Ga(M)15b F4(^)-50 b Ga(\033)t(;)10 b F6(f)-7 b Ga(c)26 b F4(:=)14664490 y F9(\()1493 4502 y Ga(z)1539 4490 y F9(\))15674502 y Ga(R)-9 b F6(g)p Ga(;)1712 4490 y FX(h)1740 4502y Ga(b)1779 4490 y FX(i)1807 4502 y Ga(N)15 b F4(^)-50b Ga(\033)s(;)10 b F6(f)-7 b Ga(c)27 b F4(:=)2205 4490y F9(\()2232 4502 y Ga(z)2278 4490 y F9(\))2306 4502y Ga(R)-9 b F6(g)q Ga(;)15 b(c)p F4(\))23 b Gg(freshly)j(introduces)gGa(c)62 b Gg(by)23 b(\(1\))549 4622 y(\(6\))702 4610y FX(h)729 4622 y Ga(c)r F4(:)r Ga(B)5 b F6(^)p Ga(C)10044610 y FX(i)1031 4622 y FL(And)1186 4636 y Gc(R)12434622 y F4(\()1278 4610 y FX(h)1306 4622 y Ga(a)1354 4610y FX(i)1382 4622 y Ga(M)15 b F4(^)-50 b Ga(\033)s(;)10b F6(f)-7 b Ga(c)26 b F4(:=)1795 4610 y F9(\()1822 4622y Ga(z)1868 4610 y F9(\))1896 4622 y Ga(R)-9 b F6(g)qGa(;)2042 4610 y FX(h)2069 4622 y Ga(b)2108 4610 y FX(i)21364622 y Ga(N)15 b F4(^)-50 b Ga(\033)s(;)10 b F6(f)-7b Ga(c)27 b F4(:=)2534 4610 y F9(\()2561 4622 y Ga(z)26074610 y F9(\))2635 4622 y Ga(R)-9 b F6(g)q Ga(;)15 b(c)pF4(\))26 b F6(2)f FB(J)p F6(h)p Ga(B)5 b F6(^)o Ga(C)iF6(i)p FB(K)2425 4743 y Gg(by)24 b(\(4\),)f(\(5\))h(and)g(De\002nition)h(2.3.3)549 4864 y(\(7\))48 b FL(And)856 4878 y Gc(R)9144864 y F4(\()949 4852 y FX(h)977 4864 y Ga(a)1025 4852y FX(i)1052 4864 y Ga(M)15 b F4(^)-50 b Ga(\033)t(;)10b F6(f)-7 b Ga(c)26 b F4(:=)1466 4852 y F9(\()1493 4864y Ga(z)1539 4852 y F9(\))1567 4864 y Ga(R)-9 b F6(g)pGa(;)1712 4852 y FX(h)1740 4864 y Ga(b)1779 4852 y FX(i)18074864 y Ga(N)15 b F4(^)-50 b Ga(\033)s(;)10 b F6(f)-7b Ga(c)27 b F4(:=)2205 4852 y F9(\()2232 4864 y Ga(z)22784852 y F9(\))2306 4864 y Ga(R)-9 b F6(g)q Ga(;)15 b(c)pF4(\))26 b F6(2)f Ga(S)5 b(N)2772 4878 y Gc(aux)28944864 y Gg(,)702 4985 y Ga(R)26 b F6(2)f Ga(S)5 b(N)10174999 y Gc(aux)2905 4985 y Gg(by)24 b(Lemma)e(2.3.13)5495106 y(\(8\))48 b FL(Cut)p F4(\()875 5094 y FX(h)9035106 y Ga(c)942 5094 y FX(i)969 5106 y FL(And)1124 5120y Gc(R)1182 5106 y F4(\()1217 5094 y FX(h)1244 5106 yGa(a)1292 5094 y FX(i)1320 5106 y Ga(M)15 b F4(^)-50b Ga(\033)s(;)10 b F6(f)-7 b Ga(c)27 b F4(:=)1733 5094y F9(\()1760 5106 y Ga(z)1806 5094 y F9(\))1834 5106y Ga(R)-9 b F6(g)q Ga(;)1980 5094 y FX(h)2008 5106 yGa(b)2047 5094 y FX(i)2074 5106 y Ga(N)15 b F4(^)-50b Ga(\033)s(;)10 b F6(f)-7 b Ga(c)27 b F4(:=)2472 5094y F9(\()2500 5106 y Ga(z)2546 5094 y F9(\))2573 5106y Ga(R)-8 b F6(g)p Ga(;)15 b(c)p F4(\))q Ga(;)2834 5094y F9(\()2862 5106 y Ga(z)2908 5094 y F9(\))2936 5106y Ga(R)q F4(\))25 b F6(2)g Ga(S)5 b(N)3286 5120 y Gc(aux)29055226 y Gg(by)24 b(Lemma)e(2.3.14)549 5347 y(\(9\))48b FL(And)856 5361 y Gc(R)914 5347 y F4(\()949 5335 yFX(h)977 5347 y Ga(a)1025 5335 y FX(i)1052 5347 y Ga(M)10b(;)1190 5335 y FX(h)1218 5347 y Ga(b)1257 5335 y FX(i)12855347 y Ga(N)g(;)15 b(c)p F4(\))31 b(^)-50 b Ga(\033)s(;)10b F6(f)-7 b Ga(c)27 b F4(:=)1823 5335 y F9(\()1851 5347y Ga(z)1897 5335 y F9(\))1924 5347 y Ga(R)-8 b F6(g)25b(2)g Ga(S)5 b(N)2275 5361 y Gc(aux)3044 5347 y Gg(by)24b(\(1\))f(and)h(\(8\))p Black Black eop end%%Page: 149 161TeXDict begin 149 160 bop Black 277 51 a Gb(B.1)23 b(Pr)n(oofs)h(of)g(Chapter)f(2)2639 b(149)p 277 88 3691 4 v Black Black277 388 a(Case)24 b FL(And)641 351 y Gc(i)641 411 y(L)693388 y F4(\()728 376 y F9(\()756 388 y Ga(x)808 376 yF9(\))836 388 y Ga(M)10 b(;)15 b(y)s F4(\))23 b(\()pGa(i)j F4(=)f(1)p Ga(;)15 b F4(2\))p Gb(:)p Black 47w Gg(W)-7 b(e)28 b(ha)n(v)o(e)h(to)f(pro)o(v)o(e)h(that)gFL(And)2502 351 y Gc(i)2502 411 y(L)2554 388 y F4(\()2589376 y F9(\()2616 388 y Ga(x)2668 376 y F9(\))2696 388y Ga(M)10 b(;)15 b(y)s F4(\))40 b(^)-50 b Ga(\033)s(;)10b F6(f)-7 b Ga(y)38 b F4(:=)3293 376 y FX(h)3321 388y Ga(a)3369 376 y FX(i)3396 388 y Ga(R)-8 b F6(g)504501 y Gg(is)21 b(strongly)h(normalising)h(for)e(an)f(arbitrary)i(co-named)g(term)2484 489 y FX(h)2511 501 y Ga(a)r F4(:)rGa(C)2653 515 y F9(1)2693 501 y F6(^)o Ga(C)2818 515y F9(2)2858 489 y FX(i)2885 501 y Ga(R)k F6(2)f FB(J)pF6(h)p Ga(C)3203 515 y F9(1)3242 501 y F6(^)p 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FB(J)p F4(\()p Ga(C)18361334 y Gc(i)1864 1320 y F4(\))q FB(K)878 b Gg(by)24 b(De\002nition)g(2.3.3)504 1437 y(\(5\))49 b FL(And)812 1400 y Gc(i)8121460 y(L)864 1437 y F4(\()899 1425 y F9(\()927 1437 yGa(x)979 1425 y F9(\))1007 1437 y Ga(M)30 b F4(^)-50b Ga(\033)s(;)10 b F6(f)-7 b Ga(y)13 b F4(:=)1412 1425y FX(h)1440 1437 y Ga(a)1488 1425 y FX(i)1516 1437 yGa(R)-9 b F6(g)q Ga(;)15 b(y)s F4(\))23 b Gg(freshly)i(introduces)iGa(y)793 b Gg(by)23 b(\(1\))504 1555 y(\(6\))658 1543y F9(\()685 1555 y Ga(y)5 b F4(:)r Ga(C)827 1569 y F9(1)8671555 y F6(^)o Ga(C)992 1569 y F9(2)1032 1543 y(\))10591555 y FL(And)1214 1518 y Gc(i)1214 1578 y(L)1266 1555y F4(\()1301 1543 y F9(\()1329 1555 y Ga(x)1381 1543y F9(\))1408 1555 y Ga(M)30 b F4(^)-50 b Ga(\033)s(;)10b F6(f)-7 b Ga(y)13 b F4(:=)1813 1543 y FX(h)1842 1555y Ga(a)1890 1543 y FX(i)1917 1555 y Ga(R)-8 b F6(g)pGa(;)15 b(y)s F4(\))26 b F6(2)f FB(J)p F4(\()p Ga(C)23951569 y F9(1)2434 1555 y F6(^)p Ga(C)2560 1569 y F9(2)25991555 y F4(\))q FB(K)2591 1672 y Gg(by)e(\(4\),)h(\(5\))g(and)g(Def.)e(2.3.3)504 1790 y(\(7\))49 b FL(And)812 1753 y Gc(i)8121813 y(L)864 1790 y F4(\()899 1778 y F9(\()927 1790 yGa(x)979 1778 y F9(\))1007 1790 y Ga(M)30 b F4(^)-50b Ga(\033)s(;)10 b F6(f)-7 b Ga(y)13 b F4(:=)1412 1778y FX(h)1440 1790 y Ga(a)1488 1778 y FX(i)1516 1790 yGa(R)-9 b F6(g)q Ga(;)15 b(y)s F4(\))p Ga(;)41 b(R)26b F6(2)f Ga(S)5 b(N)2126 1804 y Gc(aux)2861 1790 y Gg(by)23b(Lemma)g(2.3.13)504 1907 y(\(8\))49 b FL(Cut)p F4(\()8311895 y FX(h)858 1907 y Ga(a)906 1895 y FX(i)934 1907y Ga(R)q(;)1044 1895 y F9(\()1071 1907 y Ga(y)1119 1895y F9(\))1147 1907 y FL(And)1301 1870 y Gc(i)1301 1930y(L)1353 1907 y F4(\()1388 1895 y F9(\()1416 1907 y Ga(x)14681895 y F9(\))1496 1907 y Ga(M)30 b F4(^)-50 b Ga(\033)s(;)10b F6(f)-7 b Ga(y)13 b F4(:=)1901 1895 y FX(h)1930 1907y Ga(a)1978 1895 y FX(i)2005 1907 y Ga(R)-9 b F6(g)qGa(;)15 b(y)s F4(\)\))26 b F6(2)f Ga(S)5 b(N)2515 1921y Gc(aux)2861 1907 y Gg(by)23 b(Lemma)g(2.3.14)504 2024y(\(9\))49 b FL(And)812 1988 y Gc(i)812 2047 y(L)8642024 y F4(\()899 2012 y F9(\()927 2024 y Ga(x)979 2012y F9(\))1007 2024 y Ga(M)10 b(;)15 b(y)s F4(\))20 b(^)-50b Ga(\033)t(;)10 b F6(f)-7 b Ga(y)13 b F4(:=)1536 2012y FX(h)1564 2024 y Ga(a)1612 2012 y FX(i)1640 2024 yGa(R)-9 b F6(g)26 b(2)e Ga(S)5 b(N)1990 2038 y Gc(aux)30002024 y Gg(by)23 b(\(1\))h(and)g(\(8\))p Black 277 2420a Gb(Case)g FL(Imp)631 2442 y Gc(R)689 2420 y F4(\()7242408 y F9(\()752 2420 y Ga(x)804 2408 y F9(\))p FX(h)8582420 y Ga(a)906 2408 y FX(i)934 2420 y Ga(M)10 b(;)15b(b)p F4(\))p Gb(:)p Black 47 w Gg(W)-7 b(e)36 b(pro)o(v)o(e)h(that)gFL(Imp)1935 2442 y Gc(R)1992 2420 y F4(\()2027 2408 yF9(\()2055 2420 y Ga(x)2107 2408 y F9(\))q FX(h)21622420 y Ga(a)2210 2408 y FX(i)2238 2420 y Ga(M)10 b(;)15b(b)p F4(\))55 b(^)-50 b Ga(\033)t(;)10 b F6(f)-7 b Ga(b)51b F4(:=)2865 2408 y F9(\()2892 2420 y Ga(z)2938 2408y F9(\))2966 2420 y Ga(R)-9 b F6(g)36 b Gg(is)h(strongly)5042533 y(normalising)26 b(for)e(an)g(arbitrary)h(named)g(term)19892521 y F9(\()2016 2533 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b(De\002nition)g(of)g F6(f)p 3394 2884 V 34122884 V 3429 2884 V 65 w(g)504 3002 y Gg(\(2\))49 b Ga(M)40b F4(^)-50 b Ga(\033)s(;)10 b F6(f)-7 b Ga(b)27 b F4(:=)10962990 y F9(\()1123 3002 y Ga(z)1169 2990 y F9(\))11973002 y Ga(R)-9 b F6(g)p Ga(;)10 b F6(f)-7 b Ga(a)27 bF4(:=)1571 2990 y F9(\()1599 3002 y Ga(y)1647 2990 yF9(\))1674 3002 y Ga(P)s F6(g)p Ga(;)10 b F6(f)-7 b Ga(x)27b F4(:=)2053 2990 y FX(h)2081 3002 y Ga(c)2120 2990 yFX(i)2148 3002 y Ga(Q)-10 b F6(g)26 b(2)f Ga(S)5 b(N)25013016 y Gc(aux)658 3121 y Gg(for)23 b(arbitrary)1122 3109y F9(\()1150 3121 y Ga(y)5 b F4(:)r Ga(B)1301 3109 yF9(\))1328 3121 y Ga(P)38 b F6(2)25 b FB(J)p F4(\()pGa(B)5 b F4(\))p FB(K)22 b Gg(and)1904 3109 y FX(h)19313121 y Ga(c)r F4(:)r Ga(C)2071 3109 y FX(i)2099 3121y Ga(Q)j F6(2)g FB(J)p F6(h)p Ga(C)7 b F6(i)p FB(K)547b Gg(by)24 b(induction)504 3239 y(\(3\))49 b F4(\()pGa(M)15 b F4(^)-50 b Ga(\033)s(;)10 b F6(f)-7 b Ga(b)27b F4(:=)1106 3227 y F9(\()1133 3239 y Ga(z)1179 3227y F9(\))1207 3239 y Ga(R)-9 b 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F9(\))2364 4859 y Ga(N)10 b F4(])p Ga(;)25124847 y F9(\()2540 4859 y Ga(x)2592 4847 y F9(\))26204859 y Ga(N)g F4(\))694 5022 y Ga(M)g F4([)p Ga(a)25b F4(:=)1011 5010 y F9(\()1039 5022 y Ga(x)1091 5010y F9(\))1118 5022 y Ga(N)10 b F4(])189 b F6(\021)f FL(Cut)pF4(\()1847 5010 y FX(h)1875 5022 y Ga(b)1914 5010 y FX(i)19415022 y Ga(P)13 b(;)2052 5010 y F9(\()2080 5022 y Ga(y)21285010 y F9(\))2155 5022 y FL(Ax)p F4(\()p Ga(y)s(;)i(a)pF4(\))q(\)[)p Ga(a)26 b F4(:=)2720 5010 y F9(\()27485022 y Ga(x)2800 5010 y F9(\))2827 5022 y Ga(N)10 b F4(])14155159 y(=)188 b FL(Cut)p F4(\()1847 5147 y FX(h)1875 5159y Ga(b)1914 5147 y FX(i)1967 5159 y Ga(P)13 b F4([)pGa(a)25 b F4(:=)2257 5147 y F9(\()2285 5159 y Ga(x)23375147 y F9(\))2364 5159 y Ga(N)10 b F4(])p Ga(;)2512 5147y F9(\()2540 5159 y Ga(y)2588 5147 y F9(\))2641 5159y FL(Ax)o F4(\()p Ga(y)s(;)15 b(a)p F4(\)[)p Ga(a)27b F4(:=)3170 5147 y F9(\()3198 5159 y Ga(x)3250 5147y F9(\))3277 5159 y Ga(N)10 b F4(]\))1415 5295 y(=)188b FL(Cut)p F4(\()1847 5283 y FX(h)1875 5295 y Ga(b)19145283 y FX(i)1967 5295 y Ga(P)13 b F4([)p Ga(a)25 b F4(:=)22575283 y F9(\()2285 5295 y Ga(x)2337 5283 y F9(\))23645295 y Ga(N)10 b F4(])p Ga(;)2512 5283 y F9(\()2540 5295y Ga(y)2588 5283 y F9(\))2641 5295 y Ga(N)g F4([)p Ga(x)gF6(7!)g Ga(y)s F4(]\))1408 5352 y FV(\()p FC(\003)p FV(\))14155436 y F6(\021)188 b FL(Cut)p F4(\()1847 5424 y FX(h)18755436 y Ga(b)1914 5424 y FX(i)1967 5436 y Ga(P)13 b F4([)pGa(a)25 b F4(:=)2257 5424 y F9(\()2285 5436 y Ga(x)23375424 y F9(\))2364 5436 y Ga(N)10 b F4(])p Ga(;)2512 5424y F9(\()2540 5436 y Ga(x)2592 5424 y F9(\))2620 5436y Ga(N)g F4(\))510 5528 y F9(\()p FX(\003)p F9(\))6745561 y Gg(because)25 b(by)f(the)g(Barendre)o(gt-style)j(naming)d(con)l(v)o(ention)j Ga(y)f Gg(cannot)f(be)e(free)h(in)32785549 y F9(\()3305 5561 y Ga(x)3357 5549 y F9(\))33855561 y Ga(N)10 b Gg(.)p 3480 5699 4 62 v 3484 5641 554 v 3484 5699 V 3538 5699 4 62 v Black Black eop end%%Page: 151 163TeXDict begin 151 162 bop Black 277 51 a Gb(B.1)23 b(Pr)n(oofs)h(of)g(Chapter)f(2)2639 b(151)p 277 88 3691 4 v Black Black277 388 a(Pr)n(oof)24 b(of)g(Lemma)e(2.3.21.)p Black35 w Gg(W)-7 b(e)22 b(shall)j(analyse)g(all)f(possible)h(cases)g(of)2627 351 y Gc(cut)2596 388 y F6(\000)-31 b(\000)g(!)pGg(-reductions.)p Black 277 589 a Gb(Inner)23 b(Reduction:)pBlack 46 w Gg(Gi)n(v)o(en)i(that)g Ga(M)1553 552 y Gc(cut)1522589 y F6(\000)-32 b(\000)h(!)28 b Ga(N)10 b Gg(,)25 b(there)h(is)f(a)f(proper)j(subterm)f(in)f Ga(M)10 b Gg(,)25 b(say)h Ga(S)5b Gg(,)24 b(which)504 702 y(reduces)g(to)e Ga(S)956 669y FX(0)979 702 y Gg(.)27 b(This)22 b(term)g Ga(S)1461669 y FX(0)1505 702 y Gg(is)g(a)f(subterm)i(of)f Ga(N)10b Gg(.)27 b(W)-7 b(e)21 b(kno)n(w)h(by)g(induction)i(that)fGa(S)3293 665 y Gc(aux)3273 702 y F6(\000)-31 b(\000)f(!)3443669 y F9(+)504 815 y Ga(S)565 782 y FX(0)611 815 y Gg(and)24b(by)g(conte)o(xt)h(closure)g(that)f Ga(M)1756 778 yGc(aux)1736 815 y F6(\000)-31 b(\000)f(!)1906 782 y F9(+)1990815 y Ga(N)10 b Gg(.)p Black 277 1002 a 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b(From)24 b(Lemma)g(2.3.20)i(we)504 1527 y(ha)n(v)o(e)g(that)g Ga(S)q F6(f)-7 b Ga(a)29b F4(:=)1155 1515 y F9(\()1182 1527 y Ga(x)1234 1515y F9(\))1262 1527 y Ga(T)s F6(g)1412 1490 y Gc(aux)13921527 y F6(\000)-31 b(\000)f(!)1562 1494 y FX(\003)16311527 y Ga(N)34 b Gg(and)26 b(therefore)i Ga(M)2394 1490y Gc(aux)2374 1527 y F6(\000)-32 b(\000)h(!)2544 1494y F9(+)2632 1527 y Ga(N)10 b Gg(.)33 b(The)25 b(symmetric)i(case)5041640 y(is)d(analogous.)p 3436 1640 4 62 v 3440 1582 554 v 3440 1640 V 3494 1640 4 62 v Black 277 1852 a Gb(Pr)n(oof)g(of)g(Lemma)e(2.6.4.)p Black 34 w Gg(The)h(follo)n(wing)i(measure)g(reduces)g(in)f(e)n(v)o(ery)2716 1815 y Gc(x)2651 1852 y F6(\000)-32b(\000)h(!)p Gg(-reduction.)p Black Black 749 2020 aFs([)p FL(Ax)p F4(\()p Ga(x;)15 b(a)p F4(\))p Fs(])11611969 y F5(def)1168 2020 y F4(=)39 b(1)498 2164 y Fs([)qFL(Not)673 2178 y Gc(R)731 2164 y F4(\()766 2152 y F9(\()7942164 y Ga(x)846 2152 y F9(\))873 2164 y Ga(M)10 b(;)15b(a)p F4(\))p Fs(])1161 2112 y F5(def)1168 2164 y F4(=)39b Fs([)q Ga(M)10 b Fs(])21 b F4(+)f(1)282 2307 y Fs([)pFL(And)469 2321 y Gc(R)526 2307 y F4(\()561 2295 y FX(h)5892307 y Ga(a)637 2295 y FX(i)665 2307 y Ga(M)10 b(;)8032295 y FX(h)831 2307 y Ga(b)870 2295 y FX(i)897 2307y Ga(N)g(;)15 b(c)p F4(\))p Fs(])1161 2255 y F5(def)11682307 y F4(=)39 b Fs([)q Ga(M)10 b Fs(])21 b F4(+)f Fs([)pGa(N)10 b Fs(])21 b F4(+)f(1)554 2450 y Fs([)q FL(Or)6862413 y Gc(i)686 2473 y(R)744 2450 y F4(\()779 2438 yFX(h)807 2450 y Ga(a)855 2438 y FX(i)882 2450 y Ga(M)10b(;)15 b(b)p F4(\))p Fs(])1161 2398 y F5(def)1168 2450y F4(=)39 b Fs([)q Ga(M)10 b Fs(])21 b F4(+)f(1)402 2593y Fs([)q FL(Imp)579 2615 y Gc(R)637 2593 y F4(\()6722581 y F9(\()700 2593 y Ga(x)752 2581 y F9(\))p FX(h)8072593 y Ga(a)855 2581 y FX(i)882 2593 y Ga(M)10 b(;)15b(b)p F4(\))p Fs(])1161 2542 y F5(def)1168 2593 y F4(=)39b Fs([)q Ga(M)10 b Fs(])21 b F4(+)f(1)421 2760 y Fs([)pFL(Cut)532 2713 y FC(!)593 2760 y F4(\()628 2748 y FX(h)6562760 y Ga(a)704 2748 y FX(i)731 2760 y Ga(M)11 b(;)8702748 y F9(\()897 2760 y Ga(x)949 2748 y F9(\))977 2760y Ga(N)f F4(\))p Fs(])1161 2708 y F5(def)1168 2760 yF4(=)39 b(\()p Fs([)q Ga(M)10 b Fs(])21 b F4(+)f(1\))hF6(\001)f F4(\(4)p Fs([)r Ga(N)10 b Fs(])20 b F4(+)g(1\))22312020 y Fs([)q FL(Cut)o F4(\()2436 2008 y FX(h)2464 2020y Ga(a)2512 2008 y FX(i)2540 2020 y Ga(M)10 b(;)26782008 y F9(\()2706 2020 y Ga(x)2758 2008 y F9(\))27852020 y Ga(N)g F4(\))p Fs(])2969 1969 y F5(def)2976 2020y F4(=)40 b Fs([)p Ga(M)10 b Fs(])21 b F4(+)f Fs([)pGa(N)10 b Fs(])21 b F4(+)f(1)2312 2164 y Fs([)p FL(Not)24872178 y Gc(L)2539 2164 y F4(\()2574 2152 y FX(h)2602 2164y Ga(a)2650 2152 y FX(i)2678 2164 y Ga(M)10 b(;)15 b(x)pF4(\))p Fs(])2969 2112 y F5(def)2976 2164 y F4(=)40 bFs([)p Ga(M)10 b Fs(])21 b F4(+)f(1)2300 2307 y Fs([)qFL(And)2487 2270 y Gc(i)2487 2330 y(L)2540 2307 y F4(\()25752295 y F9(\()2602 2307 y Ga(x)2654 2295 y F9(\))26822307 y Ga(M)10 b(;)15 b(y)s F4(\))p Fs(])2969 2255 yF5(def)2976 2307 y F4(=)40 b Fs([)p Ga(M)10 b Fs(])21b 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F4(\()p Fs([)q Ga(N)10 b Fs(])21 b F4(+)f(1\))p3436 2912 V 3440 2854 55 4 v 3440 2912 V 3494 2912 462 v Black 277 3124 a Gb(Pr)n(oof)k(of)e(Lemma)g(2.6.10.)pBlack 34 w Gg(The)h(calculation)i(for)e(\(i\))g(is)g(as)f(follo)n(ws,)i(where)f F4(\()p F6(\003)p F4(\))g Gg(is)f(by)h(con\003uence)2773237 y(of)441 3200 y Gc(x)376 3237 y F6(\000)-32 b(\000)h(!)pGg(.)483 3465 y F6(j)p FL(Cut)587 3417 y FC( )648 3465y F4(\()683 3453 y FX(h)711 3465 y Ga(a)759 3453 y FX(i)7863465 y Ga(M)10 b(;)924 3453 y F9(\()952 3465 y Ga(x)10043453 y F9(\))1032 3465 y Ga(N)g F4(\))p F6(j)1175 3479y Gc(x)1244 3381 y FV(\()p FC(\003)p FV(\))1251 3465y F6(\021)31 b(j)p FL(Cut)1458 3417 y FC( )1518 3465y F4(\()1553 3453 y FX(h)1581 3465 y Ga(a)1629 3453 yFX(i)1672 3465 y F6(j)p Ga(M)10 b F6(j)1820 3479 y Gc(x)18643465 y Ga(;)1904 3453 y F9(\()1932 3465 y Ga(x)1984 3453y F9(\))2027 3465 y F6(j)p Ga(N)g F6(j)2160 3479 y Gc(x)22043465 y F4(\))p F6(j)2264 3479 y Gc(x)2334 3381 y FV(\(2)pFZ(:)p FV(6)p FZ(:)p FV(9\))2389 3465 y F6(\021)80 b(j)pGa(M)10 b F6(j)2688 3479 y Gc(x)2728 3465 y F6(f)-7 bGa(a)26 b F4(:=)2961 3453 y F9(\()2988 3465 y Ga(x)30403453 y F9(\))3083 3465 y F6(j)p Ga(N)10 b F6(j)3216 3479y Gc(x)3251 3465 y F6(g)p 3436 3665 V 3440 3607 55 4v 3440 3665 V 3494 3665 4 62 v Black 277 3878 a Gb(Pr)n(oof)24b(of)g(Lemma)e(2.6.11.)p Black 35 w Gg(W)-7 b(e)22 b(shall)j(analyse)g(same)f(cases)g(of)2413 3841 y Gc(l)q(oc)2372 3878 yF6(\000)-32 b(\000)h(!)p Gg(-reductions.)p Black 2774079 a Gb(Inner)23 b(Reduction:)p Black 46 w Gg(W)-7b(e)22 b(gi)n(v)o(e)i(tw)o(o)f(cases.)504 4231 y Ga(M)36b F6(\021)25 b FL(And)878 4245 y Gc(R)936 4231 y F4(\()9714219 y FX(h)999 4231 y Ga(a)1047 4219 y FX(i)1074 4231y Ga(S)5 b(;)1175 4219 y FX(h)1203 4231 y Ga(x)1255 4219y FX(i)1283 4231 y Ga(T)12 b(;)j(b)p F4(\))24 b Gg(and)gGa(N)35 b F6(\021)25 b FL(And)1998 4245 y Gc(R)2056 4231y F4(\()2091 4219 y FX(h)2119 4231 y Ga(a)2167 4219 yFX(i)2194 4231 y Ga(S)2255 4198 y FX(0)2279 4231 y Ga(;)23194219 y FX(h)2347 4231 y 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4617 y Gc(R)2111 4603 y F4(\()2146 4591y FX(h)2173 4603 y Ga(a)2221 4591 y FX(i)2249 4603 yF6(j)p Ga(S)2335 4570 y FX(0)2358 4603 y F6(j)2383 4617y Gc(x)2428 4603 y Ga(;)2468 4591 y FX(h)2495 4603 yGa(x)2547 4591 y FX(i)2575 4603 y F6(j)p Ga(T)13 b F6(j)26914617 y Gc(x)2735 4603 y Ga(;)i(b)p F4(\))196 b Gg(by)24b(induction)504 4727 y(\(4\))101 b FL(And)865 4741 yGc(R)922 4727 y F4(\()957 4715 y FX(h)985 4727 y Ga(a)10334715 y FX(i)1061 4727 y F6(j)p Ga(S)1147 4694 y FX(0)11704727 y F6(j)1195 4741 y Gc(x)1239 4727 y Ga(;)1279 4715y FX(h)1307 4727 y Ga(x)1359 4715 y FX(i)1386 4727 yF6(j)p Ga(T)13 b F6(j)1502 4741 y Gc(x)1547 4727 y Ga(;)i(b)pF4(\))26 b F6(\021)f(j)p Ga(N)10 b F6(j)1916 4741 y Gc(x)29064727 y Gg(by)24 b(Lemma)e(2.6.7)504 4897 y Ga(M)36 bF6(\021)25 b FL(Cut)803 4849 y FC( )863 4897 y F4(\()8984885 y FX(h)926 4897 y Ga(a)974 4885 y FX(i)1002 4897y Ga(S)5 b(;)1103 4885 y F9(\()1131 4897 y Ga(x)11834885 y F9(\))1210 4897 y Ga(T)13 b F4(\))23 b Gg(and)hGa(N)35 b F6(\021)25 b FL(Cut)1771 4849 y FC( )1832 4897y F4(\()1867 4885 y FX(h)1894 4897 y Ga(a)1942 4885 yFX(i)1970 4897 y Ga(S)2031 4864 y FX(0)2054 4897 y Ga(;)20944885 y F9(\()2122 4897 y Ga(x)2174 4885 y F9(\))22014897 y Ga(T)13 b F4(\))504 5021 y Gg(\(1\))101 b Ga(S)8384984 y Gc(l)q(oc)796 5021 y F6(\000)-31 b(\000)g(!)25b Ga(S)1053 4988 y FX(0)2974 5021 y Gg(by)f(assumption)5045145 y(\(2\))101 b F6(j)p Ga(M)10 b F6(j)858 5159 y Gc(x)9285145 y F6(\021)25 b(j)p Ga(S)5 b F6(j)1135 5159 y Gc(x)11745145 y F6(f)-7 b Ga(a)26 b F4(:=)1407 5133 y F9(\()14355145 y Ga(x)1487 5133 y F9(\))1529 5145 y F6(j)p Ga(T)13b F6(j)1645 5159 y Gc(x)1680 5145 y F6(g)1136 b Gg(by)23b(Lemma)g(2.6.10)504 5269 y(\(3\))101 b F6(j)p Ga(S)5b F6(j)821 5283 y Gc(x)861 5269 y F6(f)-7 b Ga(a)25 bF4(:=)1094 5257 y F9(\()1121 5269 y Ga(x)1173 5257 yF9(\))1216 5269 y F6(j)p Ga(T)13 b F6(j)1332 5283 y Gc(x)13665269 y F6(g)1457 5232 y Gc(aux)1437 5269 y F6(\000)-31b(\000)f(!)1607 5236 y FX(\003)1672 5269 y F6(j)p Ga(S)17585236 y FX(0)1781 5269 y F6(j)1806 5283 y Gc(x)1846 5269y F6(f)-7 b Ga(a)25 b F4(:=)2079 5257 y F9(\()2106 5269y Ga(x)2158 5257 y F9(\))2201 5269 y F6(j)p Ga(T)13 bF6(j)2317 5283 y Gc(x)2351 5269 y F6(g)56 b Gg(by)23b(induction)k(and)d(Lem)e(2.3.11)504 5394 y(\(4\))101b F6(j)p Ga(S)796 5361 y FX(0)820 5394 y F6(j)845 5408y Gc(x)884 5394 y F6(f)-7 b Ga(a)26 b F4(:=)1117 5382y F9(\()1144 5394 y Ga(x)1196 5382 y F9(\))1239 5394y F6(j)p Ga(T)13 b F6(j)1355 5408 y Gc(x)1390 5394 yF6(g)25 b(\021)g(j)p Ga(N)10 b F6(j)1689 5408 y Gc(x)28615394 y Gg(by)23 b(Lemma)g(2.6.10)p Black Black eop end%%Page: 152 164TeXDict begin 152 163 bop Black -144 51 a Gb(152)2658b(Details)24 b(f)n(or)g(some)g(Pr)n(oofs)p -144 88 36914 v Black Black 321 388 a(Commuting)f(Reduction:)p Black45 w Gg(W)-7 b(e)23 b(gi)n(v)o(e)h(one)g(case.)549 562y Ga(M)35 b F6(\021)25 b FL(Cut)p F4(\()941 550 y FX(h)969562 y Ga(a)1017 550 y FX(i)1044 562 y Ga(S)5 b(;)1145550 y F9(\()1173 562 y Ga(x)1225 550 y F9(\))1252 562y Ga(T)13 b F4(\))23 b Gg(and)h Ga(N)35 b F6(\021)25b FL(Cut)1813 515 y FC( )1874 562 y F4(\()1909 550 yFX(h)1937 562 y Ga(a)1985 550 y FX(i)2012 562 y Ga(S)5b(;)2113 550 y F9(\()2141 562 y Ga(x)2193 550 y F9(\))2221562 y Ga(T)12 b F4(\))549 686 y Gg(\(1\))100 b F6(j)pGa(M)10 b F6(j)902 700 y Gc(x)972 686 y F6(\021)25 bFL(Cut)p F4(\()1241 674 y FX(h)1269 686 y Ga(a)1317 674y FX(i)1344 686 y F6(j)p Ga(S)5 b F6(j)1455 700 y Gc(x)1499686 y Ga(;)1539 674 y F9(\()1567 686 y Ga(x)1619 674y F9(\))1647 686 y F6(j)p Ga(T)13 b F6(j)1763 700 y Gc(x)1807686 y F4(\))1108 b Gg(by)24 b(Lemma)f(2.6.7)549 810 y(\(2\))100b FL(Cut)p F4(\()927 798 y FX(h)955 810 y Ga(a)1003 798y FX(i)1030 810 y F6(j)p Ga(S)5 b F6(j)1141 824 y Gc(x)1186810 y Ga(;)1226 798 y F9(\()1254 810 y Ga(x)1306 798y F9(\))1333 810 y F6(j)p Ga(T)13 b F6(j)1449 824 y Gc(x)1493810 y F4(\))1574 773 y Gc(aux)1554 810 y F6(\000)-31b(\000)f(!)1724 777 y F9(0)p Gc(=)p F9(1)1859 810 y F6(j)pGa(S)5 b F6(j)1970 824 y Gc(x)2010 810 y F6(f)-7 b Ga(a)26b F4(:=)2243 798 y F9(\()2270 810 y Ga(x)2322 798 y F9(\))2365810 y F6(j)p Ga(T)13 b F6(j)2481 824 y Gc(x)2515 810y F6(g)2219 935 y Gg(`0'-case:)31 b(if)24 b F6(j)p Ga(S)5b F6(j)2755 949 y Gc(x)2822 935 y Gg(freshly)25 b(introduces)hGa(a)549 1059 y Gg(\(3\))100 b F6(j)p Ga(S)5 b F6(j)8651073 y Gc(x)905 1059 y F6(f)-7 b Ga(a)26 b F4(:=)11381047 y F9(\()1165 1059 y Ga(x)1217 1047 y F9(\))12601059 y F6(j)p Ga(T)13 b F6(j)1376 1073 y Gc(x)1410 1059y F6(g)26 b(\021)f(j)p Ga(N)10 b F6(j)1710 1073 y Gc(x)29051059 y Gg(by)24 b(Lemma)e(2.6.10)p Black 321 1290 a Gb(Labelled)h(Cut)g(Reduction:)p Black 45 w Gg(T)m(ri)n(vial,)h(because)h(if)fGa(M)2161 1253 y Gc(x)2096 1290 y F6(\000)-32 b(\000)h(!)-5b Ga(N)10 b Gg(,)22 b(we)h(ha)n(v)o(e)h F6(j)p Ga(M)10b F6(j)2857 1304 y Gc(x)2927 1290 y F6(\021)25 b(j)pGa(N)10 b F6(j)3156 1304 y Gc(x)3200 1290 y Gg(.)p Black321 1521 a Gb(Logical)25 b(Reduction:)p Black 46 w Gg(Routine)f(calculation)j(using)e(Lemma)d(2.6.7.)p Black 321 1751a Gb(Garbage)i(Reduction:)p Black 46 w Gg(T)-7 b(ak)o(e)22b(for)h(e)o(xample)h Ga(M)35 b F6(\021)25 b FL(Cut)21071704 y FC( )2168 1751 y F4(\()2203 1739 y FX(h)2231 1751y Ga(a)2279 1739 y FX(i)2306 1751 y Ga(S)5 b(;)2407 1739y F9(\()2435 1751 y Ga(x)2487 1739 y F9(\))2514 1751y Ga(T)13 b F4(\))22 b Gg(with)h Ga(a)e Gg(not)i(free)h(in)eGa(S)5 b Gg(,)22 b(then)549 1864 y(by)h(Lemma)g(2.6.10)hF6(j)p Ga(M)10 b F6(j)1361 1878 y Gc(x)1430 1864 y F6(\021)25b(j)p Ga(N)10 b F6(j)1659 1878 y Gc(x)1704 1864 y Gg(.)p3480 1864 4 62 v 3484 1806 55 4 v 3484 1864 V 3538 18644 62 v Black 321 2077 a Gb(Pr)n(oof)33 b(of)f(Lemma)g(2.6.16.)pBlack 34 w Gg(W)-7 b(e)31 b(shall)i(analyse)h(in)f(detail)g(one)g(case)g(where)f(an)3068 2040 y Gc(x)3002 2077 y F6(\000)-31b(\000)g(!)p Gg(-reduction)321 2190 y(occurs)25 b(on)f(the)g(top-le)n(v)o(el.)30 b(Suppose)p Black Black 1051 2431 a Ga(M)20b F6(\021)10 b FL(Cut)1318 2383 y FC( )1379 2431 y F4(\()14142419 y FX(h)1442 2431 y Ga(a)1490 2419 y FX(i)1518 2431y FL(Not)1660 2445 y Gc(R)1718 2431 y F4(\()1753 2419y F9(\()1781 2431 y Ga(x)1833 2419 y F9(\))1860 2431y Ga(S)5 b(;)15 b(a)p F4(\))q Ga(;)2085 2419 y F9(\()21132431 y Ga(y)2161 2419 y F9(\))2188 2431 y Ga(T)e F4(\))48b Gg(and)1051 2567 y Ga(N)20 b F6(\021)10 b FL(Cut)oF4(\()1397 2555 y FX(h)1425 2567 y Ga(a)1473 2555 y FX(i)15012567 y FL(Not)1643 2581 y Gc(R)1701 2567 y F4(\()17362555 y F9(\()1764 2567 y Ga(x)1816 2555 y F9(\))18432567 y FL(Cut)1922 2520 y FC( )1983 2567 y F4(\()20182555 y FX(h)2046 2567 y Ga(a)2094 2555 y FX(i)2121 2567y Ga(S)5 b(;)2222 2555 y F9(\()2250 2567 y Ga(y)22982555 y F9(\))2325 2567 y Ga(T)13 b F4(\))p Ga(;)i(a)pF4(\))q Ga(;)2590 2555 y F9(\()2618 2567 y Ga(y)26662555 y F9(\))2693 2567 y Ga(T)e F4(\))p Gg(.)321 2806y(Hence)24 b(we)f(ha)n(v)o(e)h Ga(M)1085 2769 y Gc(x)10192806 y F6(\000)-31 b(\000)g(!)25 b Ga(N)10 b Gg(.)28b(The)23 b(subterms)i(of)e Ga(N)33 b Gg(are:)p BlackBlack 944 3064 a(\(1\))101 b(all)23 b(subterms)i(of)fGa(S)j Gg(and)d Ga(T)13 b Gg(,)944 3177 y(\(2\))101 bFL(Cut)1228 3130 y FC( )1289 3177 y F4(\()1324 3165 yFX(h)1352 3177 y Ga(a)1400 3165 y FX(i)1428 3177 y Ga(S)5b(;)1529 3165 y F9(\()1556 3177 y Ga(y)1604 3165 y F9(\))16323177 y Ga(T)12 b F4(\))p Gg(,)944 3290 y(\(3\))101 bFL(Not)1292 3304 y Gc(R)1350 3290 y F4(\()1385 3278 yF9(\()1413 3290 y Ga(x)1465 3278 y F9(\))1492 3290 yFL(Cut)1571 3243 y FC( )1632 3290 y F4(\()1667 3278 yFX(h)1695 3290 y Ga(a)1743 3278 y FX(i)1770 3290 y Ga(S)5b(;)1871 3278 y F9(\()1899 3290 y Ga(y)1947 3278 y F9(\))19743290 y Ga(T)13 b F4(\))p Ga(;)i(a)p F4(\))24 b Gg(and)9443403 y(\(4\))101 b Ga(N)35 b F6(\021)25 b FL(Cut)p F4(\()15273391 y FX(h)1554 3403 y Ga(a)1602 3391 y FX(i)1630 3403y FL(Not)1773 3417 y Gc(R)1830 3403 y F4(\()1865 3391y F9(\()1893 3403 y Ga(x)1945 3391 y F9(\))1972 3403y FL(Cut)2051 3355 y FC( )2112 3403 y F4(\()2147 3391y FX(h)2175 3403 y Ga(a)2223 3391 y FX(i)2250 3403 yGa(S)5 b(;)2351 3391 y F9(\()2379 3403 y Ga(y)2427 3391y F9(\))2455 3403 y Ga(T)12 b F4(\))q Ga(;)j(a)p F4(\))pGa(;)2719 3391 y F9(\()2747 3403 y Ga(y)2795 3391 y F9(\))28233403 y Ga(T)d F4(\))321 3677 y Gg(W)-7 b(e)33 b(ha)n(v)o(e)i(to)e(sho)n(w)h(that)g(their)h Ga(x)p Gg(-normal)g(form)e(is)h(an)g(element)h(in)eGa(S)5 b(N)2723 3691 y Gc(aux)2846 3677 y Gg(.)58 b(Case)34b(\(1\))g(follo)n(ws)321 3790 y(by)28 b(assumption:)40b(the)27 b Ga(x)p Gg(-normal)i(form)e(of)h(e)n(v)o(ery)g(subterm)g(of)gGa(M)37 b Gg(is)27 b(an)g(element)i(in)e Ga(S)5 b(N)32423804 y Gc(aux)3365 3790 y Gg(,)27 b(and)321 3903 y(therefore)j(the)eGa(x)p Gg(-normal)g(form)g(of)f(e)n(v)o(ery)h(subterm)g(of)gGa(S)j Gg(and)d Ga(T)40 b Gg(must)27 b(be)h(in)f Ga(S)5b(N)3018 3917 y Gc(aux)3140 3903 y Gg(,)28 b(too.)41b(Case)321 4016 y(\(4\))20 b(follo)n(ws)h(by)f(Lemma)f(2.6.11,)i(which)f(says)h(that)f F6(j)p Ga(M)10 b F6(j)2133 4030 y Gc(x)22233978 y(aux)2203 4016 y F6(\000)-31 b(\000)f(!)2373 3983y FX(\003)2438 4016 y F6(j)p Ga(N)10 b F6(j)2571 4030y Gc(x)2615 4016 y Gg(,)20 b(and)g(thus)h F6(j)p Ga(N)10b F6(j)3112 4030 y Gc(x)3181 4016 y F6(2)25 b Ga(S)5b(N)3401 4030 y Gc(aux)3524 4016 y Gg(.)321 4128 y(By)23b(Lemma)g(2.6.7)g(we)g(ha)n(v)o(e)h(the)g(identities)pBlack Black 1140 4370 a F6(j)p FL(Cut)p F4(\()1338 4358y FX(h)1366 4370 y Ga(a)1414 4358 y FX(i)1441 4370 yFL(Not)1584 4384 y Gc(R)1641 4370 y F4(\()1676 4358 yF9(\()1704 4370 y Ga(x)1756 4358 y F9(\))1784 4370 yFL(Cut)1862 4322 y FC( )1923 4370 y F4(\()1958 4358 yFX(h)1986 4370 y Ga(a)2034 4358 y FX(i)2062 4370 y Ga(S)5b(;)2163 4358 y F9(\()2190 4370 y Ga(y)2238 4358 y F9(\))22664370 y Ga(T)12 b F4(\))q Ga(;)j(a)p F4(\))q Ga(;)25314358 y F9(\()2558 4370 y Ga(y)2606 4358 y F9(\))26344370 y Ga(T)e F4(\))p F6(j)2760 4384 y Gc(x)969 4483y F6(\021)100 b FL(Cut)o F4(\()1312 4471 y FX(h)13404483 y Ga(a)1388 4471 y FX(i)1416 4483 y F6(j)p FL(Not)15844497 y Gc(R)1641 4483 y F4(\()1676 4471 y F9(\()17044483 y Ga(x)1756 4471 y F9(\))1784 4483 y FL(Cut)18624435 y FC( )1923 4483 y F4(\()1958 4471 y FX(h)1986 4483y Ga(a)2034 4471 y FX(i)2062 4483 y Ga(S)5 b(;)2163 4471y F9(\()2190 4483 y Ga(y)2238 4471 y F9(\))2266 4483y Ga(T)12 b F4(\))q Ga(;)j(a)p F4(\))p F6(j)2515 4497y Gc(x)2560 4483 y Ga(;)2600 4471 y F9(\()2628 4483 yGa(y)2676 4471 y F9(\))2703 4483 y F6(j)p Ga(T)e F6(j)28194497 y Gc(x)2863 4483 y F4(\))969 4595 y F6(\021)100b FL(Cut)o F4(\()1312 4583 y FX(h)1340 4595 y Ga(a)13884583 y FX(i)1416 4595 y FL(Not)1558 4609 y Gc(R)16164595 y F4(\()1651 4583 y F9(\()1679 4595 y Ga(x)17314583 y F9(\))1758 4595 y F6(j)p FL(Cut)1862 4548 y FC( )19234595 y F4(\()1958 4583 y FX(h)1986 4595 y Ga(a)2034 4583y FX(i)2062 4595 y Ga(S)5 b(;)2163 4583 y F9(\()21904595 y Ga(y)2238 4583 y F9(\))2266 4595 y Ga(T)12 b F4(\))pF6(j)2391 4609 y Gc(x)2436 4595 y Ga(;)j(a)p F4(\))qGa(;)2600 4583 y F9(\()2628 4595 y Ga(y)2676 4583 y F9(\))27034595 y F6(j)p Ga(T)e F6(j)2819 4609 y Gc(x)2863 4595y F4(\))321 4834 y Gg(and)24 b(therefore)i(the)e Ga(x)pGg(-normal)g(form)g(of)f(\(2\))h(and)g(\(3\))g(are)g(in)fGa(S)5 b(N)2393 4848 y Gc(aux)2515 4834 y Gg(;)23 b(so)h(we)e(are)i(done.)p 3480 4834 V 3484 4776 55 4 v 3484 4834 V 35384834 4 62 v Black 321 5046 a Gb(Pr)n(oof)34 b(of)f(Lemma)f(2.6.20.)pBlack 34 w Gg(F)o(or)g(e)n(v)o(ery)h(reduction)j(we)c(ha)n(v)o(e)h(to)g(do)g(check)h(whether)g(the)f(corre-)321 5159 y(sponding)27b(terms)e(are)g(ordered)h(decreasingly)i(according)g(to)c(de\002nition)i(of)f Ga(>)2843 5126 y Gc(r)r(po)2950 5159 y Gg(.)31b(Since)25 b(there)g(are)321 5272 y(man)o(y)19 b(cases,)i(we)e(shall)h(present)h(only)f(a)f(fe)n(w)f(representati)n(v)o(e)23b(of)c(them.)27 b(W)-7 b(e)19 b(write)g(rpo)h(as)f(shorthand)3215385 y(for)24 b(De\002nition)g(2.6.12.)p Black Blackeop end%%Page: 153 165TeXDict begin 153 164 bop Black 277 51 a Gb(B.1)23 b(Pr)n(oofs)h(of)g(Chapter)f(2)2639 b(153)p 277 88 3691 4 v Black Black277 388 a(Inner)23 b(Reduction:)p Black 46 w Gg(W)-7b(e)22 b(gi)n(v)o(e)i(one)g(case.)504 533 y Ga(M)36 bF6(\021)25 b FL(Cut)p F4(\()897 521 y FX(h)924 533 yGa(a)972 521 y FX(i)1000 533 y Ga(S)5 b(;)1101 521 yF9(\()1129 533 y Ga(x)1181 521 y F9(\))1208 533 y Ga(T)13b F4(\))1376 496 y Gc(l)q(oc)1334 533 y F6(\000)-31 b(\000)g(!)25b FL(Cut)p F4(\()1703 521 y FX(h)1731 533 y Ga(a)1779521 y FX(i)1806 533 y Ga(S)1867 500 y FX(0)1890 533 yGa(;)1930 521 y F9(\()1958 533 y Ga(x)2010 521 y F9(\))2038533 y Ga(T)12 b F4(\))26 b F6(\021)f Ga(N)504 646 y Gg(\(1\))101b Ga(S)838 608 y Gc(l)q(oc)796 646 y F6(\000)-31 b(\000)g(!)25b Ga(S)1053 613 y FX(0)1099 646 y Gg(and)f Ga(S)p 1253661 61 4 v 30 w(>)1410 613 y Gc(r)r(po)1543 646 y Ga(S)1604613 y FX(0)p 1543 661 85 4 v 2454 646 a Gg(by)g(assumption)i(and)e(induction)504 758 y(\(2\))101 b Ga(M)p 710 773 99 4v 35 w F4(=)25 b Ga(S)p 929 773 61 4 v 26 w F6(\001)1036772 y Gc(m)1123 758 y Ga(T)p 1123 773 66 4 v 60 w Gg(and)50b Ga(N)p 1416 773 83 4 v 35 w F4(=)25 b Ga(S)1681 725y FX(0)p 1620 773 85 4 v 1724 758 a F6(\001)1749 772y Gc(n)1817 758 y Ga(T)p 1817 773 66 4 v 900 w Gg(by)e(De\002nition)i(2.6.17)504 871 y(\(3\))101 b Ga(m)25 b F6(\025)g Ga(n)1809b Gg(by)24 b(Lemma)e(2.6.19\(i\))504 984 y(\(4\))101b Ga(S)p 710 999 61 4 v 25 w F6(\001)816 998 y Gc(m)903984 y Ga(T)p 903 999 66 4 v 38 w(>)1065 951 y Gc(r)r(po)1198984 y Ga(S)1259 951 y FX(0)p 1198 999 85 4 v 1330 984a Gg(and)49 b Ga(S)p 1509 999 61 4 v 25 w F6(\001)1615998 y Gc(m)1703 984 y Ga(T)p 1703 999 66 4 v 38 w(>)1865951 y Gc(r)r(po)1997 984 y Ga(T)p 1997 999 V 849 w Gg(by)23b(\(1\))h(and)g(rpo\(i\))504 1097 y(\(5\))101 b F6(f)-24b(j)p Ga(S)p 756 1112 61 4 v 6 w(;)15 b(T)p 858 111266 4 v 13 w F6(j)-24 b(g)27 b Ga(>)1068 1053 y Gc(r)r(po)10681127 y(mul)q(t)1247 1097 y F6(f)-24 b(j)p Ga(S)1354 1064y FX(0)p 1293 1112 85 4 v 1379 1097 a Ga(;)15 b(T)p 14191112 66 4 v 13 w F6(j)-24 b(g)1368 b Gg(by)23 b(\(1\))h(and)g(rpo\(i\))504 1210 y(\(6\))101 b Ga(M)p 710 1225 99 4 v 35 w(>)9041177 y Gc(r)r(po)1037 1210 y Ga(N)p 1037 1225 83 4 v1180 w Gg(if)23 b Ga(m)i F4(=)g Ga(n)p Gg(,)d(then)i(by)g(\(5\))g(and)g(rpo\(iii\))2315 1323 y(if)f Ga(m)i(>)g(n)p Gg(,)d(then)j(by)e(\(4\))h(and)g(rpo\(ii\))p Black 277 1503 a Gb(Labelled)f(Cut)f(Reduction:)pBlack 46 w Gg(W)-7 b(e)23 b(gi)n(v)o(e)g(\002)n(v)o(e)g(typical)i(cases.)504 1655 y Ga(M)36 b F6(\021)22 b FL(Cut)8001608 y FC( )861 1655 y F4(\()896 1643 y FX(h)924 1655y Ga(c)963 1643 y FX(i)990 1655 y FL(And)1145 1669 yGc(R)1203 1655 y F4(\()1238 1643 y FX(h)1266 1655 y Ga(a)13141643 y FX(i)1341 1655 y Ga(S)5 b(;)1442 1643 y FX(h)14701655 y Ga(b)1509 1643 y FX(i)1536 1655 y Ga(T)13 b(;)i(c)pF4(\))q Ga(;)1757 1643 y F9(\()1785 1655 y Ga(x)18371643 y F9(\))1864 1655 y Ga(U)10 b F4(\))782 1742 y Gc(x)7171779 y F6(\000)-31 b(\000)f(!)26 b FL(Cut)o F4(\()10851767 y FX(h)1113 1779 y Ga(c)1152 1767 y FX(i)1180 1779y FL(And)1335 1793 y Gc(R)1392 1779 y F4(\()1427 1767y FX(h)1455 1779 y Ga(a)1503 1767 y FX(i)1531 1779 yFL(Cut)1609 1732 y FC( )1670 1779 y F4(\()1705 1767 yFX(h)1733 1779 y Ga(c)1772 1767 y FX(i)1800 1779 y Ga(S)5b(;)1901 1767 y F9(\()1929 1779 y Ga(x)1981 1767 y F9(\))20081779 y Ga(U)10 b F4(\))p Ga(;)2155 1767 y FX(h)2183 1779y Ga(b)2222 1767 y FX(i)2250 1779 y FL(Cut)2329 1732y FC( )2389 1779 y F4(\()2424 1767 y FX(h)2452 1779 yGa(c)2491 1767 y FX(i)2519 1779 y Ga(T)j(;)2625 1767y F9(\()2653 1779 y Ga(x)2705 1767 y F9(\))2732 1779y Ga(U)d F4(\))p Ga(;)15 b(c)p F4(\))q Ga(;)2994 1767y F9(\()3022 1779 y Ga(x)3074 1767 y F9(\))3102 1779y Ga(U)10 b F4(\))25 b F6(\021)g Ga(N)504 1903 y Gg(\(1\))146b Ga(M)p 755 1918 99 4 v 36 w F4(=)25 b FB(L)p Ga(S)p1010 1918 61 4 v 5 w(;)15 b(T)p 1111 1918 66 4 v 13 wFB(M)g F6(h)p Ga(U)p 1262 1918 72 4 v 11 w F6(i)13701917 y Gc(m)1485 1903 y Gg(and)49 b Ga(N)p 1664 191883 4 v 36 w F4(=)24 b FB(L)p Ga(S)p 1903 1918 61 4 v6 w F6(h)p Ga(U)p 2000 1918 72 4 v 10 w F6(i)2107 1917y Gc(r)2145 1903 y Ga(;)15 b(T)p 2185 1918 66 4 v 14w F6(h)p Ga(U)p 2287 1918 72 4 v 10 w F6(i)2394 1917y Gc(s)2431 1903 y FB(M)21 b F6(\001)2512 1917 y Gc(t)25621903 y Ga(U)p 2562 1918 V 146 w Gg(by)i(De\002nition)i(2.6.17)5042027 y(\(2\))146 b Ga(m)26 b F6(\025)f Ga(t;)15 b(r)m(;)g(s)1551b Gg(by)23 b(Lemma)g(2.6.19\(i,ii\))504 2152 y(\(3\))p758 2152 28 4 v 775 2152 V 793 2152 V 211 w F6(h)p 8572152 V 875 2152 V 893 2152 V 65 w(i)955 2166 y Gc(m)10472152 y F6(\035)p 1165 2152 V 1183 2152 V 1201 2152 V110 w(\001)1273 2166 y Gc(t)p 1325 2152 V 1343 2152 V1360 2152 V 2487 2152 a Gg(by)h(\(2\))f(and)h(De\002nition)h(2.6.14)5042276 y(\(4\))146 b FB(L)p Ga(S)p 790 2291 61 4 v 6 w(;)15b(T)p 892 2291 66 4 v 13 w FB(M)p F6(h)p Ga(U)p 10282291 72 4 v 11 w F6(i)1136 2290 y Gc(m)1228 2276 y Ga(>)12992243 y Gc(r)r(po)1431 2276 y Ga(S)p 1431 2291 61 4 v53 w Gg(and)50 b FB(L)p Ga(S)p 1755 2291 V 5 w(;)15 b(T)p1856 2291 66 4 v 13 w FB(M)p F6(h)p Ga(U)p 1992 229172 4 v 11 w F6(i)2100 2290 y Gc(m)2192 2276 y Ga(>)22632243 y Gc(r)r(po)2396 2276 y Ga(U)p 2396 2291 V 724 wGg(by)23 b(rpo\(i\))504 2400 y(\(5\))146 b F6(f)-24 b(j)pFB(L)p Ga(S)p 836 2415 61 4 v 7 w(;)15 b(T)p 939 241566 4 v 13 w FB(M)p Ga(;)g(U)p 1080 2415 72 4 v 11 w F6(j)-24b(g)26 b Ga(>)1296 2356 y Gc(r)r(po)1296 2429 y(mul)q(t)14762400 y F6(f)-24 b(j)p Ga(S)p 1522 2415 61 4 v 6 w(;)15b(U)p 1624 2415 72 4 v 10 w F6(j)-24 b(g)1440 b Gg(by)23b(rpo\(i\))504 2524 y(\(6\))146 b FB(L)p Ga(S)p 790 253961 4 v 6 w(;)15 b(T)p 892 2539 66 4 v 13 w FB(M)p F6(h)pGa(U)p 1028 2539 72 4 v 11 w F6(i)1136 2538 y Gc(m)12282524 y Ga(>)1299 2491 y Gc(r)r(po)1431 2524 y Ga(S)p1431 2539 61 4 v 5 w F6(h)p Ga(U)p 1527 2539 72 4 v 11w F6(i)1635 2538 y Gc(r)2301 2524 y Gg(if)23 b Ga(m)iF4(=)g Ga(r)s Gg(,)d(then)i(by)g(\(5\))g(and)g(rpo\(iii\))23262648 y(if)f Ga(m)i(>)g(r)s Gg(,)d(then)j(by)e(\(4\))h(and)g(rpo\(ii\))504 2773 y(\(7\))146 b FB(L)p Ga(S)p 790 2788 61 4 v6 w(;)15 b(T)p 892 2788 66 4 v 13 w FB(M)p F6(h)p Ga(U)p1028 2788 72 4 v 11 w F6(i)1136 2787 y Gc(m)1228 2773y Ga(>)1299 2740 y Gc(r)r(po)1431 2773 y Ga(T)p 14312788 66 4 v 13 w F6(h)p Ga(U)p 1532 2788 72 4 v 10 wF6(i)1639 2787 y Gc(s)2775 2773 y Gg(analogous)26 b(to)e(\(4,5,6\))5042897 y(\(8\))146 b FB(L)p Ga(S)p 790 2912 61 4 v 6 w(;)15b(T)p 892 2912 66 4 v 13 w FB(M)p F6(h)p Ga(U)p 10282912 72 4 v 11 w F6(i)1136 2911 y Gc(m)1228 2897 y Ga(>)12992864 y Gc(r)r(po)1431 2897 y FB(L)p Ga(S)p 1466 291261 4 v 6 w F6(h)p Ga(U)p 1563 2912 72 4 v 10 w F6(i)16702911 y Gc(r)1708 2897 y Ga(;)g(T)p 1748 2912 66 4 v 14w F6(h)p Ga(U)p 1850 2912 72 4 v 10 w F6(i)1957 2911y Gc(s)1994 2897 y FB(M)776 b Gg(by)24 b(\(6,7\))g(and)g(rpo\(ii\))5043021 y(\(9\))146 b FB(L)p Ga(S)p 790 3036 61 4 v 6 w(;)15b(T)p 892 3036 66 4 v 13 w FB(M)p F6(h)p Ga(U)p 10283036 72 4 v 11 w F6(i)1136 3035 y Gc(m)1228 3021 y Ga(>)12992988 y Gc(r)r(po)1431 3021 y Ga(U)p 1431 3036 V 1689w Gg(by)23 b(rpo\(i\))504 3145 y(\(10\))101 b Ga(M)p755 3160 99 4 v 36 w(>)950 3112 y Gc(r)r(po)1082 3145y Ga(N)p 1082 3160 83 4 v 1582 w Gg(by)24 b(\(3,8,9\))g(and)g(rpo\(ii\))504 3386 y Ga(M)36 b F6(\021)25 b FL(Cut)8033339 y FC( )863 3386 y F4(\()898 3374 y FX(h)926 3386y Ga(d)973 3374 y FX(i)1001 3386 y FL(And)1156 3400 yGc(R)1213 3386 y F4(\()1248 3374 y FX(h)1276 3386 y Ga(a)13243374 y FX(i)1352 3386 y Ga(S)5 b(;)1453 3374 y FX(h)14803386 y Ga(b)1519 3374 y FX(i)1547 3386 y Ga(T)13 b(;)i(c)pF4(\))q Ga(;)1768 3374 y F9(\()1796 3386 y Ga(x)18483374 y F9(\))1875 3386 y Ga(U)10 b F4(\))782 3473 y Gc(x)7173510 y F6(\000)-31 b(\000)f(!)26 b FL(And)1067 3524 yGc(R)1125 3510 y F4(\()1160 3498 y FX(h)1188 3510 y Ga(a)12363498 y FX(i)1263 3510 y FL(Cut)1342 3463 y FC( )14033510 y F4(\()1438 3498 y FX(h)1466 3510 y Ga(d)1513 3498y FX(i)1540 3510 y Ga(S)5 b(;)1641 3498 y F9(\()16693510 y Ga(x)1721 3498 y F9(\))1749 3510 y Ga(U)10 b F4(\))pGa(;)1896 3498 y FX(h)1924 3510 y Ga(b)1963 3498 y FX(i)19903510 y FL(Cut)2069 3463 y FC( )2130 3510 y F4(\()21653498 y FX(h)2193 3510 y Ga(d)2240 3498 y FX(i)2267 3510y Ga(T)j(;)2373 3498 y F9(\()2401 3510 y Ga(x)2453 3498y F9(\))2480 3510 y Ga(U)d F4(\))q Ga(;)15 b(c)p F4(\))26b F6(\021)f Ga(N)504 3634 y Gg(\(1\))101 b Ga(M)p 7103649 99 4 v 35 w F4(=)25 b FB(L)p Ga(S)p 964 3649 614 v 6 w(;)15 b(T)p 1066 3649 66 4 v 13 w FB(M)g F6(h)pGa(U)p 1217 3649 72 4 v 11 w F6(i)1325 3648 y Gc(m)14403634 y Gg(and)49 b Ga(N)p 1619 3649 83 4 v 35 w F4(=)25b FB(L)p Ga(S)p 1858 3649 61 4 v 5 w F6(h)p Ga(U)p 19543649 72 4 v 11 w F6(i)2062 3648 y Gc(r)2100 3634 y Ga(;)15b(T)p 2140 3649 66 4 v 13 w F6(h)p Ga(U)p 2241 3649 724 v 10 w F6(i)2348 3648 y Gc(s)2386 3634 y FB(M)349 bGg(by)23 b(De\002nition)i(2.6.17)504 3759 y(\(2\))101b Ga(m)25 b F6(\025)g Ga(r)m(;)15 b(s)1670 b Gg(by)23b(Lemma)g(2.6.19\(i,ii\))504 3883 y(\(3\))101 b FB(L)pGa(S)p 745 3898 61 4 v 5 w(;)15 b(T)p 846 3898 66 4 v14 w FB(M)p F6(h)p Ga(U)p 983 3898 72 4 v 10 w F6(i)10903897 y Gc(m)1182 3883 y Ga(>)1253 3850 y Gc(r)r(po)13863883 y Ga(S)p 1386 3898 61 4 v 53 w Gg(and)49 b FB(L)pGa(S)p 1709 3898 V 5 w(;)15 b(T)p 1810 3898 66 4 v 14w FB(M)p F6(h)p Ga(U)p 1947 3898 72 4 v 10 w F6(i)20543897 y Gc(m)2147 3883 y Ga(>)2218 3850 y Gc(r)r(po)23503883 y Ga(U)p 2350 3898 V 770 w Gg(by)23 b(rpo\(i\))5044007 y(\(4\))101 b F6(f)-24 b(j)p FB(L)p Ga(S)p 791 402261 4 v 6 w(;)15 b(T)p 893 4022 66 4 v 14 w FB(M)p Ga(;)g(U)p1035 4022 72 4 v 10 w F6(j)-24 b(g)27 b Ga(>)1251 3963y Gc(r)r(po)1251 4036 y(mul)q(t)1430 4007 y F6(f)-24b(j)p Ga(S)p 1476 4022 61 4 v 6 w(;)15 b(U)p 1578 402272 4 v 11 w F6(j)-24 b(g)1485 b Gg(by)23 b(rpo\(i\))5044131 y(\(5\))101 b FB(L)p Ga(S)p 745 4146 61 4 v 5 w(;)15b(T)p 846 4146 66 4 v 14 w FB(M)p F6(h)p Ga(U)p 983 414672 4 v 10 w F6(i)1090 4145 y Gc(m)1182 4131 y Ga(>)12534098 y Gc(r)r(po)1386 4131 y Ga(S)p 1386 4146 61 4 v5 w F6(h)p Ga(U)p 1482 4146 72 4 v 10 w F6(i)1589 4145y Gc(r)2301 4131 y Gg(if)23 b Ga(m)i F4(=)g Ga(r)s Gg(,)d(then)i(by)g(\(4\))g(and)g(rpo\(iii\))2326 4255 y(if)f Ga(m)i(>)g(r)sGg(,)d(then)j(by)e(\(3\))h(and)g(rpo\(ii\))504 4380 y(\(6\))101b FB(L)p Ga(S)p 745 4395 61 4 v 5 w(;)15 b(T)p 846 439566 4 v 14 w FB(M)p F6(h)p Ga(U)p 983 4395 72 4 v 10 wF6(i)1090 4394 y Gc(m)1182 4380 y Ga(>)1253 4347 y Gc(r)r(po)13864380 y Ga(T)p 1386 4395 66 4 v 13 w F6(h)p Ga(U)p 14874395 72 4 v 10 w F6(i)1594 4394 y Gc(s)2775 4380 y Gg(analogous)26b(to)e(\(3,4,5\))504 4504 y(\(7\))101 b Ga(M)p 710 451999 4 v 35 w(>)904 4471 y Gc(r)r(po)1037 4504 y Ga(N)p1037 4519 83 4 v 1695 w Gg(by)24 b(\(5,6\))g(and)g(rpo\(ii\))5044745 y Ga(M)36 b F6(\021)25 b FL(Cut)803 4697 y FC( )8634745 y F4(\()898 4733 y FX(h)926 4745 y Ga(a)974 4733y FX(i)1002 4745 y FL(Cut)p F4(\()1175 4733 y FX(h)12024745 y Ga(b)1241 4733 y FX(i)1269 4745 y Ga(S)5 b(;)13704733 y F9(\()1398 4745 y Ga(x)1450 4733 y F9(\))14774745 y Ga(T)13 b F4(\))p Ga(;)1618 4733 y F9(\()16464745 y Ga(y)1694 4733 y F9(\))1721 4745 y Ga(U)d F4(\))7824832 y Gc(x)717 4869 y F6(\000)-31 b(\000)f(!)26 b FL(Cut)oF4(\()1085 4857 y FX(h)1113 4869 y Ga(b)1152 4857 y FX(i)11804869 y FL(Cut)1258 4821 y FC( )1319 4869 y F4(\()13544857 y FX(h)1382 4869 y Ga(a)1430 4857 y FX(i)1458 4869y Ga(S)5 b(;)1559 4857 y F9(\()1586 4869 y Ga(y)16344857 y F9(\))1662 4869 y Ga(U)10 b F4(\))p Ga(;)18094857 y F9(\()1837 4869 y Ga(x)1889 4857 y F9(\))19164869 y FL(Cut)1995 4821 y FC( )2056 4869 y F4(\()20914857 y FX(h)2119 4869 y Ga(a)2167 4857 y FX(i)2194 4869y Ga(T)j(;)2300 4857 y F9(\()2328 4869 y Ga(y)2376 4857y F9(\))2403 4869 y Ga(U)d F4(\))q(\))25 b F6(\021)gGa(N)504 4993 y Gg(\(1\))101 b Ga(M)p 710 5008 99 4 v35 w F4(=)25 b(\()p Ga(S)p 964 5008 61 4 v 26 w F6(\001)10715007 y Gc(m)1158 4993 y Ga(T)p 1158 5008 66 4 v 13 wF4(\))p F6(h)p Ga(U)p 1294 5008 72 4 v 10 w F6(i)14015007 y Gc(n)1497 4993 y Gg(and)49 b Ga(N)p 1676 500883 4 v 35 w F4(=)25 b Ga(S)p 1880 5008 61 4 v 5 w F6(h)pGa(U)p 1976 5008 72 4 v 10 w F6(i)2083 5007 y Gc(r)21424993 y F6(\001)2167 5007 y Gc(s)2224 4993 y Ga(T)p 22245008 66 4 v 13 w F6(h)p Ga(U)p 2325 5008 72 4 v 10 wF6(i)2432 5007 y Gc(t)2770 4993 y Gg(by)e(De\002nition)i(2.6.17)5045117 y(\(2\))101 b Ga(n)25 b F6(\025)g Ga(s;)15 b(r)m(;)g(t)1622b Gg(by)23 b(Lemma)g(2.6.19\(i,ii\))504 5241 y(\(3\))p712 5241 28 4 v 730 5241 V 747 5241 V 166 w F6(h)p 8125241 V 830 5241 V 847 5241 V 64 w(i)909 5255 y Gc(n)9825241 y F6(\035)p 1100 5241 V 1118 5241 V 1135 5241 V110 w(\001)1208 5255 y Gc(s)p 1267 5241 V 1285 5241 V1302 5241 V 2487 5241 a Gg(by)h(\(2\))f(and)h(De\002nition)h(2.6.14)pBlack Black eop end%%Page: 154 166TeXDict begin 154 165 bop Black -144 51 a Gb(154)2658b(Details)24 b(f)n(or)g(some)g(Pr)n(oofs)p -144 88 36914 v Black 549 384 a Gg(\(4\))100 b F4(\()p Ga(S)p 789399 61 4 v 26 w F6(\001)896 398 y Gc(m)983 384 y Ga(T)p983 399 66 4 v 13 w F4(\))p F6(h)p Ga(U)p 1119 399 724 v 10 w F6(i)1226 398 y Gc(n)1299 384 y Ga(>)1370 351y Gc(r)r(po)1502 384 y Ga(S)p 1502 399 61 4 v 53 w Gg(and)50b F4(\()p Ga(S)p 1826 399 V 25 w F6(\001)1932 398 y Gc(m)2019384 y Ga(T)p 2019 399 66 4 v 13 w F4(\))p F6(h)p Ga(U)p2155 399 72 4 v 11 w F6(i)2263 398 y Gc(n)2335 384 yGa(>)2406 351 y Gc(r)r(po)2539 384 y Ga(U)p 2539 399V 625 w Gg(by)23 b(rpo\(i\))549 508 y(\(5\))100 b F6(f)-24b(j)p F4(\()p Ga(S)p 835 523 61 4 v 27 w F6(\001)943522 y Gc(m)1030 508 y Ga(T)p 1030 523 66 4 v 13 w F4(\))pGa(;)15 b(U)p 1171 523 72 4 v 10 w F6(j)-24 b(g)27 bGa(>)1387 464 y Gc(r)r(po)1387 537 y(mul)q(t)1566 508y F6(f)-24 b(j)p Ga(S)p 1612 523 61 4 v 6 w(;)15 b(U)p1714 523 72 4 v 11 w F6(j)-24 b(g)1393 b Gg(by)23 b(rpo\(i\))549632 y(\(6\))100 b F4(\()p Ga(S)p 789 647 61 4 v 26 wF6(\001)896 646 y Gc(m)983 632 y Ga(T)p 983 647 66 4v 13 w F4(\))p F6(h)p Ga(U)p 1119 647 72 4 v 10 w F6(i)1226646 y Gc(n)1299 632 y Ga(>)1370 599 y Gc(r)r(po)1502632 y Ga(S)p 1502 647 61 4 v 5 w F6(h)p Ga(U)p 1598 64772 4 v 11 w F6(i)1706 646 y Gc(r)2370 632 y Gg(if)23b Ga(n)i F4(=)g Ga(r)s Gg(,)d(then)i(by)g(\(5\))g(and)g(rpo\(iii\))2395756 y(if)g Ga(n)g(>)h(r)s Gg(,)d(then)j(by)e(\(4\))h(and)g(rpo\(ii\))549 881 y(\(7\))100 b F4(\()p Ga(S)p 789 896 61 4 v 26w F6(\001)896 895 y Gc(m)983 881 y Ga(T)p 983 896 664 v 13 w F4(\))p F6(h)p Ga(U)p 1119 896 72 4 v 10 w F6(i)1226895 y Gc(n)1299 881 y Ga(>)1370 848 y Gc(r)r(po)1502881 y Ga(T)p 1502 896 66 4 v 13 w F6(h)p Ga(U)p 1603896 72 4 v 10 w F6(i)1710 895 y Gc(t)2819 881 y Gg(analogous)27b(to)c(\(4,5,6\))549 1005 y(\(8\))100 b Ga(M)p 754 102099 4 v 36 w(>)949 972 y Gc(r)r(po)1081 1005 y Ga(N)p1081 1020 83 4 v 1627 w Gg(by)24 b(\(3,6,7\))g(and)g(rpo\(ii\))5491294 y Ga(M)35 b F6(\021)25 b FL(Cut)847 1247 y FC( )9081294 y F4(\()943 1282 y FX(h)970 1294 y Ga(a)1018 1282y FX(i)1046 1294 y FL(Cut)p F4(\()1219 1282 y FX(h)12471294 y Ga(b)1286 1282 y FX(i)1313 1294 y Ga(S)5 b(;)14141282 y F9(\()1442 1294 y Ga(x)1494 1282 y F9(\))15211294 y FL(Ax)p F4(\()p Ga(x;)15 b(a)p F4(\))q(\))p Ga(;)19101282 y F9(\()1938 1294 y Ga(y)1986 1282 y F9(\))20131294 y Ga(U)10 b F4(\))826 1381 y Gc(x)761 1418 y F6(\000)-31b(\000)g(!)25 b FL(Cut)p F4(\()1130 1406 y FX(h)11571418 y Ga(b)1196 1406 y FX(i)1224 1418 y FL(Cut)13031371 y FC( )1364 1418 y F4(\()1399 1406 y FX(h)1426 1418y Ga(a)1474 1406 y FX(i)1502 1418 y Ga(S)5 b(;)1603 1406y F9(\()1631 1418 y Ga(y)1679 1406 y F9(\))1706 1418y Ga(U)10 b F4(\))p Ga(;)1853 1406 y F9(\()1881 1418y Ga(y)1929 1406 y F9(\))1956 1418 y Ga(U)g F4(\))26b F6(\021)f Ga(N)549 1543 y Gg(\(1\))100 b Ga(M)p 7541558 99 4 v 36 w F4(=)25 b(\()p Ga(S)p 1009 1558 61 4v 25 w F6(\001)1115 1557 y Gc(m)1202 1543 y Ga(?)p F4(\))pF6(h)p Ga(U)p 1317 1558 72 4 v 11 w F6(i)1425 1557 yGc(n)1521 1543 y Gg(and)49 b Ga(N)p 1700 1558 83 4 v35 w F4(=)25 b Ga(S)p 1904 1558 61 4 v 5 w F6(h)p Ga(U)p2000 1558 72 4 v 10 w F6(i)2107 1557 y Gc(r)2166 1543y F6(\001)2191 1557 y Gc(s)2248 1543 y Ga(U)p 2248 1558V 504 w Gg(by)f(De\002nition)g(2.6.17)549 1667 y(\(2\))100b Ga(n)25 b F6(\025)g Ga(s;)15 b(r)1692 b Gg(by)24 b(Lemma)e(2.6.19\(i,ii\))549 1791 y(\(3\))p 756 1791 28 4 v 7741791 V 791 1791 V 165 w F6(h)p 856 1791 V 874 1791 V891 1791 V 65 w(i)954 1805 y Gc(n)1026 1791 y F6(\035)p1144 1791 V 1162 1791 V 1180 1791 V 110 w(\001)1252 1805y Gc(s)p 1311 1791 V 1329 1791 V 1347 1791 V 2531 1791a Gg(by)i(\(2\))g(and)g(De\002nition)g(2.6.14)549 1915y(\(4\))100 b F4(\()p Ga(S)p 789 1930 61 4 v 26 w F6(\001)8961929 y Gc(m)983 1915 y Ga(?)p F4(\))p F6(h)p Ga(U)p 10981930 72 4 v 11 w F6(i)1206 1929 y Gc(n)1278 1915 y Ga(>)13491882 y Gc(r)r(po)1482 1915 y Ga(S)p 1482 1930 61 4 v53 w Gg(and)49 b F4(\()p Ga(S)p 1805 1930 V 26 w F6(\001)19121929 y Gc(m)1999 1915 y Ga(?)p F4(\))p F6(h)p Ga(U)p2114 1930 72 4 v 11 w F6(i)2222 1929 y Gc(n)2295 1915y Ga(>)2366 1882 y Gc(r)r(po)2498 1915 y Ga(U)p 24981930 V 666 w Gg(by)23 b(rpo\(i\))549 2040 y(\(5\))100b F6(f)-24 b(j)p F4(\()p Ga(S)p 835 2055 61 4 v 27 wF6(\001)943 2054 y Gc(m)1030 2040 y Ga(?)p F4(\))p Ga(;)15b(U)p 1150 2055 72 4 v 11 w F6(j)-24 b(g)26 b Ga(>)13661995 y Gc(r)r(po)1366 2069 y(mul)q(t)1546 2040 y F6(f)-24b(j)p Ga(S)p 1592 2055 61 4 v 6 w(;)15 b(U)p 1694 205572 4 v 11 w F6(j)-24 b(g)1413 b Gg(by)23 b(rpo\(i\))5492164 y(\(6\))100 b F4(\()p Ga(S)p 789 2179 61 4 v 26w F6(\001)896 2178 y Gc(m)983 2164 y Ga(?)p F4(\))p F6(h)pGa(U)p 1098 2179 72 4 v 11 w F6(i)1206 2178 y Gc(n)12782164 y Ga(>)1349 2131 y Gc(r)r(po)1482 2164 y Ga(S)p1482 2179 61 4 v 5 w F6(h)p Ga(U)p 1578 2179 72 4 v 10w F6(i)1685 2178 y Gc(r)2370 2164 y Gg(if)23 b Ga(n)iF4(=)g Ga(r)s Gg(,)d(then)i(by)g(\(5\))g(and)g(rpo\(iii\))23952288 y(if)g Ga(n)g(>)h(r)s Gg(,)d(then)j(by)e(\(4\))h(and)g(rpo\(ii\))549 2412 y(\(7\))100 b Ga(M)p 754 2427 99 4 v 36 w(>)9492379 y Gc(r)r(po)1081 2412 y Ga(N)p 1081 2427 83 4 v1627 w Gg(by)24 b(\(3,4,6\))g(and)g(rpo\(ii\))549 2702y Ga(M)35 b F6(\021)25 b FL(Cut)847 2654 y FC( )908 2702y F4(\()943 2690 y FX(h)970 2702 y Ga(a)1018 2690 y FX(i)10462702 y FL(Ax)o F4(\()p Ga(x;)15 b(a)p F4(\))r Ga(;)14002690 y F9(\()1427 2702 y Ga(y)1475 2690 y F9(\))15032702 y Ga(S)5 b F4(\))1690 2664 y Gc(x)1624 2702 y F6(\000)-31b(\000)g(!)25 b FL(Cut)p F4(\()1993 2690 y FX(h)20202702 y Ga(a)2068 2690 y FX(i)2096 2702 y FL(Ax)o F4(\()pGa(x;)15 b(a)p F4(\))r Ga(;)2450 2690 y F9(\()2477 2702y Ga(y)2525 2690 y F9(\))2553 2702 y Ga(S)5 b F4(\))25b F6(\021)g Ga(N)549 2826 y Gg(\(1\))100 b Ga(M)p 7542841 99 4 v 36 w F4(=)25 b Ga(?)15 b F6(h)p Ga(S)p 10692841 61 4 v 5 w F6(i)1165 2840 y Gc(m)1280 2826 y Gg(and)50b Ga(N)p 1460 2841 83 4 v 35 w F4(=)25 b Ga(?)20 b F6(\001)17542840 y Gc(n)1822 2826 y Ga(S)p 1822 2841 61 4 v 936 wGg(by)k(De\002nition)g(2.6.17)549 2950 y(\(2\))100 bGa(m)25 b F6(\025)g Ga(n)1809 b Gg(by)24 b(Lemma)e(2.6.19\(i\))5493074 y(\(3\))p 756 3074 28 4 v 774 3074 V 791 3074 V165 w F6(h)p 856 3074 V 874 3074 V 891 3074 V 65 w(i)9543088 y Gc(m)1046 3074 y F6(\035)p 1164 3074 V 1182 3074V 1199 3074 V 110 w(\001)1272 3088 y Gc(n)p 1341 3074V 1359 3074 V 1376 3074 V 2531 3074 a Gg(by)i(\(2\))g(and)g(De\002nition)g(2.6.14)549 3198 y(\(4\))100 b Ga(?)15b F6(h)p Ga(S)p 849 3213 61 4 v 6 w F6(i)946 3212 y Gc(m)10383198 y Ga(>)1109 3165 y Gc(r)r(po)1242 3198 y Ga(?)48b Gg(and)i Ga(?)15 b F6(h)p Ga(S)p 1610 3213 V 6 w F6(i)17073212 y Gc(m)1799 3198 y Ga(>)1870 3165 y Gc(r)r(po)20023198 y Ga(S)p 2002 3213 V 1168 w Gg(by)23 b(rpo\(i\))5493323 y(\(5\))100 b Ga(M)p 754 3338 99 4 v 36 w(>)9493290 y Gc(r)r(po)1081 3323 y Ga(N)p 1081 3338 83 4 v1696 w Gg(by)23 b(\(3,4\))h(and)g(rpo\(ii\))p Black 3213603 a Gb(Commuting)f(Reduction:)p Black 45 w Gg(One)h(case)g(is)f(as)h(follo)n(ws.)549 3803 y Ga(M)35 b F6(\021)25 b FL(Cut)pF4(\()941 3791 y FX(h)969 3803 y Ga(a)1017 3791 y FX(i)10443803 y Ga(S)5 b(;)1145 3791 y F9(\()1173 3803 y Ga(x)12253791 y F9(\))1252 3803 y Ga(T)13 b F4(\))1428 3766 yGc(c)1459 3742 y FC(00)1379 3803 y F6(\000)-32 b(\000)h(!)25b FL(Cut)1653 3755 y FC( )1714 3803 y F4(\()1749 3791y FX(h)1777 3803 y Ga(a)1825 3791 y FX(i)1852 3803 yGa(S)5 b(;)1953 3791 y F9(\()1981 3803 y Ga(x)2033 3791y F9(\))2060 3803 y Ga(T)13 b F4(\))26 b F6(\021)f Ga(N)5493927 y Gg(\(1\))100 b Ga(M)p 754 3942 99 4 v 36 w F4(=)25b Ga(S)p 974 3942 61 4 v 25 w F6(\001)1080 3941 y Gc(m)11673927 y Ga(T)p 1167 3942 66 4 v 60 w Gg(and)50 b Ga(N)p1460 3942 83 4 v 35 w F4(=)25 b Ga(S)p 1664 3942 61 4v 5 w F6(h)p Ga(T)p 1760 3942 66 4 v 13 w F6(i)1861 3941y Gc(n)2814 3927 y Gg(by)f(De\002nition)g(2.6.17)5494051 y(\(2\))100 b Ga(m)25 b(>)g(n)1759 b Gg(by)23 b(Lemma)g(2.6.19\(iii\))549 4175 y(\(3\))p 756 4175 28 4 v 7744175 V 791 4175 V 185 w F6(\001)864 4189 y Gc(m)p 9534175 V 971 4175 V 988 4175 V 1041 4175 a F6(\035)p 11594175 V 1177 4175 V 1194 4175 V 89 w(h)p 1258 4175 V 12774175 V 1294 4175 V 65 w(i)1356 4189 y Gc(n)2531 4175y Gg(by)h(\(2\))g(and)g(De\002nition)g(2.6.14)549 4299y(\(4\))100 b Ga(S)p 754 4314 61 4 v 25 w F6(\001)8604313 y Gc(m)947 4299 y Ga(T)p 947 4314 66 4 v 38 w(>)11094266 y Gc(r)r(po)1242 4299 y Ga(S)p 1242 4314 61 4 v53 w Gg(and)49 b Ga(S)p 1530 4314 V 25 w F6(\001)16364313 y Gc(m)1723 4299 y Ga(T)p 1723 4314 66 4 v 38 w(>)18854266 y Gc(r)r(po)2018 4299 y Ga(T)p 2018 4314 V 1155w Gg(by)23 b(rpo\(i\))549 4424 y(\(5\))100 b Ga(M)p 7544439 99 4 v 36 w(>)949 4391 y Gc(r)r(po)1081 4424 y Ga(N)p1081 4439 83 4 v 1696 w Gg(by)23 b(\(3,4\))h(and)g(rpo\(ii\))pBlack 321 4704 a Gb(Logical)h(Reduction:)p Black 46 wGg(W)-7 b(e)22 b(tackle)j(three)g(representati)n(v)o(e)i(cases.)5494905 y Ga(M)35 b F6(\021)25 b FL(Cut)p F4(\()941 4893y FX(h)969 4905 y Ga(a)1017 4893 y FX(i)1044 4905 y FL(Ax)pF4(\()p Ga(x;)15 b(a)p F4(\))q Ga(;)1398 4893 y F9(\()14264905 y Ga(y)1474 4893 y F9(\))1501 4905 y Ga(S)5 b F4(\))16974868 y Gc(l)1622 4905 y F6(\000)-31 b(\000)g(!)25 b Ga(S)5b F4([)p Ga(y)13 b F6(7!)d Ga(x)p F4(])26 b F6(\021)fGa(N)549 5029 y Gg(\(1\))100 b Ga(M)p 754 5044 99 4 v36 w F4(=)25 b Ga(?)20 b F6(\001)1064 5043 y Gc(n)11325029 y Ga(S)p 1132 5044 61 4 v 53 w Gg(and)49 b Ga(N)p1420 5044 83 4 v 35 w F4(=)25 b Ga(S)p 1624 5044 61 4v 1134 w Gg(by)f(De\002nition)g(2.6.17)549 5153 y(\(2\))100b Ga(M)p 754 5168 99 4 v 36 w(>)949 5120 y Gc(r)r(po)10815153 y Ga(N)p 1081 5168 83 4 v 1764 w Gg(by)23 b(\(1\))h(and)g(rpo\(ii\))p Black Black eop end%%Page: 155 167TeXDict begin 155 166 bop Black 277 51 a Gb(B.1)23 b(Pr)n(oofs)h(of)g(Chapter)f(2)2639 b(155)p 277 88 3691 4 v Black 504 384a Ga(M)36 b F6(\021)25 b FL(Cut)p F4(\()897 372 y FX(h)924384 y Ga(c)963 372 y FX(i)991 384 y FL(And)1146 398 yGc(R)1203 384 y F4(\()1238 372 y FX(h)1266 384 y Ga(a)1314372 y FX(i)1342 384 y Ga(S)5 b(;)1443 372 y FX(h)1471384 y Ga(b)1510 372 y FX(i)1537 384 y Ga(T)13 b(;)i(c)pF4(\))q Ga(;)1758 372 y F9(\()1786 384 y Ga(y)1834 372y F9(\))1861 384 y FL(And)2016 347 y F9(1)2016 407 yGc(L)2068 384 y F4(\()2103 372 y F9(\()2130 384 y Ga(x)2182372 y F9(\))2210 384 y Ga(U)10 b(;)15 b(y)s F4(\)\))2540347 y Gc(l)2466 384 y F6(\000)-31 b(\000)f(!)26 b FL(Cut)oF4(\()2834 372 y FX(h)2862 384 y Ga(a)2910 372 y FX(i)2938384 y Ga(S)5 b(;)3039 372 y F9(\()3067 384 y Ga(x)3119372 y F9(\))3146 384 y Ga(U)10 b F4(\))26 b F6(\021)fGa(N)504 508 y Gg(\(1\))101 b Ga(M)p 710 523 99 4 v 35w F4(=)25 b FB(L)p Ga(S)p 964 523 61 4 v 6 w(;)15 b(T)p1066 523 66 4 v 13 w FB(M)20 b F6(\001)1212 522 y Gc(m)1299508 y FB(L)p Ga(U)p 1334 523 72 4 v 11 w FB(M)j Gg(and)hGa(N)p 1619 523 83 4 v 35 w F4(=)h Ga(S)p 1823 523 614 v 25 w F6(\001)1929 522 y Gc(n)1997 508 y Ga(U)p 1997523 72 4 v 711 w Gg(by)e(De\002nition)i(2.6.17)504 632y(\(2\))101 b Ga(m)25 b(>)g(n)1758 b Gg(by)24 b(Lemma)f(2.6.19\(iii\))504 756 y(\(3\))101 b FB(L)p Ga(S)p 745 771 61 4 v 5w(;)15 b(T)p 846 771 66 4 v 14 w FB(M)20 b F6(\001)993770 y Gc(m)1080 756 y FB(L)p Ga(U)p 1115 771 72 4 v 10w FB(M)26 b Ga(>)1319 723 y Gc(r)r(po)1452 756 y Ga(S)p1452 771 61 4 v 53 w Gg(,)47 b FB(L)p Ga(S)p 1666 771V 6 w(;)15 b(T)p 1768 771 66 4 v 13 w FB(M)20 b F6(\001)1914770 y Gc(m)2001 756 y FB(L)p Ga(U)p 2036 771 72 4 v 11w FB(M)25 b Ga(>)2240 723 y Gc(r)r(po)2373 756 y Ga(U)p2373 771 V 747 w Gg(by)e(rpo\(i\))504 881 y(\(4\))101b Ga(M)p 710 896 99 4 v 35 w(>)904 848 y Gc(r)r(po)1037881 y Ga(N)p 1037 896 83 4 v 1695 w Gg(by)24 b(\(2,3\))g(and)g(rpo\(ii\))504 1116 y Ga(M)36 b F6(\021)25 b FL(Cut)pF4(\()897 1104 y FX(h)924 1116 y Ga(b)963 1104 y FX(i)9911116 y FL(Imp)1135 1138 y Gc(R)1193 1116 y F4(\()12281104 y F9(\()1256 1116 y Ga(x)1308 1104 y F9(\))p FX(h)13631116 y Ga(a)1411 1104 y FX(i)1438 1116 y Ga(S)5 b(;)15b(b)p F4(\))q Ga(;)1654 1104 y F9(\()1682 1116 y Ga(z)17281104 y F9(\))1755 1116 y FL(Imp)1900 1138 y Gc(L)19521116 y F4(\()1987 1104 y FX(h)2015 1116 y Ga(c)2054 1104y FX(i)2082 1116 y Ga(T)d(;)2187 1104 y F9(\()2215 1116y Ga(y)2263 1104 y F9(\))2291 1116 y Ga(U)e(;)15 b(z)tF4(\))q(\))791 1203 y Gc(l)717 1240 y F6(\000)-31 b(\000)f(!)26b FL(Cut)o F4(\()1085 1228 y FX(h)1113 1240 y Ga(a)11611228 y FX(i)1189 1240 y FL(Cut)p F4(\()1362 1228 y FX(h)13891240 y Ga(c)1428 1228 y FX(i)1456 1240 y Ga(T)13 b(;)15621228 y F9(\()1590 1240 y Ga(x)1642 1228 y F9(\))16691240 y Ga(S)5 b F4(\))p Ga(;)1805 1228 y F9(\()1833 1240y Ga(y)1881 1228 y F9(\))1909 1240 y Ga(U)10 b F4(\))25b F6(\021)g Ga(N)504 1364 y Gg(\(1\))101 b Ga(M)p 7101379 99 4 v 35 w F4(=)25 b FB(L)p Ga(S)p 964 1379 614 v 6 w FB(M)20 b F6(\001)1106 1378 y Gc(m)1193 1364y FB(L)p Ga(T)p 1228 1379 66 4 v 13 w(;)15 b(U)p 13341379 72 4 v 11 w FB(M)23 b Gg(and)h Ga(N)p 1619 137983 4 v 35 w F4(=)h(\()p Ga(T)p 1858 1379 66 4 v 33 wF6(\001)1969 1378 y Gc(s)2027 1364 y Ga(S)p 2027 137961 4 v 5 w F4(\))20 b F6(\001)2168 1378 y Gc(t)2218 1364y Ga(U)p 2218 1379 72 4 v 490 w Gg(by)j(De\002nition)i(2.6.17)5041488 y(\(2\))101 b Ga(m)25 b(>)g(s;)15 b(t)1624 b Gg(by)24b(Lemma)e(2.6.19\(iii,ii\))504 1613 y(\(3\))101 b FB(L)pGa(S)p 745 1628 61 4 v 5 w FB(M)21 b F6(\001)887 1627y Gc(m)974 1613 y FB(L)p Ga(T)p 1009 1628 66 4 v 13 w(;)15b(U)p 1115 1628 72 4 v 10 w FB(M)26 b Ga(>)1319 1580y Gc(r)r(po)1452 1613 y Ga(S)p 1452 1628 61 4 v 53 wGg(,)47 b FB(L)p Ga(S)p 1666 1628 V 6 w FB(M)20 b F6(\001)18081627 y Gc(m)1895 1613 y FB(L)p Ga(T)p 1930 1628 66 4v 13 w(;)15 b(U)p 2036 1628 72 4 v 11 w FB(M)25 b Ga(>)22401580 y Gc(r)r(po)2373 1613 y Ga(T)p 2373 1628 66 4 v756 w Gg(by)e(rpo\(i\))504 1737 y(\(4\))101 b FB(L)pGa(S)p 745 1752 61 4 v 5 w FB(M)21 b F6(\001)887 1751y Gc(m)974 1737 y FB(L)p Ga(T)p 1009 1752 66 4 v 13 w(;)15b(U)p 1115 1752 72 4 v 10 w FB(M)26 b Ga(>)1319 1704y Gc(r)r(po)1452 1737 y Ga(T)p 1452 1752 66 4 v 33 wF6(\001)1563 1751 y Gc(s)1620 1737 y Ga(S)p 1620 175261 4 v 1129 w Gg(by)e(\(2,3\))g(and)g(rpo\(ii\))504 1861y(\(5\))101 b FB(L)p Ga(S)p 745 1876 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y Ga(S)5 b F4(])321 3657 y Gg(by)34 b(a)f(logical)i(reduction)h(or)d(by)g(a)g(commuting)i(reduction)h(and)e(Lemma)e(2.2.11.)58b(Thus)34 b(we)e(are)321 3770 y(done.)p 3480 3770 V 34843712 55 4 v 3484 3770 V 3538 3770 4 62 v Black 321 3958a Gb(Pr)n(oof)24 b(of)g(Lemma)f(3.2.1.)p Black 33 w Gg(The)g(dif)n(\002cult)i(case)f(is)f(as)h(follo)n(ws.)p Black Black1196 4096 a FL(Ax)o F4(\()p Ga(x;)15 b(a)p F4(\)[)p Ga(a)27b F4(:=)1729 4084 y F9(\()1756 4096 y Ga(y)1804 4084y F9(\))1832 4096 y Ga(S)5 b F4(][)p Ga(x)25 b F4(:=)21424084 y FX(h)2169 4096 y Ga(b)2208 4084 y FX(i)2235 4096y Ga(T)13 b F4(])1078 4209 y(=)47 b Ga(S)5 b F4([)p Ga(y)13b F6(7!)d Ga(x)p F4(][)p Ga(x)25 b F4(:=)1742 4197 yFX(h)1769 4209 y Ga(b)1808 4197 y FX(i)1836 4209 y Ga(T)12b F4(])1078 4322 y F6(\021)47 b Ga(S)5 b F4([)p Ga(y)28b F4(:=)1476 4310 y FX(h)1504 4322 y Ga(b)1543 4310 yFX(i)1570 4322 y Ga(T)13 b F4(][)p Ga(x)25 b F4(:=)18854310 y FX(h)1912 4322 y Ga(b)1951 4310 y FX(i)1979 4322y Ga(T)12 b F4(])1078 4439 y(=)47 b FL(Cut)o F4(\()13684427 y FX(h)1396 4439 y Ga(b)1435 4427 y FX(i)1463 4439y Ga(T)12 b(;)1568 4427 y F9(\()1596 4439 y Ga(y)16444427 y F9(\))1672 4439 y Ga(S)5 b F4(\)[)p Ga(x)25 bF4(:=)1992 4427 y FX(h)2019 4439 y Ga(b)2058 4427 y FX(i)20854439 y Ga(T)13 b F4(])2835 4406 y F9(\(1\))1078 4552y F4(=)47 b FL(Cut)o F4(\()1368 4540 y FX(h)1396 4552y Ga(b)1435 4540 y FX(i)1463 4552 y Ga(T)12 b(;)15684540 y F9(\()1596 4552 y Ga(y)1644 4540 y F9(\))16724552 y Ga(S)5 b F4([)p Ga(x)25 b F4(:=)1956 4540 y FX(h)19844552 y Ga(b)2023 4540 y FX(i)2050 4552 y Ga(T)13 b F4(]\))9784631 y Gc(int)939 4668 y F6(\000)-32 b(\000)h(!)11094635 y FX(\003)1196 4668 y Ga(T)13 b F4([)p Ga(b)25 bF4(:=)1472 4656 y F9(\()1499 4668 y Ga(y)1547 4656 yF9(\))1575 4668 y Ga(S)5 b F4([)p Ga(x)25 b F4(:=)18594656 y FX(h)1887 4668 y Ga(b)1926 4656 y FX(i)1953 4668y Ga(T)13 b F4(]])2835 4635 y F9(\(2\))1078 4785 y F6(\021)47b Ga(T)13 b F4([)p Ga(b)d F6(7!)g Ga(a)p F4(][)p Ga(a)26b F4(:=)1730 4773 y F9(\()1757 4785 y Ga(y)1805 4773y F9(\))1832 4785 y Ga(S)5 b F4([)p Ga(x)26 b F4(:=)21174773 y FX(h)2145 4785 y Ga(b)2184 4773 y FX(i)2211 4785y Ga(T)13 b F4(]])2835 4752 y F9(\(3\))1078 4898 y F4(=)47b FL(Ax)o F4(\()p Ga(x;)15 b(a)p F4(\)[)p Ga(x)27 b F4(:=)17334886 y FX(h)1760 4898 y Ga(b)1799 4886 y FX(i)1827 4898y Ga(T)13 b F4(][)p Ga(a)25 b F4(:=)2138 4886 y F9(\()21654898 y Ga(y)2213 4886 y F9(\))2240 4898 y Ga(S)5 b F4([)pGa(x)26 b F4(:=)2525 4886 y FX(h)2552 4898 y Ga(b)25914886 y FX(i)2619 4898 y Ga(T)13 b F4(]])p Black Black790 5056 a F9(\(1\))984 5089 y Gg(by)24 b(assumption)iGa(S)h Gg(freshly)e(introduces)i Ga(y)e Gg(and)f(is)g(not)g(an)f(axiom)790 5173 y F9(\(2\))984 5206 y Gg(by)h(F)o(act)f(B.2.1)7905289 y F9(\(3\))984 5322 y Gg(by)h(assumption)i Ga(a)fF6(62)g Ga(F)13 b(C)7 b F4(\()1872 5310 y FX(h)1899 5322y Ga(b)1938 5310 y FX(i)1966 5322 y Ga(T)12 b F4(\))p3480 5492 V 3484 5434 55 4 v 3484 5492 V 3538 5492 462 v Black Black eop end%%Page: 157 169TeXDict begin 157 168 bop Black 277 51 a Gb(B.2)23 b(Pr)n(oofs)h(of)g(Chapter)f(3)2639 b(157)p 277 88 3691 4 v Black Black277 388 a(Pr)n(oof)28 b(of)e(Lemma)g(3.2.3.)p Black 34w Gg(If)h Ga(M)36 b Gg(is)27 b(a)f(v)n(ariable,)j(then)f(the)f(lemma)f(is)h(by)g(routine)i(calculation.)41 b(In)277 501 y(case)27b Ga(M)36 b Gg(corresponds)30 b(to)d(a)f(term)g(gi)n(v)o(en)h(in)f(Lemma)g(3.2.2,)h(then)g F6(j)p Ga(M)10 b F6(j)2588 468y Fu(s)2588 524 y Gc(a)2656 501 y Gg(cannot)28 b(introduce)hGa(x)d Gg(and)277 614 y(hence)f(the)e(substitution)k(is)c(mo)o(v)o(ed)h(inside)h(the)e(subterm\(s\).)31 b(In)23 b(consequence,)k(one)d(can)f(apply)i(the)277 727 y(induction)30 b(hypothesis.)41b(Otherwise,)28 b(the)f(top-le)n(v)o(el)h(term)f(constructor)j(of)cGa(M)36 b Gg(corresponds)31 b(to)26 b(an)277 840 y(elimination)g(rule,)e(for)g(which)f(we)g(illustrate)j(the)e(lemma)f(with)g(one)h(case.)pBlack 277 1044 a Gb(Case)p Black 46 w Ga(M)36 b F6(\021)25b Ga(S)20 b(T)13 b Gg(:)582 1174 y F6(j)p Ga(S)20 b(T)13b F6(j)774 1141 y Fu(s)774 1196 y Gc(a)816 1174 y F4([)pGa(\033)s F4(])1659 b Gg(with)24 b F4([)p Ga(\033)s F4(])iF6(\021)f F4([)p Ga(x)g F4(:=)3215 1162 y FX(h)3243 1174y Ga(b)3282 1162 y FX(i)3309 1174 y F6(j)p Ga(N)10 bF6(j)3442 1141 y Fu(s)3442 1201 y Gc(b)3477 1174 y F4(])4391298 y(=)72 b F6(j)p Ga(S)5 b F6(j)693 1265 y Fu(s)6931320 y Gc(c)728 1298 y F4([)p Ga(c)26 b F4(:=)939 1286y F9(\()967 1298 y Ga(y)1015 1286 y F9(\))1042 1298 yFL(Imp)1186 1320 y Gc(L)1238 1298 y F4(\()1273 1286 yFX(h)1301 1298 y Ga(d)1348 1286 y FX(i)1376 1298 y F6(j)pGa(T)13 b F6(j)1492 1265 y Fu(s)1492 1326 y Gc(d)15331298 y Ga(;)1573 1286 y F9(\()1601 1298 y Ga(z)1647 1286y F9(\))1674 1298 y FL(Ax)p F4(\()p Ga(z)t(;)i(a)p F4(\))qGa(;)g(y)s F4(\))q(][)p Ga(\033)s F4(])779 b Gg(by)24b(\(6\))f(of)h F6(j)p 3383 1298 28 4 v 3401 1298 V 34181298 V 65 w(j)3471 1265 y Fu(s)378 1385 y Gc(int)3391422 y F6(\000)-31 b(\000)f(!)519 1389 y FX(\003)5821422 y F6(j)p Ga(S)5 b F6(j)693 1389 y Fu(s)693 1445y Gc(c)728 1422 y F4([)p Ga(\033)s F4(][)p Ga(c)27 bF4(:=)1045 1410 y F9(\()1072 1422 y Ga(y)1120 1410 yF9(\))1148 1422 y FL(Imp)1292 1444 y Gc(L)1344 1422 yF4(\()1379 1410 y FX(h)1407 1422 y Ga(d)1454 1410 y FX(i)14821422 y F6(j)p Ga(T)13 b F6(j)1598 1389 y Fu(s)1598 1450y Gc(d)1638 1422 y Ga(;)1678 1410 y F9(\()1706 1422 yGa(z)1752 1410 y F9(\))1780 1422 y FL(Ax)o F4(\()p Ga(z)t(;)i(a)pF4(\))r Ga(;)g(y)s F4(\)[)p Ga(\033)s F4(]])565 b Gg(by)24b(Lemma)e(3.2.1)439 1546 y F4(=)72 b F6(j)p Ga(S)5 bF6(j)693 1513 y Fu(s)693 1569 y Gc(c)728 1546 y F4([)pGa(\033)s F4(][)p Ga(c)27 b F4(:=)1045 1534 y F9(\()10721546 y Ga(y)1120 1534 y F9(\))1148 1546 y FL(Imp)12921568 y Gc(L)1344 1546 y F4(\()1379 1534 y FX(h)1407 1546y Ga(d)1454 1534 y FX(i)1482 1546 y F6(j)p Ga(T)13 bF6(j)1598 1513 y Fu(s)1598 1574 y Gc(d)1638 1546 y F4([)pGa(\033)s F4(])q Ga(;)1784 1534 y F9(\()1812 1546 y Ga(z)18581534 y F9(\))1886 1546 y FL(Ax)o F4(\()p Ga(z)t(;)i(a)pF4(\))r Ga(;)g(y)s F4(\)])378 1633 y Gc(int)339 1671y F6(\000)-31 b(\000)f(!)519 1638 y FX(\003)582 1671y F6(j)p Ga(S)5 b F4([)p Ga(x)26 b F4(:=)f Ga(N)10 bF4(])p F6(j)1025 1638 y Fu(s)1025 1693 y Gc(c)1060 1671y F4([)p Ga(c)26 b F4(:=)1271 1659 y F9(\()1298 1671y Ga(y)1346 1659 y F9(\))1374 1671 y FL(Imp)1518 1692y Gc(L)1570 1671 y F4(\()1605 1659 y FX(h)1633 1671 yGa(d)1680 1659 y FX(i)1708 1671 y F6(j)p Ga(T)13 b F4([)pGa(x)25 b F4(:=)g Ga(N)10 b F4(])p F6(j)2155 1638 y Fu(s)21551698 y Gc(d)2196 1671 y Ga(;)2236 1659 y F9(\()2264 1671y Ga(z)2310 1659 y F9(\))2338 1671 y FL(Ax)p F4(\()pGa(z)t(;)15 b(a)p F4(\))q Ga(;)g(y)s F4(\))q(])498 bGg(by)23 b(IH)439 1795 y F4(=)72 b F6(j)p Ga(S)5 b F4([)pGa(x)26 b F4(:=)f Ga(N)10 b F4(])25 b Ga(T)13 b F4([)pGa(x)25 b F4(:=)h Ga(N)10 b F4(])p F6(j)1448 1762 y Fu(s)14481817 y Gc(a)3015 1795 y Gg(by)24 b(\(6\))f(of)h F6(j)p3383 1795 V 3401 1795 V 3418 1795 V 65 w(j)3471 1762y Fu(s)439 1919 y F6(\021)72 b(j)p F4(\()p Ga(S)21 b(T)13b F4(\)[)p Ga(x)25 b F4(:=)g Ga(N)10 b F4(])p F6(j)11761886 y Fu(s)1176 1941 y Gc(a)p 3436 2026 4 62 v 34401968 55 4 v 3440 2026 V 3494 2026 4 62 v Black 277 2238a Gb(Pr)n(oof)32 b(of)f(Pr)n(oposition)i(3.2.4.)p Black33 w Gg(W)-7 b(e)31 b(shall)h(be)o(gin)g(by)f(gi)n(ving)i(in)e(turn)h(the)f(details)i(where)f(a)e(beta-)277 2351 y(reduction)c(occurs)f(on)f(the)g(top-le)n(v)o(el.)p Black 277 2555 a Gb(Case)pBlack 46 w Ga(M)36 b F6(\021)25 b F4(\()p Ga(\025x:S)5b F4(\))15 b Ga(T)1160 2518 y Gc(\014)1097 2555 y F6(\000)-31b(\000)f(!)25 b Ga(S)5 b F4([)p Ga(x)26 b F4(:=)f Ga(T)13b F4(])25 b F6(\021)g Ga(M)1887 2522 y FX(0)1911 2555y Gg(:)315 2706 y(\(i\))201 b F6(j)p F4(\()p Ga(\025)q(x:S)5b F4(\))15 b Ga(T)e F6(j)994 2673 y Fu(s)994 2729 y Gc(c)4392830 y F4(=)91 b FL(Imp)746 2852 y Gc(R)804 2830 y F4(\()8392818 y F9(\()866 2830 y Ga(x)918 2818 y F9(\))q FX(h)9732830 y Ga(a)1021 2818 y FX(i)1049 2830 y F6(j)p Ga(S)5b F6(j)1160 2797 y Fu(s)1160 2853 y Gc(a)1202 2830 yGa(;)15 b(b)p F4(\)[)p Ga(b)26 b F4(:=)1527 2818 y F9(\()15552830 y Ga(y)1603 2818 y F9(\))1630 2830 y FL(Imp)17742852 y Gc(L)1827 2830 y F4(\()1862 2818 y FX(h)1889 2830y Ga(d)1936 2818 y FX(i)1964 2830 y F6(j)p Ga(T)13 bF6(j)2080 2797 y Fu(s)2080 2858 y Gc(d)2121 2830 y Ga(;)21612818 y F9(\()2189 2830 y Ga(z)2235 2818 y F9(\))22622830 y FL(Ax)p F4(\()p Ga(z)t(;)i(c)p F4(\))r Ga(;)g(y)sF4(\)])237 b Gg(by)24 b(\(2,6\))f(of)h F6(j)p 3383 283028 4 v 3401 2830 V 3418 2830 V 65 w(j)3471 2797 y Fu(s)4392955 y F4(=)91 b FL(Cut)p F4(\()774 2943 y FX(h)802 2955y Ga(b)841 2943 y FX(i)869 2955 y FL(Imp)1013 2976 yGc(R)1071 2955 y F4(\()1106 2943 y F9(\()1133 2955 yGa(x)1185 2943 y F9(\))q FX(h)1240 2955 y Ga(a)1288 2943y FX(i)1316 2955 y F6(j)p Ga(S)5 b F6(j)1427 2922 y Fu(s)14272977 y Gc(a)1469 2955 y Ga(;)15 b(b)p F4(\))q Ga(;)16242943 y F9(\()1652 2955 y Ga(y)1700 2943 y F9(\))17272955 y FL(Imp)1871 2976 y Gc(L)1923 2955 y F4(\()19582943 y FX(h)1986 2955 y Ga(d)2033 2943 y FX(i)2061 2955y F6(j)p Ga(T)e F6(j)2177 2922 y Fu(s)2177 2982 y Gc(d)22182955 y Ga(;)2258 2943 y F9(\()2286 2955 y Ga(z)2332 2943y F9(\))2359 2955 y FL(Ax)p F4(\()p Ga(z)t(;)i(c)p F4(\))rGa(;)g(y)s F4(\)\))178 b Gg(by)23 b(Lem.)f(3.2.2)3783042 y Gc(int)339 3079 y F6(\000)-31 b(\000)f(!)92 bFL(Cut)p F4(\()774 3067 y FX(h)802 3079 y Ga(a)850 3067y FX(i)878 3079 y FL(Cut)o F4(\()1050 3067 y FX(h)10783079 y Ga(d)1125 3067 y FX(i)1153 3079 y F6(j)p Ga(T)13b F6(j)1269 3046 y Fu(s)1269 3107 y Gc(d)1310 3079 yGa(;)1350 3067 y F9(\()1378 3079 y Ga(x)1430 3067 y F9(\))14573079 y F6(j)p Ga(S)5 b F6(j)1568 3046 y Fu(s)1568 3101y Gc(a)1610 3079 y F4(\))p Ga(;)1685 3067 y F9(\()17133079 y Ga(z)1759 3067 y F9(\))1787 3079 y FL(Ax)p F4(\()pGa(z)t(;)15 b(c)p F4(\))q(\))53 b Ga(y)26 b Gg(is)d(freshly)j(introduced)g(by)e(\(6\))f(of)h F6(j)p 3383 3079 V 34013079 V 3418 3079 V 65 w(j)3471 3046 y Fu(s)378 3166 yGc(int)339 3203 y F6(\000)-31 b(\000)f(!)519 3170 y F9(+)6013203 y FL(Cut)p F4(\()774 3191 y FX(h)802 3203 y Ga(d)8493191 y FX(i)877 3203 y F6(j)p Ga(T)13 b F6(j)993 3170y Fu(s)993 3231 y Gc(d)1034 3203 y Ga(;)1074 3191 y F9(\()11013203 y Ga(x)1153 3191 y F9(\))1181 3203 y F6(j)p Ga(S)5b F6(j)1292 3170 y Fu(s)1292 3226 y Gc(a)1334 3203 yF4(\)[)p Ga(a)10 b F6(7!)g Ga(c)p F4(])476 b Gg(by)24b(a)f(comm.)g(reduction)j(and)e(Lem.)e(2.2.11)439 3327y F6(\021)91 b FL(Cut)p F4(\()774 3315 y FX(h)802 3327y Ga(d)849 3315 y FX(i)877 3327 y F6(j)p Ga(T)13 b F6(j)9933294 y Fu(s)993 3355 y Gc(d)1034 3327 y Ga(;)1074 3315y F9(\()1101 3327 y Ga(x)1153 3315 y F9(\))1181 3327y F6(j)p Ga(S)5 b F6(j)1292 3294 y Fu(s)1292 3350 y Gc(c)13273327 y F4(\))880 b Ga(a)25 b F6(62)g Ga(F)13 b(C)7 bF4(\()2579 3315 y FX(h)2607 3327 y Ga(d)2654 3315 y FX(i)26813327 y F6(j)p Ga(T)13 b F6(j)2797 3294 y Fu(s)2797 3355y Gc(d)2838 3327 y F4(\))23 b Gg(by)h(Remark)f(2.2.7)3783414 y Gc(int)339 3451 y F6(\000)-31 b(\000)f(!)519 3418y FX(\003)601 3451 y F6(j)p Ga(S)5 b F6(j)712 3418 yFu(s)712 3474 y Gc(c)748 3451 y F4([)p Ga(x)25 b F4(:=)9713439 y FX(h)999 3451 y Ga(d)1046 3439 y FX(i)1073 3451y F6(j)p Ga(T)13 b F6(j)1189 3418 y Fu(s)1189 3479 yGc(d)1230 3451 y F4(])1759 b Gg(by)23 b(F)o(act)g(B.2.1)3783539 y Gc(int)339 3576 y F6(\000)-31 b(\000)f(!)519 3543y FX(\003)601 3576 y F6(j)p Ga(S)5 b F4([)p Ga(x)26 bF4(:=)f Ga(T)13 b F4(])p F6(j)1027 3543 y Fu(s)1027 3598y Gc(c)2906 3576 y Gg(by)24 b(Lemma)e(3.2.3)315 3741y(\(ii\))157 b F6(j)p F4(\()p Ga(\025x:S)5 b F4(\))15b Ga(T)e F6(j)974 3708 y Fu(s)974 3764 y Gc(c)1010 3741y F4([)p Ga(\033)s F4(])1554 b Gg(with)23 b F4([)p Ga(\033)sF4(])j F6(\021)f F4([)p Ga(c)h F4(:=)3291 3729 y F9(\()33193741 y Ga(y)3367 3729 y F9(\))3394 3741 y Ga(N)10 b F4(])4393866 y(=)72 b FL(Imp)726 3887 y Gc(R)784 3866 y F4(\()8193854 y F9(\()847 3866 y Ga(x)899 3854 y F9(\))p FX(h)9543866 y Ga(c)993 3854 y FX(i)1020 3866 y F6(j)p Ga(S)5b F6(j)1131 3833 y Fu(s)1131 3888 y Gc(c)1167 3866 yGa(;)15 b(a)p F4(\)[)p Ga(a)26 b F4(:=)1510 3854 y F9(\()15383866 y Ga(z)1584 3854 y F9(\))1611 3866 y FL(Imp)17563887 y Gc(L)1808 3866 y F4(\()1843 3854 y FX(h)1871 3866y Ga(b)1910 3854 y FX(i)1937 3866 y F6(j)p Ga(T)13 bF6(j)2053 3833 y Fu(s)2053 3893 y Gc(b)2088 3866 y Ga(;)21283854 y F9(\()2156 3866 y Ga(x)2208 3854 y F9(\))22353866 y FL(Ax)p F4(\()p Ga(x;)i(c)p F4(\))q Ga(;)g(z)tF4(\))q(][)p Ga(\033)s F4(])155 b Gg(by)24 b(\(2,6\))f(of)hF6(j)p 3383 3866 V 3401 3866 V 3418 3866 V 65 w(j)34713833 y Fu(s)439 3990 y F4(=)72 b FL(Cut)p F4(\()755 3978y FX(h)782 3990 y Ga(a)830 3978 y FX(i)858 3990 y FL(Imp)10024012 y Gc(R)1060 3990 y F4(\()1095 3978 y F9(\()11233990 y Ga(x)1175 3978 y F9(\))p FX(h)1230 3990 y Ga(c)12693978 y FX(i)1297 3990 y F6(j)p Ga(S)5 b F6(j)1408 3957y Fu(s)1408 4012 y Gc(c)1443 3990 y Ga(;)15 b(a)p F4(\))qGa(;)1607 3978 y F9(\()1634 3990 y Ga(z)1680 3978 y F9(\))17083990 y FL(Imp)1853 4012 y Gc(L)1905 3990 y F4(\()19403978 y FX(h)1968 3990 y Ga(b)2007 3978 y FX(i)2034 3990y F6(j)p Ga(T)e F6(j)2150 3957 y Fu(s)2150 4017 y Gc(b)21853990 y Ga(;)2225 3978 y F9(\()2252 3990 y Ga(x)2304 3978y F9(\))2332 3990 y FL(Ax)o F4(\()p Ga(x;)i(c)p F4(\))rGa(;)g(z)t F4(\))q(\)[)p Ga(\033)s F4(])96 b Gg(by)23b(Lem.)f(3.2.2)439 4114 y F4(=)72 b FL(Cut)p F4(\()7554102 y FX(h)782 4114 y Ga(a)830 4102 y FX(i)858 4114y FL(Imp)1002 4136 y Gc(R)1060 4114 y F4(\()1095 4102y F9(\()1123 4114 y Ga(x)1175 4102 y F9(\))p FX(h)12304114 y Ga(c)1269 4102 y FX(i)1297 4114 y F6(j)p Ga(S)5b F6(j)1408 4081 y Fu(s)1408 4136 y Gc(c)1443 4114 yGa(;)15 b(a)p F4(\))q Ga(;)1607 4102 y F9(\()1634 4114y Ga(z)1680 4102 y F9(\))1708 4114 y FL(Imp)1853 4136y Gc(L)1905 4114 y F4(\()1940 4102 y FX(h)1968 4114 yGa(b)2007 4102 y FX(i)2034 4114 y F6(j)p Ga(T)e F6(j)21504081 y Fu(s)2150 4142 y Gc(b)2185 4114 y Ga(;)2225 4102y F9(\()2252 4114 y Ga(y)2300 4102 y F9(\))2328 4114y Ga(N)d(;)15 b(z)t F4(\))q(\))45 b Ga(c)26 b F6(62)fGa(F)13 b(C)7 b F4(\()2942 4102 y FX(h)2969 4114 y Ga(b)30084102 y FX(i)3035 4114 y F6(j)p Ga(T)13 b F6(j)3151 4081y Fu(s)3151 4142 y Gc(b)3186 4114 y Ga(;)3226 4102 yFX(h)3254 4114 y Ga(c)3293 4102 y FX(i)3321 4114 y F6(j)pGa(S)5 b F6(j)3432 4081 y Fu(s)3432 4136 y Gc(c)34674114 y F4(\))378 4201 y Gc(int)339 4238 y F6(\000)-31b(\000)f(!)73 b FL(Cut)p F4(\()755 4226 y FX(h)782 4238y Ga(b)821 4226 y FX(i)849 4238 y F6(j)p Ga(T)13 b F6(j)9654205 y Fu(s)965 4266 y Gc(b)1000 4238 y Ga(;)1040 4226y F9(\()1067 4238 y Ga(x)1119 4226 y F9(\))1147 4238y FL(Cut)p F4(\()1320 4226 y FX(h)1347 4238 y Ga(c)13864226 y FX(i)1414 4238 y F6(j)p Ga(S)5 b F6(j)1525 4205y Fu(s)1525 4261 y Gc(c)1560 4238 y Ga(;)1600 4226 yF9(\()1628 4238 y Ga(y)1676 4226 y F9(\))1704 4238 yGa(N)10 b F4(\)\))319 b Ga(z)27 b Gg(is)c(freshly)j(introduced)g(by)e(\(6\))f(of)h F6(j)p 3383 4238 V 3401 4238 V 3418 4238V 65 w(j)3471 4205 y Fu(s)378 4325 y Gc(int)339 4362y F6(\000)-31 b(\000)f(!)73 b FL(Cut)p F4(\()755 4350y FX(h)782 4362 y Ga(c)821 4350 y FX(i)849 4362 y F6(j)pGa(S)5 b F6(j)960 4329 y Fu(s)960 4385 y Gc(c)995 4362y Ga(;)1035 4350 y F9(\()1063 4362 y Ga(y)1111 4350 yF9(\))1139 4362 y Ga(N)10 b F4(\)[)p Ga(x)25 b F4(:=)14814350 y FX(h)1508 4362 y Ga(b)1547 4350 y FX(i)1574 4362y F6(j)p Ga(T)13 b F6(j)1690 4329 y Fu(s)1690 4390 yGc(b)1725 4362 y F4(])439 4487 y(=)72 b FL(Cut)p F4(\()7554475 y FX(h)782 4487 y Ga(c)821 4475 y FX(i)849 4487y F6(j)p Ga(S)5 b F6(j)960 4454 y Fu(s)960 4509 y Gc(c)9954487 y F4([)p Ga(x)26 b F4(:=)1219 4475 y FX(h)1247 4487y Ga(b)1286 4475 y FX(i)1313 4487 y F6(j)p Ga(T)13 bF6(j)1429 4454 y Fu(s)1429 4514 y Gc(b)1464 4487 y F4(])pGa(;)1529 4475 y F9(\()1557 4487 y Ga(y)1605 4475 y F9(\))16324487 y Ga(N)d F4(\))550 b Ga(x)25 b F6(62)g Ga(F)13 b(N)dF4(\()2652 4475 y F9(\()2680 4487 y Ga(y)2728 4475 yF9(\))2755 4487 y Ga(N)g F4(\))23 b Gg(by)h(Remark)f(2.2.7)3784574 y Gc(int)339 4611 y F6(\000)-31 b(\000)f(!)519 4578y FX(\003)582 4611 y FL(Cut)p F4(\()755 4599 y FX(h)7824611 y Ga(c)821 4599 y FX(i)849 4611 y F6(j)p Ga(S)5b F4([)p Ga(x)26 b F4(:=)f Ga(T)13 b F4(])p F6(j)12754578 y Fu(s)1275 4633 y Gc(c)1310 4611 y Ga(;)1350 4599y F9(\()1378 4611 y Ga(y)1426 4599 y F9(\))1453 4611y Ga(N)d F4(\))1335 b Gg(by)24 b(Lemma)e(3.2.3)378 4698y Gc(int)339 4735 y F6(\000)-31 b(\000)f(!)519 4702 yFX(\003)582 4735 y F6(j)p Ga(S)5 b F4([)p Ga(x)26 b F4(:=)fGa(T)13 b F4(])p F6(j)1008 4702 y Fu(s)1008 4757 y Gc(c)10434735 y F4([)p Ga(\033)s F4(])1866 b Gg(by)23 b(F)o(act)g(B.2.1)2774933 y(W)-7 b(e)21 b(omit)g(the)g(other)i(base)f(cases)g(and)g(proceed)h(with)e(the)g(details)i(for)f(inner)g(reductions.)31b(In)21 b(case)h Ga(M)277 5046 y Gg(corresponds)29 b(to)d(a)f(term)g(gi)n(v)o(en)i(in)e(Lemma)g(3.2.2,)h(\(i\))f(and)i(\(ii\))e(are)h(by)g(routine)h(calculation)i(using)277 5159 y(the)f(induction)j(hypothesis)g(\(note)d(in)g(\(ii\))h F6(j)p Ga(M)10 b F6(j)1800 5126y Fu(s)1800 5182 y Gc(c)1835 5159 y F4([)p Ga(c)34 bF4(:=)2062 5147 y F9(\()2090 5159 y Ga(x)2142 5147 yF9(\))2169 5159 y Ga(N)10 b F4(])27 b Gg(e)o(xpands)j(to)e(a)f(cut\).)43 b(W)-7 b(e)27 b(are)h(left)g(to)277 5272 y(check)d(the)f(cases)h(where)f(the)g(top-le)n(v)o(el)h(term)f(constructor)j(of)cGa(M)33 b Gg(corresponds)28 b(to)23 b(an)h(elimination)2775385 y(rule.)p Black Black eop end%%Page: 158 170TeXDict begin 158 169 bop Black -144 51 a Gb(158)2658b(Details)24 b(f)n(or)g(some)g(Pr)n(oofs)p -144 88 36914 v Black Black 321 388 a(Case)p Black 47 w Ga(M)35 bF6(\021)25 b Ga(S)20 b(T)1004 351 y Gc(\014)940 388 yF6(\000)-31 b(\000)f(!)26 b Ga(S)1197 355 y FX(0)1235388 y Ga(T)38 b F6(\021)25 b Ga(M)1520 355 y FX(0)1566388 y Gg(with)e Ga(S)1900 351 y Gc(\014)1837 388 y F6(\000)-32b(\000)h(!)25 b Ga(S)2093 355 y FX(0)2116 388 y Gg(:)549539 y(By)k(IH)g(we)g(ha)n(v)o(e)h F6(j)p Ga(S)5 b F6(j)1252506 y Fu(s)1252 562 y Gc(c)1363 502 y(int)1324 539 yF6(\000)-31 b(\000)g(!)1494 506 y F9(+)1590 539 y F6(j)pGa(S)5 b F6(j)1701 506 y Fu(s)1701 562 y Gc(c)1766 539y Gg(and)30 b F6(j)p Ga(S)5 b F6(j)2037 506 y Fu(s)2037562 y Gc(c)2072 539 y F4([)p Ga(c)38 b F4(:=)2306 527y F9(\()2334 539 y Ga(y)2382 527 y F9(\))2409 539 y Ga(P)13b F4(])2581 502 y Gc(int)2542 539 y F6(\000)-31 b(\000)g(!)2713506 y F9(+)2808 539 y F6(j)p Ga(S)2894 506 y FX(0)2918539 y F6(j)2943 506 y Fu(s)2943 562 y Gc(c)2978 539 yF4([)p Ga(c)37 b F4(:=)3212 527 y F9(\()3240 539 y Ga(y)3288527 y F9(\))3315 539 y Ga(P)13 b F4(])29 b Gg(for)549652 y(an)o(y)22 b(substitution)j(where)d Ga(P)35 b Gg(freshly)23b(introduces)i Ga(y)f Gg(and)e(is)g(not)g(an)g(axiom.)29b(T)-7 b(ak)o(e)3174 640 y F9(\()3201 652 y Ga(y)3249640 y F9(\))3276 652 y Ga(P)35 b Gg(to)22 b(be)549 753y F9(\()576 765 y Ga(y)624 753 y F9(\))651 765 y FL(Imp)796787 y Gc(L)848 765 y F4(\()883 753 y FX(h)911 765 y Ga(b)950753 y FX(i)977 765 y F6(j)p Ga(T)13 b F6(j)1093 732 yFu(s)1093 793 y Gc(b)1128 765 y Ga(;)1168 753 y F9(\()1196765 y Ga(z)1242 753 y F9(\))1269 765 y FL(Ax)p F4(\()pGa(z)t(;)i(c)p F4(\))r Ga(;)g(y)s F4(\))p Gg(,)23 b(then)h(we)f(ha)n(v)o(e)h(the)g(follo)n(wing)h(reduction.)360 926 y(\(i\))201b F6(j)p Ga(S)20 b(T)13 b F6(j)838 893 y Fu(s)838 949y Gc(c)483 1051 y F4(=)92 b F6(j)p Ga(S)5 b F6(j)7571018 y Fu(s)757 1073 y Gc(a)799 1051 y F4([)p Ga(a)25b F4(:=)1018 1039 y F9(\()1046 1051 y Ga(y)1094 1039y F9(\))1121 1051 y FL(Imp)1266 1072 y Gc(L)1318 1051y F4(\()1353 1039 y FX(h)1381 1051 y Ga(b)1420 1039 yFX(i)1447 1051 y F6(j)p Ga(T)13 b F6(j)1563 1018 y Fu(s)15631078 y Gc(b)1598 1051 y Ga(;)1638 1039 y F9(\()1665 1051y Ga(z)1711 1039 y F9(\))1739 1051 y FL(Ax)p F4(\()pGa(z)t(;)i(c)p F4(\))q Ga(;)g(y)s F4(\))q(])872 b Gg(by)24b(\(6\))g(of)f F6(j)p 3427 1051 28 4 v 3445 1051 V 34631051 V 65 w(j)3515 1018 y Fu(s)422 1138 y Gc(int)3831175 y F6(\000)-31 b(\000)g(!)563 1142 y F9(+)646 1175y F6(j)p Ga(S)732 1142 y FX(0)755 1175 y F6(j)780 1142y Fu(s)780 1197 y Gc(a)822 1175 y F4([)p Ga(a)26 b F4(:=)10421163 y F9(\()1069 1175 y Ga(y)1117 1163 y F9(\))11441175 y FL(Imp)1289 1197 y Gc(L)1341 1175 y F4(\()13761163 y FX(h)1404 1175 y Ga(b)1443 1163 y FX(i)1470 1175y F6(j)p Ga(T)13 b F6(j)1586 1142 y Fu(s)1586 1203 yGc(b)1621 1175 y Ga(;)1661 1163 y F9(\()1689 1175 y Ga(z)17351163 y F9(\))1762 1175 y FL(Ax)p F4(\()p Ga(z)t(;)i(c)pF4(\))r Ga(;)g(y)s F4(\)])1127 b Gg(by)23 b(IH)483 1299y F4(=)92 b F6(j)p Ga(S)732 1266 y FX(0)770 1299 y Ga(T)13b F6(j)861 1266 y Fu(s)861 1322 y Gc(c)3059 1299 y Gg(by)24b(\(6\))g(of)f F6(j)p 3427 1299 V 3445 1299 V 3463 1299V 65 w(j)3515 1266 y Fu(s)549 1451 y Gg(In)g(\(ii\))h(we)f(tak)o(e)10831439 y F9(\()1110 1451 y Ga(y)1158 1439 y F9(\))11861451 y Ga(P)35 b Gg(to)24 b(be)1481 1439 y F9(\()15091451 y Ga(z)1555 1439 y F9(\))1582 1451 y FL(Imp)17271473 y Gc(L)1779 1451 y F4(\()1814 1439 y FX(h)1842 1451y Ga(b)1881 1439 y FX(i)1908 1451 y F6(j)p Ga(T)13 bF6(j)2024 1418 y Fu(s)2024 1479 y Gc(b)2059 1451 y Ga(;)20991439 y F9(\()2127 1451 y Ga(u)2179 1439 y F9(\))22061451 y FL(Ax)p F4(\()p Ga(u;)i(c)p F4(\))q Ga(;)g(z)tF4(\))q([)p Ga(c)26 b F4(:=)2844 1439 y F9(\()2872 1451y Ga(y)2920 1439 y F9(\))2947 1451 y Ga(N)10 b F4(])pGg(.)360 1612 y(\(ii\))176 b F6(j)p Ga(S)20 b(T)13 bF6(j)838 1579 y Fu(s)838 1635 y Gc(c)873 1612 y F4([)pGa(c)26 b F4(:=)1084 1600 y F9(\()1111 1612 y Ga(y)11591600 y F9(\))1186 1612 y Ga(N)10 b F4(])483 1736 y(=)92b F6(j)p Ga(S)5 b F6(j)757 1704 y Fu(s)757 1759 y Gc(a)7991736 y F4([)p Ga(a)25 b F4(:=)1018 1724 y F9(\()10461736 y Ga(z)1092 1724 y F9(\))1120 1736 y FL(Imp)12641758 y Gc(L)1316 1736 y F4(\()1351 1724 y FX(h)1379 1736y Ga(b)1418 1724 y FX(i)1445 1736 y F6(j)p Ga(T)13 bF6(j)1561 1704 y Fu(s)1561 1764 y Gc(b)1596 1736 y Ga(;)16361724 y F9(\()1664 1736 y Ga(u)1716 1724 y F9(\))17431736 y FL(Ax)p F4(\()p Ga(u;)i(c)p F4(\))q Ga(;)g(z)tF4(\))q(][)p Ga(c)27 b F4(:=)2407 1724 y F9(\()2434 1736y Ga(y)2482 1724 y F9(\))2509 1736 y Ga(N)10 b F4(])442b Gg(by)24 b(\(6\))g(of)f F6(j)p 3427 1736 V 3445 1736V 3463 1736 V 65 w(j)3515 1704 y Fu(s)483 1861 y F6(\021)92b(j)p Ga(S)5 b F6(j)757 1828 y Fu(s)757 1883 y Gc(a)7991861 y F4([)p Ga(a)25 b F4(:=)1018 1849 y F9(\()10461861 y Ga(z)1092 1849 y F9(\))1120 1861 y FL(Imp)12641883 y Gc(L)1316 1861 y F4(\()1351 1849 y FX(h)1379 1861y Ga(b)1418 1849 y FX(i)1445 1861 y F6(j)p Ga(T)13 bF6(j)1561 1828 y Fu(s)1561 1888 y Gc(b)1596 1861 y Ga(;)16361849 y F9(\()1664 1861 y Ga(u)1716 1849 y F9(\))17431861 y FL(Ax)p F4(\()p Ga(u;)i(c)p F4(\))q Ga(;)g(z)tF4(\))q([)p Ga(c)26 b F4(:=)2382 1849 y F9(\()2409 1861y Ga(y)2457 1849 y F9(\))2484 1861 y Ga(N)10 b F4(]])4221948 y Gc(int)383 1985 y F6(\000)-31 b(\000)g(!)563 1952y F9(+)646 1985 y F6(j)p Ga(S)732 1952 y FX(0)755 1985y F6(j)780 1952 y Fu(s)780 2007 y Gc(a)822 1985 y F4([)pGa(a)26 b F4(:=)1042 1973 y F9(\()1069 1985 y Ga(z)11151973 y F9(\))1143 1985 y FL(Imp)1287 2007 y Gc(L)13401985 y F4(\()1375 1973 y FX(h)1402 1985 y Ga(b)1441 1973y FX(i)1469 1985 y F6(j)p Ga(T)13 b F6(j)1585 1952 yFu(s)1585 2013 y Gc(b)1619 1985 y Ga(;)1659 1973 y F9(\()16871985 y Ga(u)1739 1973 y F9(\))1767 1985 y FL(Ax)o F4(\()pGa(u;)i(c)p F4(\))r Ga(;)g(z)t F4(\))q([)p Ga(c)26 bF4(:=)2405 1973 y F9(\()2432 1985 y Ga(y)2480 1973 yF9(\))2508 1985 y Ga(N)9 b F4(]])697 b Gg(by)23 b(IH)4832109 y F6(\021)92 b(j)p Ga(S)732 2076 y FX(0)755 2109y F6(j)780 2076 y Fu(s)780 2132 y Gc(a)822 2109 y F4([)pGa(a)26 b F4(:=)1042 2097 y F9(\()1069 2109 y Ga(z)11152097 y F9(\))1143 2109 y FL(Imp)1287 2131 y Gc(L)13402109 y F4(\()1375 2097 y FX(h)1402 2109 y Ga(b)1441 2097y FX(i)1469 2109 y F6(j)p Ga(T)13 b F6(j)1585 2076 yFu(s)1585 2137 y Gc(b)1619 2109 y Ga(;)1659 2097 y F9(\()16872109 y Ga(u)1739 2097 y F9(\))1767 2109 y FL(Ax)o F4(\()pGa(u;)i(c)p F4(\))r Ga(;)g(z)t F4(\))q(][)p Ga(c)26 bF4(:=)2430 2097 y F9(\()2458 2109 y Ga(y)2506 2097 yF9(\))2533 2109 y Ga(N)10 b F4(])483 2233 y(=)92 b F6(j)pGa(S)732 2200 y FX(0)770 2233 y Ga(T)13 b F6(j)861 2200y Fu(s)861 2256 y Gc(c)896 2233 y F4([)p Ga(c)26 b F4(:=)11072221 y F9(\()1134 2233 y Ga(y)1182 2221 y F9(\))12102233 y Ga(N)10 b F4(])1741 b Gg(by)24 b(\(6\))g(of)fF6(j)p 3427 2233 V 3445 2233 V 3463 2233 V 65 w(j)35152200 y Fu(s)p Black 321 2425 a Gb(Case)p Black 47 w Ga(M)35b F6(\021)25 b Ga(S)20 b(T)1004 2388 y Gc(\014)940 2425y F6(\000)-31 b(\000)f(!)26 b Ga(S)20 b(T)1278 2392 yFX(0)1326 2425 y F6(\021)25 b Ga(M)1520 2392 y FX(0)15662425 y Gg(with)e Ga(T)1905 2388 y Gc(\014)1841 2425 yF6(\000)-31 b(\000)g(!)25 b Ga(T)2103 2392 y FX(0)21262425 y Gg(:)549 2577 y(By)j(IH)g(we)g(ha)n(v)o(e)i F6(j)pGa(T)13 b F6(j)1254 2544 y Fu(s)1254 2599 y Gc(c)13632539 y(int)1324 2577 y F6(\000)-31 b(\000)f(!)1494 2544y F9(+)1588 2577 y F6(j)p Ga(T)13 b F6(j)1704 2544 yFu(s)1704 2599 y Gc(c)1768 2577 y Gg(and)29 b F6(j)pGa(T)13 b F6(j)2043 2544 y Fu(s)2043 2599 y Gc(c)20782577 y F4([)p Ga(c)36 b F4(:=)2309 2565 y F9(\()23362577 y Ga(y)2384 2565 y F9(\))2412 2577 y Ga(P)13 b F4(])25822539 y Gc(int)2543 2577 y F6(\000)-31 b(\000)g(!)27142544 y F9(+)2808 2577 y F6(j)p Ga(T)2899 2544 y FX(0)29222577 y F6(j)2947 2544 y Fu(s)2947 2599 y Gc(c)2982 2577y F4([)p Ga(c)36 b F4(:=)3213 2565 y F9(\()3241 2577y Ga(y)3289 2565 y F9(\))3316 2577 y Ga(P)13 b F4(])28b Gg(for)549 2689 y(an)o(y)23 b(substitution)k(where)dGa(P)36 b Gg(freshly)25 b(introduces)h Ga(y)g Gg(and)e(is)f(not)h(an)g(axiom.)360 2843 y(\(i\))201 b F6(j)p Ga(S)20 b(T)13b F6(j)838 2810 y Fu(s)838 2865 y Gc(c)483 2967 y F4(=)92b F6(j)p Ga(S)5 b F6(j)757 2934 y Fu(s)757 2989 y Gc(a)7992967 y F4([)p Ga(a)25 b F4(:=)1018 2955 y F9(\()10462967 y Ga(y)1094 2955 y F9(\))1121 2967 y FL(Imp)12662989 y Gc(L)1318 2967 y F4(\()1353 2955 y FX(h)1381 2967y Ga(b)1420 2955 y FX(i)1447 2967 y F6(j)p Ga(T)13 bF6(j)1563 2934 y Fu(s)1563 2994 y Gc(b)1598 2967 y Ga(;)16382955 y F9(\()1665 2967 y Ga(z)1711 2955 y F9(\))17392967 y FL(Ax)p F4(\()p Ga(z)t(;)i(c)p F4(\))q Ga(;)g(y)sF4(\))q(])872 b Gg(by)24 b(\(6\))g(of)f F6(j)p 3427 2967V 3445 2967 V 3463 2967 V 65 w(j)3515 2934 y Fu(s)4223054 y Gc(int)383 3091 y F6(\000)-31 b(\000)g(!)563 3058y F9(+)646 3091 y F6(j)p Ga(S)5 b F6(j)757 3058 y Fu(s)7573113 y Gc(a)799 3091 y F4([)p Ga(a)25 b F4(:=)1018 3079y F9(\()1046 3091 y Ga(y)1094 3079 y F9(\))1121 3091y FL(Imp)1266 3113 y Gc(L)1318 3091 y F4(\()1353 3079y FX(h)1381 3091 y Ga(b)1420 3079 y FX(i)1447 3091 yF6(j)p Ga(T)1538 3058 y FX(0)1561 3091 y F6(j)1586 3058y Fu(s)1586 3119 y Gc(b)1621 3091 y Ga(;)1661 3079 yF9(\()1689 3091 y Ga(z)1735 3079 y F9(\))1762 3091 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Ga(y)2474 3498 y F9(\))2501 3510 y Ga(N)10 b F4(])450b Gg(by)24 b(\(6\))g(of)f F6(j)p 3427 3510 V 3445 3510V 3463 3510 V 65 w(j)3515 3477 y Fu(s)483 3634 y F6(\021)92b(j)p Ga(S)5 b F6(j)757 3601 y Fu(s)757 3657 y Gc(a)7993634 y F4([)p Ga(a)25 b F4(:=)1018 3622 y F9(\()10463634 y Ga(y)1094 3622 y F9(\))1121 3634 y FL(Imp)12663656 y Gc(L)1318 3634 y F4(\()1353 3622 y FX(h)1381 3634y Ga(b)1420 3622 y FX(i)1447 3634 y F6(j)p Ga(T)13 bF6(j)1563 3601 y Fu(s)1563 3662 y Gc(b)1598 3634 y Ga(;)16383622 y F9(\()1665 3634 y Ga(z)1711 3622 y F9(\))17393634 y FL(Ax)p F4(\()p Ga(z)t(;)i(c)p F4(\))q Ga(;)g(y)sF4(\))q([)p Ga(c)26 b F4(:=)2373 3622 y F9(\()2401 3634y Ga(y)2449 3622 y F9(\))2476 3634 y Ga(N)10 b F4(]])4223722 y Gc(int)383 3759 y F6(\000)-31 b(\000)g(!)563 3726y F9(+)646 3759 y F6(j)p Ga(S)5 b F6(j)757 3726 y Fu(s)7573781 y Gc(a)799 3759 y F4([)p Ga(a)25 b F4(:=)1018 3747y F9(\()1046 3759 y Ga(y)1094 3747 y F9(\))1121 3759y FL(Imp)1266 3780 y Gc(L)1318 3759 y F4(\()1353 3747y FX(h)1381 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4006y F4(=)42 b FL(Ax)o F4(\()p Ga(y)s(;)15 b(a)p F4(\)[)pGa(a)27 b F4(:=)1191 3994 y F9(\()1219 4006 y Ga(z)12653994 y F9(\))1292 4006 y FL(And)1447 3969 y Gc(i)14474029 y(L)1499 4006 y F4(\()1534 3994 y F9(\()1562 4006y Ga(x)1614 3994 y F9(\))1641 4006 y F6(j)p Ga(N)10 bF6(j)1774 3973 y Fu(S)1818 4006 y Ga(;)15 b(z)t F4(\))q(])1082b Gg(by)24 b(\(1\))f(of)h F6(j)p 3415 4006 V 3433 4006V 3450 4006 V 65 w(j)3503 3973 y Fu(S)549 4125 y F4(=)42b FL(And)816 4088 y Gc(i)816 4148 y(L)869 4125 y F4(\()9044113 y F9(\()931 4125 y Ga(x)983 4113 y F9(\))1011 4125y F6(j)p Ga(N)10 b F6(j)1144 4092 y Fu(S)1188 4125 yGa(;)15 b(y)s F4(\))1019 b Gg(by)24 b(assumption)i Ga(z)jF6(62)c Ga(F)13 b(N)d F4(\()3227 4113 y F9(\()3255 4125y Ga(x)3307 4113 y F9(\))3334 4125 y F6(j)p Ga(N)g F6(j)34674092 y Fu(S)3511 4125 y F4(\))549 4243 y(=)42 b F6(j)pFL(And)842 4206 y Gc(i)842 4266 y(E)901 4243 y F4(\()9364231 y FX(h)964 4243 y Ga(a)1012 4231 y FX(i)1039 4243y FL(Id)q F4(\()p Ga(y)s(;)15 b(a)p F4(\))q 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F9(\()25704924 y Ga(x)2622 4912 y F9(\))2649 4924 y F6(j)p Ga(N)10b F6(j)2782 4891 y Fu(S)2826 4924 y Ga(;)15 b(z)t F4(\))q(\))5495043 y F6(\021)42 b FL(Cut)p F4(\()835 5031 y FX(h)8625043 y Ga(a)910 5031 y FX(i)938 5043 y FL(And)1093 5057y Gc(R)1150 5043 y F4(\()1185 5031 y FX(h)1213 5043 yGa(c)1252 5031 y FX(i)1280 5043 y F6(j)p Ga(S)5 b Fs(^)qGa(\033)s Fs(_)p F6(j)1511 5010 y Fu(S)1555 5043 y Ga(;)15955031 y FX(h)1623 5043 y Ga(d)1670 5031 y FX(i)1697 5043y F6(j)p Ga(T)13 b Fs(^)q Ga(\033)s Fs(_)q F6(j)19345010 y Fu(S)1977 5043 y Ga(;)i(a)p F4(\))q Ga(;)21415031 y F9(\()2169 5043 y Ga(z)2215 5031 y F9(\))22435043 y FL(And)2397 5006 y Gc(i)2397 5066 y(L)2449 5043y F4(\()2484 5031 y F9(\()2512 5043 y Ga(x)2564 5031y F9(\))2591 5043 y F6(j)p Ga(N)10 b F6(j)2724 5010 yFu(S)2768 5043 y Ga(;)15 b(z)t F4(\))q(\))412 b Gg(by)23b(IH)549 5161 y F4(=)42 b F6(j)p FL(And)842 5124 y Gc(i)8425184 y(E)901 5161 y F4(\()936 5149 y FX(h)964 5161 yGa(a)1012 5149 y FX(i)1039 5161 y FL(And)1194 5175 yGc(I)1234 5161 y F4(\()1269 5149 y FX(h)1297 5161 y Ga(c)13365149 y FX(i)1364 5161 y Ga(S)5 b Fs(^)p Ga(\033)s Fs(_)qGa(;)1585 5149 y FX(h)1613 5161 y Ga(d)1660 5149 y FX(i)16875161 y Ga(T)13 b Fs(^)p Ga(\033)s Fs(_)q Ga(;)i(a)p F4(\))qGa(;)2037 5149 y F9(\()2065 5161 y Ga(x)2117 5149 y F9(\))21445161 y Ga(N)10 b F4(\))p F6(j)2287 5128 y Fu(S)2933 5161y Gg(by)24 b(\(2,11\))g(of)g F6(j)p 3415 5161 V 34335161 V 3450 5161 V 65 w(j)3503 5128 y Fu(S)549 5280 yF4(=)42 b F6(j)p FL(And)842 5294 y Gc(I)882 5280 y F4(\()9175268 y FX(h)944 5280 y Ga(c)983 5268 y FX(i)1011 5280y Ga(S)5 b(;)1112 5268 y FX(h)1140 5280 y Ga(d)1187 5268y FX(i)1215 5280 y Ga(T)12 b(;)j(a)p F4(\))p Fs(^)r Ga(\033)sFs(_)p F6(j)1549 5247 y Fu(S)3076 5280 y Gg(by)24 b(\(2\))f(of)hFs(^)p 3451 5280 V 3469 5280 V 3487 5280 V 65 w(_)p 34805385 4 62 v 3484 5327 55 4 v 3484 5385 V 3538 5385 462 v Black Black eop end%%Page: 163 175TeXDict begin 163 174 bop Black 277 51 a Gb(B.2)23 b(Pr)n(oofs)h(of)g(Chapter)f(3)2639 b(163)p 277 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F9(\))25071039 y F6(j)p Ga(P)j F6(j)2628 1006 y Fu(S)2672 1039y Ga(;)i(z)t F4(\))q(\))60 b Gg(by)24 b(\(5,13\))g(of)gF6(j)p 3371 1039 28 4 v 3389 1039 V 3406 1039 V 65 w(j)34591006 y Fu(S)535 1120 y Gc(cut)504 1157 y F6(\000)-31b(\000)g(!)23 b FL(Cut)p F4(\()871 1145 y FX(h)899 1157y Ga(c)938 1145 y FX(i)966 1157 y F6(j)p Ga(N)10 b F6(j)10991124 y Fu(S)1143 1157 y Ga(;)1183 1145 y F9(\()1210 1157y Ga(x)1262 1145 y F9(\))1290 1157 y FL(Cut)p F4(\()14631145 y FX(h)1490 1157 y Ga(a)1538 1145 y FX(i)1566 1157y F6(j)p Ga(M)g F6(j)1714 1124 y Fu(S)1758 1157 y Ga(;)17981145 y F9(\()1826 1157 y Ga(y)1874 1145 y F9(\))19011157 y F6(j)p Ga(P)j F6(j)2022 1124 y Fu(S)2066 1157y F4(\)\))1575 1276 y Ga(z)27 b Gg(is)d(freshly)h(introduced)i(by)c(side-condition)28 b(\(13\))c(of)g F6(j)p 3371 1276 V3389 1276 V 3406 1276 V 65 w(j)3459 1243 y Fu(S)22321394 y Gg(and)g Ga(b)f Gg(is)h(freshly)h(introduced)h(by)33961357 y Gc(\014)3332 1394 y F6(\000)-31 b(\000)f(!)6041513 y F4(=)23 b F6(j)p FL(Subst)p F4(\()971 1501 y FX(h)9981513 y Ga(c)1037 1501 y FX(i)1065 1513 y Ga(N)10 b(;)11881501 y F9(\()1216 1513 y Ga(x)1268 1501 y F9(\))12951513 y FL(Subst)p F4(\()1543 1501 y FX(h)1570 1513 yGa(a)1618 1501 y FX(i)1646 1513 y Ga(M)g(;)1784 1501y F9(\()1812 1513 y Ga(y)1860 1501 y F9(\))1887 1513y Ga(P)j F4(\)\))p F6(j)2053 1480 y Fu(S)3003 1513 yGg(by)24 b(\(2\))f(of)h F6(j)p 3371 1513 V 3389 1513V 3406 1513 V 65 w(j)3459 1480 y Fu(S)p Black 277 1713a Gb(Commuting)e(Reduction:)p Black 504 1850 a FL(And)6591813 y Gc(i)659 1873 y(E)719 1850 y F4(\()754 1838 yFX(h)781 1850 y Ga(a)829 1838 y FX(i)857 1850 y Ga(M)10b(;)995 1838 y F9(\()1023 1850 y Ga(x)1075 1838 y F9(\))11021850 y Ga(N)g F4(\))1311 1813 y Gc(\015)1246 1850 y F6(\000)-31b(\000)f(!)25 b Ga(M)10 b Fs(^)q FL(And)1726 1813 y Gc(i)17261873 y(E)1786 1850 y F4(\()1821 1838 y FX(h)1849 1850y Ga(a)1897 1838 y FX(i)p 1926 1850 V 1944 1850 V 19621850 V 1989 1850 a Ga(;)2029 1838 y F9(\()2057 1850 yGa(x)2109 1838 y F9(\))2136 1850 y Ga(N)g F4(\))p Fs(_)7172011 y F6(j)p FL(And)897 1974 y Gc(i)897 2034 y(E)9572011 y F4(\()992 1999 y FX(h)1019 2011 y Ga(a)1067 1999y FX(i)1095 2011 y Ga(M)g(;)1233 1999 y F9(\()1261 2011y Ga(x)1313 1999 y F9(\))1340 2011 y Ga(N)g F4(\))p F6(j)14831978 y Fu(S)604 2130 y F4(=)42 b FL(Cut)p F4(\()890 2118y FX(h)918 2130 y Ga(a)966 2118 y FX(i)993 2130 y F6(j)pGa(M)10 b F6(j)1141 2097 y Fu(S)1185 2130 y Ga(;)12252118 y F9(\()1253 2130 y Ga(z)1299 2118 y F9(\))13272130 y FL(And)1481 2093 y Gc(i)1481 2153 y(L)1534 2130y F4(\()1569 2118 y F9(\()1596 2130 y Ga(x)1648 2118y F9(\))1676 2130 y F6(j)p Ga(N)g F6(j)1809 2097 y Fu(S)18532130 y Ga(;)15 b(z)t F4(\))q(\))947 b Gg(by)24 b(\(11\))g(of)gF6(j)p 3371 2130 V 3389 2130 V 3406 2130 V 65 w(j)34592097 y Fu(S)535 2211 y Gc(cut)504 2248 y F6(\000)-31b(\000)g(!)42 b(j)p Ga(M)10 b F6(j)865 2215 y Fu(S)9092248 y F4([)p Ga(a)26 b F4(:=)1129 2236 y F9(\()11562248 y Ga(z)1202 2236 y F9(\))1230 2248 y FL(And)13852211 y Gc(i)1385 2271 y(L)1437 2248 y F4(\()1472 2236y F9(\()1500 2248 y Ga(x)1552 2236 y F9(\))1579 2248y F6(j)p Ga(N)10 b F6(j)1712 2215 y Fu(S)1756 2248 yGa(;)15 b(z)t F4(\))q(])335 b Ga(a)23 b Gg(is)h(not)g(freshly)h(introduced)h(by)3397 2211 y Gc(\015)3332 2248 y F6(\000)-31b(\000)f(!)604 2367 y(\021)42 b(j)p Ga(M)10 b Fs(^)qFL(And)1028 2330 y Gc(i)1028 2390 y(E)1087 2367 y F4(\()11222355 y FX(h)1150 2367 y Ga(a)1198 2355 y FX(i)p 12282367 V 1245 2367 V 1263 2367 V 1290 2367 a Ga(;)13302355 y F9(\()1358 2367 y Ga(x)1410 2355 y F9(\))14372367 y Ga(N)g F4(\))p Fs(_)q F6(j)1613 2334 y Fu(S)29062367 y Gg(by)24 b(Lemma)e(3.4.3)p Black 277 2567 a Gb(Substitution)h(Elimination:)p Black 504 2704 a FL(Subst)p F4(\()7522692 y FX(h)779 2704 y Ga(a)827 2692 y FX(i)855 2704y Ga(M)10 b(;)993 2692 y F9(\()1021 2704 y Ga(x)10732692 y F9(\))1100 2704 y Ga(N)g F4(\))1382 2667 y Gc(\033)13182704 y F6(\000)-31 b(\000)f(!)100 b Ga(M)10 b Fs(\()-7b Ga(a)26 b F4(:=)1906 2692 y F9(\()1933 2704 y Ga(x)19852692 y F9(\))2013 2704 y Ga(N)s Fs(\))717 2880 y 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y F9(\()1240 4727y Ga(z)1286 4715 y F9(\))1314 4727 y FL(And)1469 4691y Gc(i)1469 4750 y(L)1521 4727 y F4(\()1556 4715 y F9(\()15844727 y Ga(x)1636 4715 y F9(\))1663 4727 y F6(j)p Ga(T)13b F6(j)1779 4694 y Fu(S)1823 4727 y Ga(;)i(z)t F4(\))q(\))977b Gg(by)24 b(\(11\))g(of)g F6(j)p 3371 4727 V 3389 4727V 3406 4727 V 65 w(j)3459 4694 y Fu(S)550 4809 y Gc(cut)5204846 y F6(\000)-32 b(\000)h(!)690 4813 y FX(\003)7414846 y FL(Cut)p F4(\()914 4834 y FX(h)942 4846 y Ga(a)9904834 y FX(i)1018 4846 y F6(j)p Ga(S)1104 4813 y FX(0)11274846 y F6(j)1152 4813 y Fu(S)1196 4846 y Ga(;)1236 4834y F9(\()1264 4846 y Ga(z)1310 4834 y F9(\))1337 4846y FL(And)1492 4809 y Gc(i)1492 4869 y(L)1544 4846 y F4(\()15794834 y F9(\()1607 4846 y Ga(x)1659 4834 y F9(\))16864846 y F6(j)p Ga(T)13 b F6(j)1802 4813 y Fu(S)1846 4846y Ga(;)i(z)t F4(\))q(\))1290 b Gg(by)23 b(IH)559 4927y Gc(cut)529 4964 y F6(\000)-32 b(\000)h(!)42 b FL(And)8964928 y Gc(i)896 4988 y(L)948 4964 y F4(\()983 4952 yF9(\()1011 4964 y Ga(x)1063 4952 y F9(\))1090 4964 yF6(j)p Ga(T)13 b F6(j)1206 4931 y Fu(S)1250 4964 y Ga(;)i(z)tF4(\)[)p Ga(z)f F6(7!)c Ga(y)s F4(])628 5083 y F6(\021)42b FL(And)896 5046 y Gc(i)896 5106 y(L)948 5083 y F4(\()9835071 y F9(\()1011 5083 y Ga(x)1063 5071 y F9(\))10905083 y F6(j)p Ga(T)13 b F6(j)1206 5050 y Fu(S)1250 5083y Ga(;)i(y)s F4(\))1020 b Ga(z)30 b F6(62)24 b Ga(F)13b(N)d F4(\()p F6(j)p Ga(T)j F6(j)2855 5050 y Fu(S)28995083 y F4(\))23 b Gg(by)h(\(11\))g(of)g F6(j)p 3371 5083V 3389 5083 V 3406 5083 V 65 w(j)3459 5050 y Fu(S)6285202 y F4(=)42 b F6(j)p FL(And)921 5165 y Gc(i)921 5225y(E)981 5202 y F4(\()1016 5190 y FX(h)1044 5202 y Ga(a)10925190 y FX(i)1119 5202 y FL(Id)p F4(\()p Ga(y)s(;)15 b(a)pF4(\))q Ga(;)1438 5190 y F9(\()1466 5202 y Ga(x)15185190 y F9(\))1546 5202 y Ga(T)d F4(\))p F6(j)1671 5169y Fu(S)1741 5202 y F6(\021)25 b(j)p Ga(N)10 b F6(j)19705169 y Fu(S)3003 5202 y Gg(by)24 b(\(7\))f(of)h F6(j)p3371 5202 V 3389 5202 V 3406 5202 V 65 w(j)3459 5169y Fu(S)p 3436 5307 4 62 v 3440 5249 55 4 v 3440 5307V 3494 5307 4 62 v Black Black eop end%%Page: 164 176TeXDict begin 164 175 bop Black -144 51 a Gb(164)2658b(Details)24 b(f)n(or)g(some)g(Pr)n(oofs)p -144 88 36914 v Black Black 321 412 a(Pr)n(oof)i(of)f(Lemma)f(3.4.6.)pBlack 34 w Gg(The)h(cases)h(corresponding)j(to)c(the)g(clauses)i(\(1\)\226\(5\))g(and)f(\(14\))f(of)g F6(j)p 3404 41228 4 v 3422 412 V 3440 412 V 65 w(j)3492 379 y Fu(N)321525 y Gg(are)j(routine.)43 b(Belo)n(w)27 b(we)f(gi)n(v)o(e)i(the)g(details)h(for)f(the)g(clauses)h(\(6\))f(and)g(\(10\).)41b(Let)27 b F4([)p Ga(\033)s F4(])h Gg(and)g Fs(\()p Ga(\033)sFs(\))3380 483 y Fu(N)3461 525 y Gg(be)321 638 y F4([)pGa(x)e F4(:=)545 626 y FX(h)572 638 y Ga(a)620 626 yFX(i)648 638 y Ga(N)10 b F4(])23 b Gg(and)h Fs(\()-7b Ga(x)25 b F4(:=)1157 626 y FX(h)1184 638 y Ga(a)1232626 y FX(i)1260 638 y F6(j)p Ga(N)10 b F6(j)1393 605y Fu(N)1440 638 y Fs(\))p Gg(,)23 b(respecti)n(v)o(ely)-6b(.)p Black 321 907 a Gb(Case)p Black 47 w Ga(M)35 bF6(\021)25 b FL(And)927 870 y Gc(i)927 930 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F4(\))1328 b Gg(by)24 b(\(10\))g(of)f F6(j)p 3404 1312V 3422 1312 V 3440 1312 V 65 w(j)3492 1279 y Fu(N)5491435 y F6(\021)54 b FL(And)828 1398 y Gc(i)828 1458 y(E)8881435 y F4(\()923 1423 y FX(h)951 1435 y Ga(a)999 1423y FX(i)1026 1435 y F6(j)p Ga(N)10 b F6(j)1159 1402 yFu(N)1213 1435 y Ga(;)1253 1423 y F9(\()1281 1435 y Ga(y)13291423 y F9(\))1357 1435 y F6(j)p Ga(S)5 b F6(j)1468 1402y Fu(N)1522 1435 y Fs(\()q Ga(\033)s Fs(\))1642 1393y Fu(N)1696 1435 y F4(\))1606 b Gg(by)23 b(IH)549 1559y F6(\021)54 b FL(And)828 1522 y Gc(i)828 1582 y(E)8881559 y F4(\()923 1547 y FX(h)951 1559 y Ga(a)999 1547y FX(i)1026 1559 y FL(Id)p F4(\()p Ga(x;)15 b(a)p F4(\))pFs(\()r Ga(\033)s Fs(\))1430 1517 y Fu(N)1483 1559 yGa(;)1523 1547 y F9(\()1551 1559 y Ga(y)1599 1547 y F9(\))16271559 y F6(j)p Ga(S)5 b F6(j)1738 1526 y Fu(N)1792 1559y Fs(\()q Ga(\033)s Fs(\))1912 1517 y Fu(N)1966 1559y F4(\))549 1682 y(=)54 b FL(And)828 1646 y Gc(i)8281705 y(E)888 1682 y F4(\()923 1670 y FX(h)951 1682 yGa(a)999 1670 y 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2409 y Fu(N)1706 2442y F4(\))1250 b Gg(by)24 b(\(10\))g(of)f F6(j)p 3404 2442V 3422 2442 V 3440 2442 V 65 w(j)3492 2409 y Fu(N)5492566 y F6(\021)54 b FL(And)828 2529 y Gc(i)828 2589 y(E)8882566 y F4(\()923 2554 y FX(h)951 2566 y Ga(b)990 2554y FX(i)1017 2566 y F6(j)p Ga(S)5 b F6(j)1128 2533 y Fu(N)11822566 y Fs(\()q Ga(\033)s Fs(\))1303 2524 y Fu(N)13572566 y Ga(;)1397 2554 y F9(\()1424 2566 y Ga(z)1470 2554y F9(\))1498 2566 y F6(j)p Ga(T)13 b F6(j)1614 2533 yFu(N)1668 2566 y Fs(\()q Ga(\033)s Fs(\))1788 2524 yFu(N)1842 2566 y F4(\))1460 b Gg(by)23 b(IH)549 2689y F4(=)54 b FL(And)828 2652 y Gc(i)828 2712 y(E)888 2689y F4(\()923 2677 y FX(h)951 2689 y Ga(b)990 2677 y FX(i)10172689 y F6(j)p Ga(S)5 b F6(j)1128 2656 y Fu(N)1182 2689y Ga(;)1222 2677 y F9(\()1250 2689 y Ga(z)1296 2677 yF9(\))1324 2689 y F6(j)p Ga(T)13 b F6(j)1440 2656 y Fu(N)14942689 y F4(\))p Fs(\()q Ga(\033)s Fs(\))1650 2647 y Fu(N)5492813 y F4(=)54 b F6(j)p FL(Cut)p F4(\()872 2801 y FX(h)9002813 y Ga(b)939 2801 y FX(i)966 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3244 y Ga(P)13 b(;)i(x)pF4(\))q(])38 b Gg(and)321 3356 y Fs(^)q FL(And)508 3320y Gc(i)508 3380 y(E)568 3356 y F4(\()603 3344 y FX(h)6313356 y Ga(a)679 3344 y FX(i)p 708 3356 28 4 v 726 3356V 743 3356 V 771 3356 a Ga(;)811 3344 y F9(\()839 3356y Ga(y)887 3344 y F9(\))914 3356 y F6(j)p Ga(P)13 b F6(j)10353323 y Fu(N)1089 3356 y F4(\))p Fs(_)q Gg(,)23 b(respecti)n(v)o(ely)-6b(.)p Black 321 3593 a Gb(Case)p Black 47 w Ga(M)35 bF6(\021)25 b FL(And)927 3607 y Gc(R)985 3593 y F4(\()10203581 y FX(h)1048 3593 y Ga(d)1095 3581 y FX(i)1123 3593y Ga(S)5 b(;)1224 3581 y FX(h)1252 3593 y Ga(e)1294 3581y FX(i)1321 3593 y Ga(T)13 b(;)i(a)p F4(\))813 3765 yF6(j)p FL(And)992 3779 y Gc(R)1050 3765 y F4(\()10853753 y FX(h)1113 3765 y Ga(d)1160 3753 y FX(i)1188 3765y Ga(S)5 b(;)1289 3753 y FX(h)1316 3765 y Ga(e)1358 3753y FX(i)1386 3765 y Ga(T)13 b(;)i(a)p F4(\))p F6(j)16003732 y Fu(N)1655 3765 y Fs(^)q Ga(\033)s Fs(_)1775 3723y Fu(N)648 3890 y F4(=)94 b FL(And)967 3904 y Gc(I)10073890 y F4(\()1042 3878 y 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4621 y F4(\()1484 4609y F9(\()1512 4621 y Ga(u)1564 4609 y F9(\))1592 4621y Ga(T)12 b(;)j(z)t F4(\))q(\))813 4794 y F6(j)p FL(Cut)pF4(\()1011 4782 y FX(h)1039 4794 y Ga(b)1078 4782 y FX(i)11054794 y Ga(S)5 b(;)1206 4782 y F9(\()1234 4794 y Ga(z)12804782 y F9(\))1308 4794 y FL(And)1462 4757 y Gc(i)14624817 y(L)1514 4794 y F4(\()1549 4782 y F9(\()1577 4794y Ga(u)1629 4782 y F9(\))1657 4794 y Ga(T)12 b(;)j(z)tF4(\))q(\))p F6(j)1904 4761 y Fu(N)1959 4794 y Fs(^)pGa(\033)s Fs(_)2079 4752 y Fu(N)648 4919 y F4(=)94 bFL(And)967 4882 y Gc(i)967 4942 y(E)1027 4919 y F4(\()10624907 y FX(h)1090 4919 y Ga(b)1129 4907 y FX(i)1156 4919y F6(j)p Ga(S)5 b F6(j)1267 4886 y Fu(N)1321 4919 y Ga(;)13614907 y F9(\()1389 4919 y Ga(u)1441 4907 y F9(\))14694919 y F6(j)p Ga(T)13 b F6(j)1585 4886 y Fu(N)1639 4919y F4(\))p Fs(^)q Ga(\033)s Fs(_)1794 4877 y Fu(N)29914919 y Gg(by)24 b(\(10\))g(of)f F6(j)p 3404 4919 V 34224919 V 3440 4919 V 65 w(j)3492 4886 y Fu(N)648 5045 yF4(=)94 b FL(And)967 5008 y Gc(i)967 5068 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Gc(i)1745 870 y(E)1805 847 y F4(\()1840 835 y FX(h)1868847 y Ga(a)1916 835 y FX(i)1943 847 y FL(Id)q F4(\()pGa(z)t(;)15 b(a)p F4(\))q Ga(;)2261 835 y F9(\()2289847 y Ga(y)2337 835 y F9(\))2364 847 y F6(j)p Ga(P)eF6(j)2485 814 y Fu(N)2540 847 y F4(\)\))422 b Gg(by)24b(\(1\))f(of)h Fs(^)p 3407 847 V 3425 847 V 3442 847V 65 w(_)569 934 y Gc(\024)504 971 y F6(\000)-31 b(\000)g(!)686938 y FX(\003)768 971 y FL(Subst)p F4(\()1016 959 y FX(h)1043971 y Ga(b)1082 959 y FX(i)1110 971 y F6(j)p Ga(S)5 bF4([)p Ga(\033)s F4(])p F6(j)1326 938 y Fu(N)1381 971y Ga(;)1421 959 y F9(\()1449 971 y Ga(z)1495 959 y F9(\))1523971 y FL(And)1677 934 y Gc(i)1677 994 y(E)1737 971 yF4(\()1772 959 y FX(h)1799 971 y Ga(a)1847 959 y FX(i)1875971 y FL(Id)p F4(\()p Ga(z)t(;)15 b(a)p F4(\))r Ga(;)2193959 y F9(\()2220 971 y Ga(y)2268 959 y F9(\))2296 971y F6(j)p Ga(P)e F6(j)2417 938 y Fu(N)2471 971 y F4(\))q(\))751b Gg(by)23 b(IH)569 1058 y Gc(\024)504 1095 y F6(\000)-31b(\000)g(!)93 b FL(And)923 1058 y Gc(i)923 1118 y(E)9831095 y F4(\()1018 1083 y FX(h)1045 1095 y Ga(b)1084 1083y FX(i)1112 1095 y F6(j)p Ga(S)5 b F4([)p Ga(\033)s F4(])pF6(j)1328 1062 y Fu(N)1383 1095 y Ga(;)1423 1083 y F9(\()14511095 y Ga(y)1499 1083 y F9(\))1526 1095 y F6(j)p Ga(P)13b F6(j)1647 1062 y Fu(N)1702 1095 y F4(\))839 b Ga(z)30b F6(62)24 b Ga(F)13 b(N)d F4(\()2922 1083 y F9(\()29501095 y Ga(y)2998 1083 y F9(\))3026 1095 y F6(j)p Ga(P)jF6(j)3147 1062 y Fu(N)3201 1095 y F4(\))23 b Gg(by)hFs(^)p 3407 1095 V 3425 1095 V 3442 1095 V 65 w(_)6041220 y F4(=)93 b F6(j)p FL(Cut)q F4(\()967 1208 y FX(h)9941220 y Ga(b)1033 1208 y FX(i)1061 1220 y Ga(S)5 b F4([)pGa(\033)s F4(])q Ga(;)1268 1208 y F9(\()1295 1220 y Ga(x)13471208 y F9(\))1375 1220 y FL(And)1529 1183 y Gc(i)15291243 y(L)1581 1220 y F4(\()1616 1208 y F9(\()1644 1220y Ga(y)1692 1208 y F9(\))1720 1220 y Ga(P)13 b(;)i(x)pF4(\)\))p F6(j)1978 1187 y Fu(N)2947 1220 y Gg(by)24b(\(10\))g(of)f F6(j)p 3360 1220 V 3378 1220 V 3396 1220V 65 w(j)3448 1187 y Fu(N)604 1344 y F4(=)93 b 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Gb(Logical)25b(Cut)d Fb(\033)882 2907 y Fy(R)948 2893 y FO(=)p Fb(\033)10812907 y Fy(L)1139 2893 y Gb(:)p Black 598 3046 a Ga(M)36b F6(\021)f FL(Cut)p F4(\()1001 3034 y FX(h)1029 3046y Ga(b)1068 3034 y FX(i)1095 3046 y FL(Imp)1239 3068y Gc(R)1297 3046 y F4(\()1332 3034 y F9(\()1360 3046y Ga(x)1412 3034 y F9(\))p FX(h)1467 3046 y Ga(a)15153034 y FX(i)1542 3046 y Ga(S)5 b(;)15 b(b)p F4(\))q Ga(;)17583034 y F9(\()1786 3046 y Ga(z)1832 3034 y F9(\))18603046 y FL(Imp)2004 3068 y Gc(L)2056 3046 y F4(\()20913034 y FX(h)2119 3046 y Ga(c)2158 3034 y FX(i)2186 3046y Ga(T)e(;)2292 3034 y F9(\()2319 3046 y Ga(y)2367 3034y F9(\))2395 3046 y Ga(P)g(;)i(z)t F4(\))q(\))859 3122y Gc(cut)828 3159 y F6(\000)-31 b(\000)f(!)25 b FL(Cut)pF4(\()1196 3147 y FX(h)1224 3159 y Ga(c)1263 3147 y FX(i)12913159 y Ga(T)13 b(;)1397 3147 y F9(\()1424 3159 y Ga(x)14763147 y F9(\))1504 3159 y FL(Cut)p F4(\()1677 3147 y FX(h)17053159 y Ga(a)1753 3147 y FX(i)1780 3159 y Ga(S)5 b(;)18813147 y F9(\()1909 3159 y Ga(y)1957 3147 y F9(\))19843159 y Ga(P)13 b F4(\)\))26 b F6(\021)f Ga(N)771 3324y F6(j)p FL(Cut)p F4(\()969 3312 y FX(h)997 3324 y Ga(b)10363312 y FX(i)1063 3324 y FL(Imp)1208 3346 y Gc(R)12653324 y F4(\()1300 3312 y F9(\()1328 3324 y Ga(x)13803312 y F9(\))q FX(h)1435 3324 y Ga(a)1483 3312 y FX(i)15103324 y Ga(S)5 b(;)15 b(b)p F4(\))q Ga(;)1726 3312 y F9(\()17543324 y Ga(z)1800 3312 y F9(\))1828 3324 y FL(Imp)19723346 y Gc(L)2024 3324 y F4(\()2059 3312 y FX(h)2087 3324y Ga(c)2126 3312 y FX(i)2154 3324 y Ga(T)e(;)2260 3312y F9(\()2288 3324 y Ga(y)2336 3312 y F9(\))2363 3324y Ga(P)g(;)i(z)t F4(\))q(\))p F6(j)2616 3291 y Fu(N)6483448 y F4(=)52 b FL(Imp)915 3470 y Gc(E)975 3448 y F4(\()10103436 y FX(h)1038 3448 y Ga(b)1077 3436 y FX(i)1104 3448y FL(Imp)1249 3470 y Gc(I)1288 3448 y F4(\()1323 3436y F9(\()1351 3448 y Ga(x)1403 3436 y F9(\))q FX(h)14583448 y Ga(a)1506 3436 y FX(i)1534 3448 y F6(j)p Ga(S)5b F6(j)1645 3415 y Fu(N)1699 3448 y Ga(;)15 b(b)p F4(\))qGa(;)1854 3436 y FX(h)1882 3448 y Ga(c)1921 3436 y FX(i)19483448 y F6(j)p Ga(T)e F6(j)2064 3415 y Fu(N)2119 3448y Ga(;)2159 3436 y F9(\()2187 3448 y Ga(y)2235 3436 yF9(\))2262 3448 y F6(j)p Ga(P)g F6(j)2383 3415 y Fu(N)24373448 y F4(\))451 b Gg(by)23 b(\(4,12\))i(of)e F6(j)p3404 3448 V 3422 3448 V 3440 3448 V 65 w(j)3492 3415y Fu(N)613 3535 y Gc(\024)549 3572 y F6(\000)-32 b(\000)h(!)52b FL(Subst)o F4(\()1018 3560 y FX(h)1046 3572 y Ga(c)10853560 y FX(i)1113 3572 y F6(j)p Ga(N)10 b F6(j)1246 3539y Fu(N)1300 3572 y Ga(;)1340 3560 y F9(\()1368 3572 yGa(x)1420 3560 y F9(\))1447 3572 y FL(Subst)o F4(\()16943560 y FX(h)1722 3572 y Ga(a)1770 3560 y FX(i)1798 3572y F6(j)p Ga(M)g F6(j)1946 3539 y Fu(N)2000 3572 y Ga(;)20403560 y F9(\()2068 3572 y Ga(y)2116 3560 y F9(\))21433572 y F6(j)p Ga(P)j F6(j)2264 3539 y Fu(N)2319 3572y F4(\)\))42 b Ga(b)22 b Gg(is)i(freshly)h(introduced)h(by)34073535 y Gc(cut)3376 3572 y F6(\000)-31 b(\000)f(!)5493715 y Gg(Again)33 b(we)g(ha)n(v)o(e)h(tw)o(o)f(subcases)j(depending)g(on)e(whether)g Ga(P)46 b Gg(freshly)35 b(introduces)hGa(x)p Gg(,)f(b)n(ut)549 3828 y(is)f(not)h(an)g(axiom.)62b(In)35 b(this)g(case,)j(we)33 b(reason)j(analogous)i(as)c(in)h(the)g(case)g(gi)n(v)o(en)g(abo)o(v)o(e.)549 3941 y(Otherwise)24b(by)g(\(14\))g(of)f F6(j)p 1358 3941 V 1376 3941 V 13943941 V 65 w(j)1446 3908 y Fu(N)1500 3941 y Gg(:)p BlackBlack 1323 4154 a FL(Subst)o F4(\()1570 4142 y FX(h)15984154 y Ga(c)1637 4142 y FX(i)1665 4154 y F6(j)p Ga(N)10b F6(j)1798 4121 y Fu(N)1852 4154 y Ga(;)1892 4142 yF9(\()1920 4154 y Ga(x)1972 4142 y F9(\))2000 4154 yFL(Subst)o F4(\()2247 4142 y FX(h)2275 4154 y Ga(a)23234142 y FX(i)2350 4154 y F6(j)p Ga(M)g F6(j)2498 4121y Fu(N)2553 4154 y Ga(;)2593 4142 y F9(\()2621 4154 yGa(y)2669 4142 y F9(\))2696 4154 y F6(j)p Ga(P)j F6(j)28174121 y Fu(N)2871 4154 y F4(\))q(\))1153 4267 y(=)99 bF6(j)p FL(Cut)p F4(\()1521 4255 y FX(h)1549 4267 y Ga(c)15884255 y FX(i)1616 4267 y Ga(N)10 b(;)1739 4255 y F9(\()17674267 y Ga(x)1819 4255 y F9(\))1846 4267 y FL(Cut)p F4(\()20194255 y FX(h)2047 4267 y Ga(a)2095 4255 y FX(i)2122 4267y Ga(M)g(;)2260 4255 y F9(\()2288 4267 y Ga(y)2336 4255y F9(\))2364 4267 y Ga(P)j F4(\)\))p F6(j)2530 4234 yFu(N)2610 4267 y F6(\021)25 b(j)p Ga(N)10 b F6(j)28394234 y Fu(N)p Black 321 4474 a Gb(Commuting)23 b(Cut:)pBlack 549 4629 a Ga(M)35 b F6(\021)25 b FL(Cut)p F4(\()9414617 y FX(h)969 4629 y Ga(a)1017 4617 y FX(i)1044 4629y Ga(S)5 b(;)1145 4617 y F9(\()1173 4629 y Ga(x)12254617 y F9(\))1252 4629 y Ga(T)13 b F4(\))1409 4592 yGc(cut)1379 4629 y F6(\000)-32 b(\000)h(!)25 b Ga(S)5b F4([)p Ga(a)26 b F4(:=)1855 4617 y F9(\()1882 4629y Ga(x)1934 4617 y F9(\))1962 4629 y Ga(T)13 b F4(])25b F6(\021)g Ga(N)549 4778 y Gg(If)33 b(one)g(of)h(the)f(clauses)i(\(10\22613\))h(applies)f(to)e Ga(M)10 b Gg(,)35 b(then)f(we)e(ha)n(v)o(e)i(for)g(e)o(xample)g(for)f Ga(T)57 b F6(\021)549 4890y FL(And)703 4854 y Gc(i)703 4914 y(L)755 4890 y F4(\()7904878 y F9(\()818 4890 y Ga(y)866 4878 y F9(\))893 4890y Ga(P)13 b(;)i(x)p F4(\))810 5045 y F6(j)p FL(Cut)pF4(\()1008 5033 y FX(h)1036 5045 y Ga(a)1084 5033 y FX(i)11125045 y Ga(S)5 b(;)1213 5033 y F9(\()1240 5045 y Ga(x)12925033 y F9(\))1320 5045 y FL(And)1474 5008 y Gc(i)14745068 y(L)1527 5045 y F4(\()1562 5033 y F9(\()1589 5045y Ga(y)1637 5033 y F9(\))1665 5045 y Ga(P)13 b(;)i(x)pF4(\)\))p F6(j)1923 5012 y Fu(N)648 5169 y F4(=)91 bFL(And)965 5132 y Gc(i)965 5192 y(E)1024 5169 y F4(\()10595157 y FX(h)1087 5169 y Ga(a)1135 5157 y FX(i)1163 5169y F6(j)p Ga(S)5 b F6(j)1274 5136 y Fu(N)1328 5169 y Ga(;)13685157 y F9(\()1396 5169 y Ga(y)1444 5157 y F9(\))14715169 y F6(j)p Ga(P)13 b F6(j)1592 5136 y Fu(N)1647 5169y F4(\))1309 b Gg(by)24 b(\(10\))g(of)f F6(j)p 3404 5169V 3422 5169 V 3440 5169 V 65 w(j)3492 5136 y Fu(N)6135256 y Gc(\024)549 5293 y F6(\000)-32 b(\000)h(!)91 b(j)pGa(S)5 b F6(j)921 5260 y Fu(N)976 5293 y Fs(^)p FL(And)11635256 y Gc(i)1163 5316 y(E)1222 5293 y F4(\()1257 5281y FX(h)1285 5293 y Ga(a)1333 5281 y FX(i)p 1363 5293V 1380 5293 V 1398 5293 V 1425 5293 a Ga(;)1465 5281y F9(\()1493 5293 y Ga(y)1541 5281 y F9(\))1568 5293y F6(j)p Ga(P)13 b F6(j)1689 5260 y Fu(N)1744 5293 yF4(\))p Fs(_)613 5380 y Gc(\024)549 5417 y F6(\000)-32b(\000)h(!)728 5384 y FX(\003)810 5417 y F6(j)p Ga(S)5b F4([)p Ga(a)26 b F4(:=)1116 5405 y F9(\()1144 5417y Ga(x)1196 5405 y F9(\))1223 5417 y Ga(T)13 b F4(])pF6(j)1339 5384 y Fu(N)1419 5417 y F6(\021)25 b(j)p Ga(N)10b F6(j)1648 5384 y Fu(N)2950 5417 y Gg(by)24 b(Lemma)f(3.4.7)pBlack Black eop end%%Page: 167 179TeXDict begin 167 178 bop Black 277 51 a Gb(B.3)23 b(Pr)n(oofs)h(of)g(Chapter)f(4)2639 b(167)p 277 88 3691 4 v Black 504 412a Gg(Otherwise)25 b(we)d(ha)n(v)o(e)727 545 y F6(j)pFL(Cut)p F4(\()925 533 y FX(h)953 545 y Ga(a)1001 533y FX(i)1028 545 y Ga(S)5 b(;)1129 533 y F9(\()1157 545y Ga(x)1209 533 y F9(\))1236 545 y Ga(T)13 b F4(\))pF6(j)1362 512 y Fu(N)604 670 y F4(=)52 b FL(Subst)o F4(\()974658 y FX(h)1002 670 y Ga(a)1050 658 y FX(i)1077 670 yF6(j)p Ga(S)5 b F6(j)1188 637 y Fu(N)1242 670 y Ga(;)1282658 y F9(\()1310 670 y Ga(x)1362 658 y F9(\))1390 670y F6(j)p Ga(T)13 b F6(j)1506 637 y Fu(N)1560 670 y F4(\))1352b Gg(by)24 b(\(14\))g(of)f F6(j)p 3360 670 28 4 v 3378670 V 3396 670 V 65 w(j)3448 637 y Fu(N)569 757 y Gc(\024)504794 y F6(\000)-31 b(\000)g(!)52 b(j)p Ga(S)5 b F6(j)838761 y Fu(N)892 794 y Fs(\()-7 b Ga(a)26 b F4(:=)1112782 y F9(\()1139 794 y Ga(x)1191 782 y F9(\))1219 794y F6(j)p Ga(T)13 b F6(j)1335 761 y Fu(N)1382 794 y Fs(\))604918 y F6(\021)52 b(j)p Ga(S)5 b F4([)p Ga(a)25 b F4(:=)1033906 y F9(\()1060 918 y Ga(x)1112 906 y F9(\))1139 918y Ga(T)13 b F4(])p F6(j)1255 885 y Fu(N)2906 918 y Gg(by)24b(Lemma)e(3.4.8)504 1080 y Ga(M)36 b F6(\021)25 b FL(Cut)pF4(\()897 1068 y FX(h)924 1080 y Ga(a)972 1068 y FX(i)10001080 y Ga(S)5 b(;)1101 1068 y F9(\()1129 1080 y Ga(x)11811068 y F9(\))1208 1080 y Ga(T)13 b F4(\))1365 1042 yGc(cut)1334 1079 y F6(\000)-31 b(\000)g(!)1530 1080 yGa(T)13 b F4([)p Ga(x)25 b F4(:=)1819 1068 y FX(h)18471080 y Ga(a)1895 1068 y FX(i)1922 1080 y Ga(S)5 b F4(])26b F6(\021)f Ga(N)727 1246 y F6(j)p FL(Cut)p F4(\()9251234 y FX(h)953 1246 y Ga(a)1001 1234 y FX(i)1028 1246y Ga(S)5 b(;)1129 1234 y F9(\()1157 1246 y Ga(x)12091234 y F9(\))1236 1246 y Ga(T)13 b F4(\))p F6(j)13621213 y Fu(N)604 1370 y F4(=)52 b FL(Subst)o F4(\()9741358 y FX(h)1002 1370 y Ga(a)1050 1358 y FX(i)1077 1370y F6(j)p Ga(S)5 b F6(j)1188 1337 y Fu(N)1242 1370 y Ga(;)12821358 y F9(\()1310 1370 y Ga(x)1362 1358 y F9(\))13901370 y F6(j)p Ga(T)13 b F6(j)1506 1337 y Fu(N)1560 1370y F4(\))1352 b Gg(by)24 b(\(14\))g(of)f F6(j)p 3360 1370V 3378 1370 V 3396 1370 V 65 w(j)3448 1337 y Fu(N)5691457 y Gc(\024)504 1494 y F6(\000)-31 b(\000)g(!)52 b(j)pGa(T)13 b F6(j)843 1461 y Fu(N)897 1494 y Fs(\()-7 bGa(x)25 b F4(:=)1121 1482 y FX(h)1148 1494 y Ga(a)11961482 y FX(i)1224 1494 y F6(j)p Ga(S)5 b F6(j)1335 1461y Fu(N)1382 1494 y Fs(\))604 1618 y F6(\021)52 b(j)pGa(T)13 b F4([)p Ga(x)25 b F4(:=)1041 1606 y FX(h)10691618 y Ga(a)1117 1606 y FX(i)1144 1618 y Ga(S)5 b F4(])pF6(j)1255 1585 y Fu(N)1335 1618 y F6(\021)25 b(j)p Ga(N)10b F6(j)1564 1585 y Fu(N)2906 1618 y Gg(by)24 b(Lemma)e(3.4.6)pBlack 277 1800 a Gb(Inner)h(Reduction:)p Black 46 w Gg(The)d(inner)i(reductions)i(are)d(by)g(simple)g(induction)j(ar)n(guments)f(e)o(xcept)f(where)504 1913 y Ga(M)38 b Gg(is)28 b(translated)j(by)e(clause)g(\(14\))g(of)g F6(j)p 1782 1913 V 1800 1913 V 1817 1913V 65 w(j)1870 1880 y Fu(N)1951 1913 y Gg(and)g Ga(N)38b Gg(by)28 b(one)h(of)f(the)h(clauses)h(\(10\22613\).)45b(W)-7 b(e)504 2026 y(gi)n(v)o(e)24 b(the)g(details)h(for)f(one)g(such)g(case.)29 b(Suppose)c Ga(y)h Gg(is)d(free)h(in)24962014 y F9(\()2523 2026 y Ga(x)2575 2014 y F9(\))26022026 y Ga(T)13 b Gg(,)23 b(b)n(ut)h(not)g(in)3083 2014y F9(\()3111 2026 y Ga(x)3163 2014 y F9(\))3190 2026y Ga(T)3256 1993 y FX(0)3279 2026 y Gg(.)504 2176 y Ga(M)36b F6(\021)25 b FL(Cut)p F4(\()897 2164 y FX(h)924 2176y Ga(c)963 2164 y FX(i)991 2176 y Ga(S)5 b(;)1092 2164y F9(\()1120 2176 y Ga(y)1168 2164 y F9(\))1195 2176y FL(And)1350 2139 y 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