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%%BeginDocument: pics/cam.arms.ps
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%%Title: Arms of University of Cambridge
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/cuarmsdict 50 dict def cuarmsdict begin
/mtrx matrix def
/lionfix{filled{gsave lioncolour fill grestore}if stroke}def
/toefix{gsave lioncolour fill grestore stroke} def
/ea{/savematrix mtrx currentmatrix def
translate 5 -1 roll rotate scale 0 0 1 5 -2 roll arc
savematrix setmatrix}def
/ec{/savematrix mtrx currentmatrix def
translate 5 -1 roll rotate scale 0 0 1 5 -2 roll arcn
savematrix setmatrix}def
/db /rlineto load def /dt /lineto load def /mt /moveto load def
/lion1{0.77 0.77 scale
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406 338 mt 440 375 45 -115 38 arc
120 -90 90 15 11 445 425 ea
120 -90 90 15 15 402 442 ea
130 -143 25 33 20 360 454 ea
360 485 32 217 73 arcn 397 507 dt
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270 -41 185 23 15 265 517 ea
260 540 dt -4 20 db -6 10 db -16 -2 db -14 -8 db
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90 -5 221 23 15 135 517 ea
98 55 125 80 55 200 465 ea
420 340 285 164 183 arc
} def
/lion2{126 299 27 70 126 arc
98 333 15 271 190 arcn
287 438 230 207 170 arcn
307 0 145 50 25 33 522 ea
240 485 240 162 177 arc
20 496 18 177 270 arc
96 -10 190 26 12 7 450 ea
111 -25 180 36 12 15 388 ea 40 350 dt
119 -30 190 33 10 36 318 ea 70 296 dt
127 -15 180 28 7 66 260 ea
130 213 45 138 120 arcn
120 296 36 -75 -40 arc
}def
/lion3{69 255 81 11 -37 arcn
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40 57 160 30 11 49 98 ea
40 175 350 40 15 57 90 ea
72 150 345 50 18 115 123 ea
90 150 330 45 14 155 177 ea
80 150 340 50 10 186 230 ea
110 105 240 32 22 218 284 ea
}def
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307 160 31 40 -55 arcn
160 390 305 -58 -70 arcn
22 30 160 20 7 243 90 ea
27 170 330 30 12 250 77 ea 288 90 dt
60 125 300 45 15 312 100 ea 340 125 dt
72 155 360 30 12 356 140 ea
380 190 25 210 400 arc
90 230 50 18 13 383 208 ec
363 240 22 300 356 arc
}def
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412 171 32 50 -30 arcn
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498 102 54 200 235 arc
93 200 360 40 11 470 105 ea
95 165 350 30 8 474 173 ea
479 205 5 210 360 arc 490 270 dt
470 260 13 350 195 arcn
348 247 108 10 60 arc
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/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 toefix
317 280 mt 335 292 18 235 380 arc
385 238 dt stroke}def
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228 156 36 42 -50 arcn
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% setmatrix } def
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% DG/SR modification end
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%%Creation Date: May 7, 1993
10 dict dup begin
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dup (C) 0 get /BoldCircle put
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dup (T) 0 get /BoldTriangle put
dup (r) 0 get /SolidSquare put
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/Metrics 13 dict def
Metrics begin
/Bullet 1000 def
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/SolidTriangle 1344 def
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/SolidPentagon 1093.2 def
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/Square { SquarePath .89 .89 scale SquarePath eofill } def
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%!
% PostScript prologue for pst-node.tex.
% Version 97 patch 1, 97/05/09.
% For distribution, see pstricks.tex.
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sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul
add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add
y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul
mul 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 cleartomark
VPosEnd } def
/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
def grestore exec /LPutVar /SaveLPutVar load def } def
/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
GetEdgeA 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 pop
end } def
/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub
Atan /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 xA1
yA1 ] 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 -1
roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
begin 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 rotate
def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx
itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2
yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1
yB1 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 xB2
yB2 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 yA1
tx@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 def
xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx
transform 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 ArmB
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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
/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if
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/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 ED
GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin
false 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 rotate
def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2
mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3
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Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]
cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {
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% 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
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%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 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 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 add
AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r
Div def /y ED /x ED } def
/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB
180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos
mul 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 dy
add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos
{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar
tx@Dict begin false Polygon end } def
/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan
def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2
mul 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 div
def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def
GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul
sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0
eq { 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 def
0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2
roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0
0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2
roll 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 add
add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub
mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t
sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse
y0 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 yB
sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
w 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 neg
exch X sub neg exch moveto setmatrix CP grestore } def
/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0
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/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 } if
r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop }
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def
end
% 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 def
tx@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
} def
end
% END pst-text.pro
%%EndProcSet
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%!
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%!
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/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 def
end
/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 begin
tx@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 end
grestore } 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 exch
Sin 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 } { dx
dup 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 dup
Cos mul exch Sin mul } def
/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h
mul 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 /d
ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d
sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan
sin def /NodePos { TriNodePos } def } def
/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos
hh 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 { Dist
Dist 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 idtransform
exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx
dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop
XYPos } ifelse } def
/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1
roll sin mul sub exch } ifelse } def
/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA
AddOffset yA add /yA1 ED xA add /xA1 ED } def
/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB
AddOffset yB add /yB1 ED xB add /xB1 ED } def
/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA
AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED
ArmA 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 ArmB
AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED
ArmB 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 b
known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA
ED /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 sub
mul 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 3
mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx
sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul
add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add
y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul
mul 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 cleartomark
VPosEnd } def
/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
def grestore exec /LPutVar /SaveLPutVar load def } def
/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
GetEdgeA 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 pop
end } def
/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub
Atan /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 xA1
yA1 ] 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 -1
roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
begin 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 rotate
def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx
itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2
yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1
yB1 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 xB2
yB2 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 yA1
tx@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 def
xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx
transform 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 ArmB
0 ne { xB1 yB1 } if xB2 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
/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if
xB2 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 ED
GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin
false 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 rotate
def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2
mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3
mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2
xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false
Line 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 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 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 add
AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r
Div def /y ED /x ED } def
/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB
180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos
mul 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 dy
add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos
{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar
tx@Dict begin false Polygon end } def
/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan
def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2
mul 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 div
def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def
GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul
sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0
eq { 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 def
0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2
roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0
0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2
roll 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 add
add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub
mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t
sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse
y0 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 yB
sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
w 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 neg
exch X sub neg exch moveto setmatrix CP grestore } def
/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0
def } 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 } if
r 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 }
def
end
% 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 def
tx@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
} def
end
% END pst-text.pro
%%EndProcSet
%%BeginProcSet: special.pro
%!
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x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
y0 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 div
round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div
round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub
0 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 add
exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n
div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1
dy 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 dup
stringwidth 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 i
w 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 mul
n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n
div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop
1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs
dup 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 g
exch 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 0
1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add
exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
mul 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 [ RAngle
dup 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 s
abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
div 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 s
mul 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 add
exch } 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 OLUnit
neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
/IfVisible true def } def
end
% 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, 1993
10 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 def
end
/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 begin
tx@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 end
grestore } 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 exch
Sin 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 } { dx
dup 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 dup
Cos mul exch Sin mul } def
/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h
mul 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 /d
ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d
sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan
sin def /NodePos { TriNodePos } def } def
/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos
hh 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 { Dist
Dist 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 idtransform
exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx
dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop
XYPos } ifelse } def
/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1
roll sin mul sub exch } ifelse } def
/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA
AddOffset yA add /yA1 ED xA add /xA1 ED } def
/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB
AddOffset yB add /yB1 ED xB add /xB1 ED } def
/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA
AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED
ArmA 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 ArmB
AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED
ArmB 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 b
known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA
ED /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 sub
mul 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 3
mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx
sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul
add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add
y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul
mul 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 cleartomark
VPosEnd } def
/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
def grestore exec /LPutVar /SaveLPutVar load def } def
/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
GetEdgeA 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 pop
end } def
/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub
Atan /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 xA1
yA1 ] 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 -1
roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
begin 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 rotate
def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx
itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2
yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1
yB1 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 xB2
yB2 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 yA1
tx@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 def
xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx
transform 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 ArmB
0 ne { xB1 yB1 } if xB2 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
/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if
xB2 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 ED
GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin
false 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 rotate
def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2
mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3
mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2
xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false
Line 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 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 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 add
AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r
Div def /y ED /x ED } def
/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB
180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos
mul 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 dy
add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos
{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar
tx@Dict begin false Polygon end } def
/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan
def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2
mul 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 div
def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def
GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul
sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0
eq { 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 def
0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2
roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0
0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2
roll 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 add
add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub
mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t
sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse
y0 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 yB
sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
w 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 neg
exch X sub neg exch moveto setmatrix CP grestore } def
/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0
def } 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 } if
r 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 }
def
end
% 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 def
tx@TextPathDict begin
% Syntax: <dist> PathPosition -
% Function: Searches for position of currentpath distance <dist> from
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/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
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/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 /y1
ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1
moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto
Lineto pop pop closepath } ifelse } def
/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul
neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add
def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2
div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
setmatrix } 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 dup
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 mark 0 d w neg d 0 h w d 0
d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
% setmatrix } def
setmatrix pop } def
% DG/SR modification end
/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
def } def
/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
def } def
/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos
abs 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 mul
m 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 def
n { 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 { pop
pop } 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 matrix
rotate matrix concatmatrix exch findfont exch makefont setfont } def
/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
x1 y1 lineto closepath } def
/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
exch { 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 arcto
x2 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 { 6
2 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 1
sub { 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 x1
sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
y0 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 div
round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div
round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub
0 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 add
exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n
div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1
dy 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 dup
stringwidth 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 i
w 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 mul
n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n
div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop
1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs
dup 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 g
exch 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 0
1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add
exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
mul 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 [ RAngle
dup 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 s
abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
div 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 s
mul 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 add
exch } 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 OLUnit
neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
/IfVisible true def } def
end
% 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, 1993
10 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 def
end
/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 begin
tx@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 end
grestore } 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 exch
Sin 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 } { dx
dup 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 dup
Cos mul exch Sin mul } def
/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h
mul 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 /d
ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d
sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan
sin def /NodePos { TriNodePos } def } def
/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos
hh 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 { Dist
Dist 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 idtransform
exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx
dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop
XYPos } ifelse } def
/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1
roll sin mul sub exch } ifelse } def
/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA
AddOffset yA add /yA1 ED xA add /xA1 ED } def
/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB
AddOffset yB add /yB1 ED xB add /xB1 ED } def
/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA
AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED
ArmA 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 ArmB
AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED
ArmB 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 b
known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA
ED /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 sub
mul 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 3
mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx
sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul
add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add
y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul
mul 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 cleartomark
VPosEnd } def
/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
def grestore exec /LPutVar /SaveLPutVar load def } def
/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
GetEdgeA 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 pop
end } def
/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub
Atan /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 xA1
yA1 ] 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 -1
roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
begin 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 rotate
def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx
itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2
yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1
yB1 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 xB2
yB2 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 yA1
tx@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 def
xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx
transform 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 ArmB
0 ne { xB1 yB1 } if xB2 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
/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if
xB2 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 ED
GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin
false 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 rotate
def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2
mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3
mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2
xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false
Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]
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% 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 def
PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y
mul 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 add
def } 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 1
setlinecap stroke } def
/LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch
2 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 a
itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
% DG/SR modification end
Div 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 }
% def
a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore
pop pop } def
% DG/SR modification end
/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg
exch 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 -1
scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill
grestore } def
/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0
CLW moveto } def
/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2
div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0
CLW moveto } def
/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW
2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0
curveto -.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 DS
CLW 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 /moveto
load } if ] cvx newpath 3 1 roll T exec } def
/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch
cvi def } def
/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if
f { ] 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 sub
def 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 eq
and { 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 /y1
ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1
moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto
Lineto pop pop closepath } ifelse } def
/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul
neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add
def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2
div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
setmatrix } 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 dup
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 mark 0 d w neg d 0 h w d 0
d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
% setmatrix } def
setmatrix pop } def
% DG/SR modification end
/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
def } def
/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
def } def
/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos
abs 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 mul
m 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 def
n { 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 { pop
pop } 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 matrix
rotate matrix concatmatrix exch findfont exch makefont setfont } def
/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
x1 y1 lineto closepath } def
/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
exch { 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 arcto
x2 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 { 6
2 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 1
sub { 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 x1
sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
y0 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 div
round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div
round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub
0 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 add
exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n
div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1
dy 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 dup
stringwidth 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 i
w 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 mul
n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n
div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop
1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs
dup 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 g
exch 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 0
1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add
exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
mul 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 [ RAngle
dup 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 s
abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
div 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 s
mul 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 add
exch } 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 OLUnit
neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
/IfVisible true def } def
end
% 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, 1993
10 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 def
end
/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 begin
tx@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 end
grestore } 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 exch
Sin 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 } { dx
dup 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 dup
Cos mul exch Sin mul } def
/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h
mul 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 /d
ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d
sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan
sin def /NodePos { TriNodePos } def } def
/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos
hh 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 { Dist
Dist 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 idtransform
exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx
dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop
XYPos } ifelse } def
/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1
roll sin mul sub exch } ifelse } def
/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA
AddOffset yA add /yA1 ED xA add /xA1 ED } def
/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB
AddOffset yB add /yB1 ED xB add /xB1 ED } def
/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA
AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED
ArmA 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 ArmB
AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED
ArmB 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 b
known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA
ED /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 sub
mul 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 3
mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx
sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul
add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add
y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul
mul 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 cleartomark
VPosEnd } def
/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
def grestore exec /LPutVar /SaveLPutVar load def } def
/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
GetEdgeA 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 pop
end } def
/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub
Atan /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 xA1
yA1 ] 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 -1
roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
begin 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 rotate
def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx
itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2
yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1
yB1 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 xB2
yB2 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 yA1
tx@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 def
xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx
transform 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 ArmB
0 ne { xB1 yB1 } if xB2 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
/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if
xB2 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 ED
GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin
false 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 rotate
def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2
mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3
mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2
xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false
Line 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 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 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 add
AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r
Div def /y ED /x ED } def
/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB
180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos
mul 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 dy
add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos
{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar
tx@Dict begin false Polygon end } def
/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan
def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2
mul 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 div
def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def
GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul
sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0
eq { 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 def
0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2
roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0
0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2
roll 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 add
add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub
mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t
sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse
y0 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 yB
sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
w 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 neg
exch X sub neg exch moveto setmatrix CP grestore } def
/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0
def } 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 } if
r 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 }
def
end
% 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 def
tx@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
} def
end
% 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 /t /u /v /w
/x /y /z /braceleft /bar /braceright /asciitilde
/.notdef % rubout; ASCII ends
% 0x80
/.notdef /.notdef /quotesinglbase /florin
/quotedblbase /ellipsis /dagger /daggerdbl
/circumflex /perthousand /Scaron /guilsinglleft
/OE /.notdef /.notdef /.notdef
% 0x90
/.notdef /.notdef /.notdef /quotedblleft
/quotedblright /bullet /endash /emdash
/tilde /trademark /scaron /guilsinglright
/oe /.notdef /.notdef /Ydieresis
% 0xA0
/.notdef % nobreakspace
/exclamdown /cent /sterling
/currency /yen /brokenbar /section
/dieresis /copyright /ordfeminine /guillemotleft
/logicalnot
/hyphen % Y&Y (also at 45); Windows' softhyphen
/registered
/macron
% 0xD0
/degree /plusminus /twosuperior /threesuperior
/acute /mu /paragraph /periodcentered
/cedilla /onesuperior /ordmasculine /guillemotright
/onequarter /onehalf /threequarters /questiondown
% 0xC0
/Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla
/Egrave /Eacute /Ecircumflex /Edieresis
/Igrave /Iacute /Icircumflex /Idieresis
% 0xD0
/Eth /Ntilde /Ograve /Oacute
/Ocircumflex /Otilde /Odieresis /multiply
/Oslash /Ugrave /Uacute /Ucircumflex
/Udieresis /Yacute /Thorn /germandbls
% 0xE0
/agrave /aacute /acircumflex /atilde
/adieresis /aring /ae /ccedilla
/egrave /eacute /ecircumflex /edieresis
/igrave /iacute /icircumflex /idieresis
% 0xF0
/eth /ntilde /ograve /oacute
/ocircumflex /otilde /odieresis /divide
/oslash /ugrave /uacute /ucircumflex
/udieresis /yacute /thorn /ydieresis
] def
%%EndProcSet
%%BeginProcSet: texps.pro
%!
TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2
index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll
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exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub
dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def}
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dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}
if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}
def end
%%EndProcSet
%%BeginProcSet: special.pro
%!
TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N
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%%BeginProcSet: color.pro
%!
TeXDict begin/setcmykcolor where{pop}{/setcmykcolor{dup 10 eq{pop
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Black eop end
%%Page: 28 40
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eop end
%%Page: 29 41
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F9(\()1622 1036 y Ga(y)1670 1024 y F9(\))1697 1036 y
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y Ga(a)1248 1944 y FX(i)1276 1956 y Ga(M)10 b(;)15 b(b)p
F4(\))q Ga(;)1529 1944 y F9(\()1556 1956 y Ga(y)1604
1944 y F9(\))1632 1956 y FL(Or)1731 1970 y Gc(L)1783
1956 y F4(\()1818 1944 y F9(\()1846 1956 y Ga(x)1898
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y F9(1)2077 1956 y Ga(;)2117 1944 y F9(\()2145 1956 y
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2153 y Gc(L)1226 2139 y F4(\()1261 2127 y F9(\()1288
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b F4(\))26 b F6(\022)f Ga(op)p F4(\()p Ga(S)2858 5032
y FX(0)2881 5065 y F4(\))p Gg(,)e(and)774 5213 y(decreasing,)103
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b Ga(S)2114 5180 y FX(0)2188 5213 y F6(\))50 b Ga(op)p
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Ga(S)2858 5180 y FX(0)2881 5213 y F4(\))p Gg(.)p Black
Black eop end
%%Page: 35 47
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a F5(N)t(O)q(T)t(R)t(I)t(G)t(H)t(T)1075 849 y FQ(h:)p
FS(B)s FQ(i)1231 834 y FG(\()p FU(X)7 b FG(\))1471 787
y F5(def)1481 834 y FG(=)1655 664 y FI(8)1655 738 y(<)1655
888 y(:)1771 721 y FQ(h)1798 733 y FU(a)r FG(:)r FT(:)p
FU(B)1991 721 y FQ(i)2019 733 y FF(Not)2149 745 y FS(R)2204
733 y FG(\()2236 721 y FJ(\()2262 733 y FU(x)r FG(:)r
FU(B)2403 721 y FJ(\))2430 733 y FU(M)i(;)14 b(a)p FG(\))23
b FT(j)1960 833 y FF(Not)2090 845 y FS(R)2144 833 y FG(\()2176
821 y FJ(\()2203 833 y FU(x)r FG(:)r FU(B)2344 821 y
FJ(\))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(\()1986 932 y FU(x)r
FG(:)r FU(B)2127 920 y FJ(\))2154 932 y FU(M)32 b FT(2)23
b FU(X)3326 664 y FI(9)3326 738 y(=)3326 888 y(;)759
1279 y F5(N)t(O)q(T)t(L)t(E)t(F)t(T)1079 1294 y FJ(\()p
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1232 y F5(def)1481 1279 y FG(=)1655 1109 y FI(8)1655
1184 y(<)1655 1333 y(:)1771 1167 y FJ(\()1797 1179 y
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y FF(Not)2151 1191 y FS(L)2200 1179 y FG(\()2232 1167
y FQ(h)2260 1179 y FU(a)r FG(:)r FU(B)2398 1167 y FQ(i)2426
1179 y FU(M)h(;)14 b(x)p FG(\))24 b FT(j)1960 1279 y
FF(Not)2090 1291 y FS(L)2140 1279 y FG(\()2172 1267 y
FQ(h)2199 1279 y FU(a)r FG(:)r FU(B)2337 1267 y FQ(i)2365
1279 y FU(M)8 b(;)14 b(x)p FG(\))24 b Gd(freshly)19 b(introduces)i
FU(x;)1960 1366 y FQ(h)1987 1378 y FU(a)r FG(:)r FU(B)2125
1366 y FQ(i)2152 1378 y FU(M)32 b FT(2)23 b FU(X)3326
1109 y FI(9)3326 1184 y(=)3326 1333 y(;)548 1775 y F5(A)t(N)t(D)t(R)t
(I)t(G)t(H)t(T)925 1790 y FQ(h)p FS(B)s FQ(^)p FS(C)t
FQ(i)1132 1775 y FG(\()p FU(X)r(;)14 b(Y)19 b FG(\))1471
1728 y F5(def)1481 1775 y FG(=)1655 1555 y FI(8)1655
1630 y(>)1655 1655 y(>)1655 1680 y(<)1655 1829 y(>)1655
1854 y(>)1655 1879 y(:)1771 1613 y FQ(h)1798 1625 y FU(c)r
FG(:)r FU(B)t FT(^)q FU(C)2049 1613 y FQ(i)2076 1625
y FF(And)2217 1637 y FS(R)2272 1625 y FG(\()2304 1613
y FQ(h)2331 1625 y FU(a)r FG(:)r FU(B)2469 1613 y FQ(i)2497
1625 y FU(M)8 b(;)2623 1613 y FQ(h)2650 1625 y FU(b)r
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b(c)p FG(\))23 b FT(j)1960 1724 y FF(And)2101 1736 y
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FG(:)r FU(B)2352 1712 y FQ(i)2380 1724 y FU(M)9 b(;)2507
1712 y FQ(h)2534 1724 y FU(b)r FG(:)r FU(C)2662 1712
y FQ(i)2689 1724 y FU(N)g(;)14 b(c)p FG(\))23 b Gd(freshly)d
(introduces)h FU(c;)1960 1812 y FQ(h)1987 1824 y FU(a)r
FG(:)r FU(B)2125 1812 y FQ(i)2152 1824 y FU(M)32 b FT(2)23
b FU(X)r(;)1960 1912 y FQ(h)1987 1924 y FU(b)r FG(:)r
FU(C)2115 1912 y FQ(i)2142 1924 y FU(N)32 b FT(2)24 b
FU(Y)3614 1555 y FI(9)3614 1630 y(>)3614 1655 y(>)3614
1680 y(=)3614 1829 y(>)3614 1854 y(>)3614 1879 y(;)636
2276 y F5(A)t(N)t(D)t(L)t(E)t(F)t(T)966 2246 y FS(i)966
2303 y FJ(\()p FS(B)1042 2311 y FP(1)1074 2303 y FQ(^)p
FS(B)1169 2311 y FP(2)1201 2303 y FJ(\))1231 2276 y FG(\()p
FU(X)7 b FG(\))1471 2229 y F5(def)1481 2276 y FG(=)1655
2106 y FI(8)1655 2181 y(<)1655 2330 y(:)1771 2164 y FJ(\()1797
2176 y FU(y)e FG(:)r FU(B)1931 2188 y FJ(1)1969 2176
y FT(^)p FU(B)2087 2188 y FJ(2)2124 2164 y(\))2150 2176
y FF(And)2291 2139 y FS(i)2291 2197 y(L)2341 2176 y FG(\()2373
2164 y FJ(\()2399 2176 y FU(x)r FG(:)r FU(B)2536 2188
y FS(i)2565 2164 y FJ(\))2591 2176 y FU(M)k(;)14 b(y)s
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2302 y(L)2150 2281 y FG(\()2182 2269 y FJ(\()2209 2281
y FU(x)r FG(:)r FU(B)2346 2293 y FS(i)2375 2269 y FJ(\))2401
2281 y FU(M)8 b(;)14 b(y)s FG(\))23 b Gd(freshly)d(introduces)g
FU(y)s(;)1960 2369 y FJ(\()1986 2381 y FU(x)r FG(:)r
FU(B)2123 2393 y FS(i)2152 2369 y FJ(\))2178 2381 y FU(M)31
b FT(2)24 b FU(X)3355 2106 y FI(9)3355 2181 y(=)3355
2330 y(;)642 2734 y F5(O)t(R)t(R)t(I)t(G)t(H)t(T)963
2704 y FS(i)963 2761 y FQ(h)p FS(B)1040 2769 y FP(1)1073
2761 y FQ(_)p FS(B)1168 2769 y FP(2)1200 2761 y FQ(i)1231
2734 y FG(\()p FU(X)7 b FG(\))1471 2687 y F5(def)1481
2734 y FG(=)1655 2564 y FI(8)1655 2638 y(<)1655 2788
y(:)1771 2621 y FQ(h)1798 2633 y FU(b)r FG(:)r FU(B)1924
2645 y FJ(1)1961 2633 y FT(_)q FU(B)2080 2645 y FJ(2)2117
2621 y FQ(i)2144 2633 y FF(Or)2234 2596 y FS(i)2234 2654
y(R)2289 2633 y FG(\()2321 2621 y FQ(h)2348 2633 y FU(a)r
FG(:)r FU(B)2482 2645 y FS(i)2511 2621 y FQ(i)2537 2633
y FU(M)i(;)14 b(b)p FG(\))23 b FT(j)1960 2739 y FF(Or)2050
2702 y FS(i)2050 2759 y(R)2105 2739 y FG(\()2137 2727
y FQ(h)2164 2739 y FU(a)r FG(:)r FU(B)2298 2751 y FS(i)2326
2727 y FQ(i)2353 2739 y FU(M)9 b(;)14 b(b)p FG(\))23
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2839 y FU(a)r FG(:)r FU(B)2121 2851 y FS(i)2149 2827
y FQ(i)2176 2839 y FU(M)32 b FT(2)23 b FU(X)3291 2564
y FI(9)3291 2638 y(=)3291 2788 y(;)654 3235 y F5(O)t(R)t(L)t(E)t(F)t(T)
928 3250 y FJ(\()p FS(B)s FQ(_)o FS(C)t FJ(\))1132 3235
y FG(\()p FU(X)r(;)14 b(Y)19 b FG(\))1471 3188 y F5(def)1481
3235 y FG(=)1655 3015 y FI(8)1655 3090 y(>)1655 3115
y(>)1655 3140 y(<)1655 3289 y(>)1655 3314 y(>)1655 3339
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3185 y FG(\()2132 3173 y FJ(\()2158 3185 y FU(x)r FG(:)r
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FU(z)t(;)1960 3272 y FJ(\()1986 3284 y FU(x)r FG(:)r
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b(Y)19 b FG(\))1471 3833 y F5(def)1481 3880 y FG(=)1655
3561 y FI(8)1655 3635 y(>)1655 3660 y(>)1655 3685 y(>)1655
3710 y(>)1655 3735 y(>)1655 3760 y(>)1655 3785 y(<)1655
3934 y(>)1655 3959 y(>)1655 3984 y(>)1655 4009 y(>)1655
4034 y(>)1655 4059 y(>)1655 4084 y(:)1771 3618 y FQ(h)1798
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y FG(\()2303 3618 y FJ(\()2330 3630 y FU(x)r FG(:)r FU(B)2471
3618 y FJ(\))q FQ(h)2525 3630 y FU(a)r FG(:)r FU(C)2661
3618 y FQ(i)2689 3630 y FU(M)9 b(;)14 b(b)p FG(\))23
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y FG(\()2178 3718 y FJ(\()2204 3730 y FU(x)r FG(:)r FU(B)2345
3718 y FJ(\))r FQ(h)2400 3730 y FU(a)r FG(:)r FU(C)2536
3718 y FQ(i)2564 3730 y FU(M)8 b(;)14 b(b)p FG(\))23
b Gd(freshly)c(introduces)i FU(b;)1960 3830 y Gd(for)e(all)2183
3818 y FJ(\()2209 3830 y FU(z)6 b FG(:)r FU(C)2344 3818
y FJ(\))2371 3830 y FU(P)35 b FT(2)23 b FU(Y)42 b(:)2290
3917 y FJ(\()2316 3929 y FU(x)r FG(:)r FU(B)2457 3917
y FJ(\))2485 3929 y FU(M)t FT(f)-7 b FU(a)22 b FG(:=)2782
3917 y FJ(\()2808 3929 y FU(z)2851 3917 y FJ(\))2876
3929 y FU(P)r FT(g)h(2)g FU(X)r(;)1960 4029 y Gd(for)c(all)2183
4017 y FQ(h)2210 4029 y FU(c)r FG(:)r FU(B)2340 4017
y FQ(i)2368 4029 y FU(Q)k FT(2)g FU(X)30 b(:)2290 4117
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4129 y FU(c)2845 4117 y FQ(i)2871 4129 y FU(Q)-9 b FT(g)22
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4305 y FI(8)1655 4380 y(>)1655 4405 y(>)1655 4430 y(<)1655
4579 y(>)1655 4604 y(>)1655 4629 y(:)1771 4363 y FJ(\()1797
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4363 y FQ(i)2498 4375 y FU(M)j(;)2624 4363 y FJ(\()2650
4375 y FU(x)r FG(:)r FU(C)2789 4363 y FJ(\))2817 4375
y FU(N)h(;)14 b(y)s FG(\))23 b FT(j)1960 4475 y FF(Imp)2092
4495 y FS(L)2141 4475 y FG(\()2173 4463 y FQ(h)2200 4475
y FU(a)r FG(:)r FU(B)2338 4463 y FQ(i)2366 4475 y FU(M)9
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y FU(N)32 b FT(2)23 b FU(Y)3626 4305 y FI(9)3626 4380
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%%Page: 36 48
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%%Page: 46 58
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%%Page: 47 59
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FU(x)1648 2584 y FJ(\))1674 2596 y FF(Cut)1741 2549 y
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2584 y FQ(i)1924 2596 y FU(M)8 b(;)2050 2584 y FJ(\()2076
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y FQ(i)406 2732 y FF(Not)536 2744 y FS(L)586 2732 y FG(\()618
2720 y FQ(h)645 2732 y FU(a)689 2720 y FQ(i)716 2732
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y FQ(i)525 2868 y FU(M)9 b(;)652 2856 y FQ(h)679 2868
y FU(b)715 2856 y FQ(i)741 2868 y FU(N)g(;)14 b(c)p FG(\))p
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y FJ(\))2162 2868 y FU(P)j FG(\))p FU(;)2296 2856 y FQ(h)2323
2868 y FU(b)2359 2856 y FQ(i)2386 2868 y FF(Cut)2453
2821 y FC( )2513 2868 y FG(\()2545 2856 y FQ(h)2573 2868
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3024 y(L)589 3004 y FG(\()621 2992 y FJ(\()648 3004 y
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2957 y FC( )1808 3004 y FG(\()1840 2992 y FQ(h)1867 3004
y FU(a)1911 2992 y FQ(i)1938 3004 y FU(M)8 b(;)2064 2992
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3160 y(R)594 3140 y FG(\()626 3128 y FQ(h)653 3140 y
FU(a)697 3128 y FQ(i)724 3140 y FU(M)8 b(;)14 b(b)p FG(\))p
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y FG(\()1792 3128 y FQ(h)1820 3140 y FU(c)1856 3128 y
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y FU(x)2082 3128 y FJ(\))2108 3140 y FU(P)j FG(\))p FU(;)i(b)p
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3264 y FQ(h)170 3276 y FU(a)214 3264 y FQ(i)241 3276
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3276 y FU(x)487 3264 y FJ(\))513 3276 y FU(M)9 b(;)640
3264 y FJ(\()666 3276 y FU(y)710 3264 y FJ(\))735 3276
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3264 y FJ(\))2339 3276 y FF(Cut)2405 3229 y FC( )2466
3276 y FG(\()2498 3264 y FQ(h)2525 3276 y FU(a)2569 3264
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y FU(v)2778 3264 y FJ(\))2804 3276 y FU(P)j FG(\))p FU(;)i(z)t
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3400 y FQ(h)249 3412 y FU(c)285 3400 y FQ(i)312 3412
y FF(Imp)444 3432 y FS(R)498 3412 y FG(\()530 3400 y
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y FU(a)701 3400 y FQ(i)728 3412 y FU(M)8 b(;)14 b(b)p
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3548 y FG(\()2532 3536 y FQ(h)2560 3548 y FU(b)2596 3536
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y FU(z)2804 3536 y FJ(\))2829 3548 y FU(P)j FG(\))p FU(;)i(y)s
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3719 y FQ(h)573 3731 y FU(b)609 3719 y FQ(i)636 3731
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3855 y FQ(i)332 3867 y FU(P)e(;)434 3855 y FJ(\()460
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3855 y FQ(h)715 3867 y FU(a)759 3855 y FQ(i)785 3867
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y FQ(h)1800 3867 y FU(b)1836 3855 y FQ(i)1863 3867 y
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3820 y FC(!)2446 3867 y FG(\()2478 3855 y FQ(h)2505 3867
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y FJ(\()2695 3867 y FU(y)2739 3855 y FJ(\))2765 3867
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y FQ(i)403 4003 y FU(P)j(;)505 3991 y FJ(\()531 4003
y FU(y)575 3991 y FJ(\))600 4003 y FF(Not)731 4015 y
FS(R)785 4003 y FG(\()817 3991 y FJ(\()843 4003 y FU(x)890
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3991 y FJ(\()2051 4003 y FU(y)2095 3991 y FJ(\))2121
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FF(Cut)223 4092 y FC(!)284 4139 y FG(\()316 4127 y FQ(h)343
4139 y FU(b)379 4127 y FQ(i)406 4139 y FU(P)e(;)508 4127
y FJ(\()533 4139 y FU(y)577 4127 y FJ(\))603 4139 y FF(Not)733
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y FU(a)1641 4127 y FQ(i)1668 4139 y FF(Cut)1734 4092
y FC(!)1795 4139 y FG(\()1827 4127 y FQ(h)1855 4139 y
FU(b)1891 4127 y FQ(i)1917 4139 y FU(P)12 b(;)2019 4127
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y FU(d)173 4263 y FQ(i)200 4275 y FU(P)e(;)302 4263 y
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y FU(a)696 4263 y FQ(i)723 4275 y FU(M)c(;)849 4263 y
FQ(h)876 4275 y FU(b)912 4263 y FQ(i)938 4275 y FU(N)h(;)14
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y FQ(h)1870 4275 y FU(d)1913 4263 y FQ(i)1940 4275 y
FU(P)12 b(;)2042 4263 y FJ(\()2068 4275 y FU(y)2112 4263
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4275 y FU(b)2359 4263 y FQ(i)2386 4275 y FF(Cut)2453
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FJ(\()526 4411 y FU(z)569 4399 y FJ(\))594 4411 y FF(And)735
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FJ(\()843 4411 y FU(x)890 4399 y FJ(\))917 4411 y FU(M)c(;)14
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4399 y FJ(\))1680 4411 y FF(Cut)1747 4364 y FC(!)1808
4411 y FG(\()1840 4399 y FQ(h)1867 4411 y FU(a)1911 4399
y FQ(i)1938 4411 y FU(P)12 b(;)2040 4399 y FJ(\()2066
4411 y FU(z)2109 4399 y FJ(\))2134 4411 y FU(M)c FG(\))q
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4547 y FG(\()359 4535 y FQ(h)386 4547 y FU(c)422 4535
y FQ(i)449 4547 y FU(P)e(;)551 4535 y FJ(\()576 4547
y FU(x)623 4535 y FJ(\))650 4547 y FF(Or)740 4510 y FS(i)740
4568 y(R)795 4547 y FG(\()827 4535 y FQ(h)854 4547 y
FU(a)898 4535 y FQ(i)925 4547 y FU(M)c(;)14 b(b)p FG(\)\))1236
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4510 y FS(i)1448 4568 y(R)1503 4547 y FG(\()1535 4535
y FQ(h)1562 4547 y FU(a)1606 4535 y FQ(i)1633 4547 y
FF(Cut)1700 4500 y FC(!)1760 4547 y FG(\()1792 4535 y
FQ(h)1820 4547 y FU(c)1856 4535 y FQ(i)1882 4547 y FU(P)12
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FF(Cut)50 4636 y FC(!)111 4683 y FG(\()143 4671 y FQ(h)170
4683 y FU(a)214 4671 y FQ(i)241 4683 y FU(P)e(;)343 4671
y FJ(\()369 4683 y FU(v)412 4671 y FJ(\))438 4683 y FF(Or)529
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y FU(x)684 4671 y FJ(\))710 4683 y FU(M)d(;)837 4671
y FJ(\()862 4683 y FU(y)906 4671 y FJ(\))932 4683 y FU(N)g(;)14
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4671 y FQ(h)1817 4683 y FU(a)1861 4671 y FQ(i)1887 4683
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y FJ(\()2269 4683 y FU(y)2313 4671 y FJ(\))2339 4683
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y FQ(h)2525 4683 y FU(a)2569 4671 y FQ(i)2596 4683 y
FU(P)j(;)2698 4671 y FJ(\()2724 4683 y FU(v)2767 4671
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y FQ(h)249 4819 y FU(c)285 4807 y FQ(i)312 4819 y FU(P)e(;)414
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4807 y FQ(i)1773 4819 y FF(Cut)1840 4772 y FC(!)1901
4819 y FG(\()1933 4807 y FQ(h)1960 4819 y FU(c)1996 4807
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4819 y FU(y)2195 4807 y FJ(\))2220 4819 y FU(M)d FG(\))p
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4955 y FG(\()108 4943 y FQ(h)135 4955 y FU(b)171 4943
y FQ(i)197 4955 y FU(P)e(;)299 4943 y FJ(\()325 4955
y FU(z)368 4943 y FJ(\))393 4955 y FF(Imp)525 4975 y
FS(L)575 4955 y FG(\()607 4943 y FQ(h)634 4955 y FU(a)678
4943 y FQ(i)705 4955 y FU(M)c(;)831 4943 y FJ(\()857
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y FQ(h)1598 4955 y FU(a)1642 4943 y FQ(i)1669 4955 y
FF(Cut)1736 4908 y FC(!)1797 4955 y FG(\()1829 4943 y
FQ(h)1856 4955 y FU(b)1892 4943 y FQ(i)1919 4955 y FU(P)11
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roll sin mul sub exch } ifelse } def
/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA
AddOffset yA add /yA1 ED xA add /xA1 ED } def
/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB
AddOffset yB add /yB1 ED xB add /xB1 ED } def
/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA
AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED
ArmA 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 ArmB
AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED
ArmB 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 b
known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA
ED /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 sub
mul 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 3
mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx
sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul
add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add
y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul
mul 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 cleartomark
VPosEnd } def
/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
def grestore exec /LPutVar /SaveLPutVar load def } def
/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
GetEdgeA 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 pop
end } def
/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub
Atan /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 xA1
yA1 ] 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 -1
roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
begin 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 rotate
def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx
itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2
yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1
yB1 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 xB2
yB2 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 yA1
tx@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 def
xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx
transform 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 ArmB
0 ne { xB1 yB1 } if xB2 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
/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if
xB2 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 ED
GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin
false 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 rotate
def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2
mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3
mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2
xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false
Line 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 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 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 add
AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r
Div def /y ED /x ED } def
/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB
180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos
mul 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 dy
add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos
{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar
tx@Dict begin false Polygon end } def
/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan
def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2
mul 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 div
def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def
GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul
sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0
eq { 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 def
0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2
roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0
0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2
roll 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 add
add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub
mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t
sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse
y0 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 yB
sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
w 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 neg
exch X sub neg exch moveto setmatrix CP grestore } def
/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0
def } 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 } if
r 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 }
def
end
% 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 def
tx@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
} def
end
% END pst-text.pro
%%EndProcSet
%%BeginProcSet: special.pro
%!
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%%EndProcSet
%%BeginProcSet: color.pro
%!
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%%Page: 87 99
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0 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 add
exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n
div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1
dy 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 dup
stringwidth 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 i
w 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 mul
n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n
div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop
1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs
dup 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 g
exch 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 0
1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add
exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
mul 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 [ RAngle
dup 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 s
abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
div 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 s
mul 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 add
exch } 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 OLUnit
neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
/IfVisible true def } def
end
% 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, 1993
10 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 def
end
/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 begin
tx@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 end
grestore } 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 exch
Sin 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 } { dx
dup 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 dup
Cos mul exch Sin mul } def
/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h
mul 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 /d
ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d
sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan
sin def /NodePos { TriNodePos } def } def
/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos
hh 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 { Dist
Dist 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 idtransform
exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx
dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop
XYPos } ifelse } def
/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1
roll sin mul sub exch } ifelse } def
/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA
AddOffset yA add /yA1 ED xA add /xA1 ED } def
/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB
AddOffset yB add /yB1 ED xB add /xB1 ED } def
/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA
AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED
ArmA 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 ArmB
AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED
ArmB 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 b
known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA
ED /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 sub
mul 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 3
mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx
sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul
add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add
y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul
mul 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 cleartomark
VPosEnd } def
/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
def grestore exec /LPutVar /SaveLPutVar load def } def
/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
GetEdgeA 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 pop
end } def
/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub
Atan /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 xA1
yA1 ] 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 -1
roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
begin 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 rotate
def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx
itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2
yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1
yB1 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 xB2
yB2 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 yA1
tx@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 def
xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx
transform 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 ArmB
0 ne { xB1 yB1 } if xB2 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
/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if
xB2 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 ED
GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin
false 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 rotate
def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2
mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3
mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2
xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false
Line 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 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 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 add
AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r
Div def /y ED /x ED } def
/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB
180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos
mul 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 dy
add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos
{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar
tx@Dict begin false Polygon end } def
/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan
def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2
mul 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 div
def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def
GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul
sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0
eq { 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 def
0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2
roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0
0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2
roll 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 add
add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub
mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t
sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse
y0 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 yB
sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
w 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 neg
exch X sub neg exch moveto setmatrix CP grestore } def
/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0
def } 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 } if
r 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 }
def
end
% 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 def
tx@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
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%%Creation Date: May 7, 1993
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% PostScript prologue for pst-node.tex.
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ArmB 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 b
known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA
ED /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 sub
mul 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 3
mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx
sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul
add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add
y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul
mul 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 cleartomark
VPosEnd } def
/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
def grestore exec /LPutVar /SaveLPutVar load def } def
/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
GetEdgeA 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 pop
end } def
/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub
Atan /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 xA1
yA1 ] 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 -1
roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
begin 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 rotate
def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx
itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2
yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1
yB1 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 xB2
yB2 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 yA1
tx@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 def
xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx
transform 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 ArmB
0 ne { xB1 yB1 } if xB2 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
/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if
xB2 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 ED
GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin
false 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 rotate
def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2
mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3
mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2
xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false
Line 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 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 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 add
AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r
Div def /y ED /x ED } def
/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB
180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos
mul 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 dy
add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos
{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar
tx@Dict begin false Polygon end } def
/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan
def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2
mul 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 div
def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def
GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul
sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0
eq { 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 def
0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2
roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0
0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2
roll 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 add
add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub
mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t
sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse
y0 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 yB
sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
w 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 neg
exch X sub neg exch moveto setmatrix CP grestore } def
/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0
def } 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 } if
r 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 }
def
end
% 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 def
tx@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
} def
end
% END pst-text.pro
%%EndProcSet
%%BeginProcSet: special.pro
%!
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%%EndProcSet
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%!
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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 def
end
/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 begin
tx@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 end
grestore } 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 exch
Sin 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 } { dx
dup 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 dup
Cos mul exch Sin mul } def
/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h
mul 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 /d
ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d
sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan
sin def /NodePos { TriNodePos } def } def
/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos
hh 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 { Dist
Dist 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 idtransform
exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx
dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop
XYPos } ifelse } def
/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1
roll sin mul sub exch } ifelse } def
/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA
AddOffset yA add /yA1 ED xA add /xA1 ED } def
/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB
AddOffset yB add /yB1 ED xB add /xB1 ED } def
/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA
AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED
ArmA 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 ArmB
AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED
ArmB 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 b
known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA
ED /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 sub
mul 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 3
mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx
sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul
add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add
y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul
mul 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 cleartomark
VPosEnd } def
/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
def grestore exec /LPutVar /SaveLPutVar load def } def
/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
GetEdgeA 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 pop
end } def
/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub
Atan /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 xA1
yA1 ] 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 -1
roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
begin 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 rotate
def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx
itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2
yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1
yB1 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 xB2
yB2 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 yA1
tx@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 def
xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx
transform 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 ArmB
0 ne { xB1 yB1 } if xB2 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
/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if
xB2 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 ED
GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin
false 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 rotate
def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2
mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3
mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2
xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false
Line 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 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 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 add
AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r
Div def /y ED /x ED } def
/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB
180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos
mul 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 dy
add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos
{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar
tx@Dict begin false Polygon end } def
/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan
def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2
mul 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 div
def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def
GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul
sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0
eq { 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 def
0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2
roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0
0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2
roll 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 add
add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub
mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t
sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse
y0 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 yB
sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
w 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 neg
exch X sub neg exch moveto setmatrix CP grestore } def
/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0
def } 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 } if
r 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 }
def
end
% 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 def
tx@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
} def
end
% END pst-text.pro
%%EndProcSet
%%BeginProcSet: special.pro
%!
TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N
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X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B
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@SpecialDefaults count/ocount X/dcount countdictstack N}N/@setspecial{
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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 { 6
2 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 1
sub { 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 x1
sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
y0 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 div
round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div
round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub
0 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 add
exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n
div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1
dy 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 dup
stringwidth 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 i
w 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 mul
n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n
div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop
1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs
dup 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 g
exch 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 0
1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add
exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
mul 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 [ RAngle
dup 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 s
abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
div 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 s
mul 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 add
exch } 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 OLUnit
neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
/IfVisible true def } def
end
% 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, 1993
10 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 def
end
/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 begin
tx@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 end
grestore } 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 exch
Sin 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 } { dx
dup 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 dup
Cos mul exch Sin mul } def
/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h
mul 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 /d
ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d
sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan
sin def /NodePos { TriNodePos } def } def
/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos
hh 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 { Dist
Dist 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 idtransform
exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx
dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop
XYPos } ifelse } def
/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1
roll sin mul sub exch } ifelse } def
/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA
AddOffset yA add /yA1 ED xA add /xA1 ED } def
/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB
AddOffset yB add /yB1 ED xB add /xB1 ED } def
/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA
AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED
ArmA 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 ArmB
AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED
ArmB 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 b
known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA
ED /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 sub
mul 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 3
mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx
sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul
add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add
y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul
mul 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 cleartomark
VPosEnd } def
/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
def grestore exec /LPutVar /SaveLPutVar load def } def
/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
GetEdgeA 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 pop
end } def
/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub
Atan /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 xA1
yA1 ] 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 -1
roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
begin 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 rotate
def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx
itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2
yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1
yB1 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 xB2
yB2 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 yA1
tx@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 def
xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx
transform 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 ArmB
0 ne { xB1 yB1 } if xB2 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
/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if
xB2 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 ED
GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin
false 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 rotate
def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2
mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3
mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2
xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false
Line 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 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 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 add
AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r
Div def /y ED /x ED } def
/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB
180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos
mul 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 dy
add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos
{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar
tx@Dict begin false Polygon end } def
/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan
def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2
mul 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 div
def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def
GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul
sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0
eq { 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 def
0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2
roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0
0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2
roll 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 add
add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub
mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t
sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse
y0 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 yB
sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
w 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
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ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx
dup 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 dup
Cos mul exch Sin mul } def
/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h
mul 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 /d
ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d
sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan
sin def /NodePos { TriNodePos } def } def
/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos
hh 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 { Dist
Dist 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 idtransform
exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx
dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop
XYPos } ifelse } def
/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1
roll sin mul sub exch } ifelse } def
/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA
AddOffset yA add /yA1 ED xA add /xA1 ED } def
/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB
AddOffset yB add /yB1 ED xB add /xB1 ED } def
/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA
AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED
ArmA 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 ArmB
AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED
ArmB 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 b
known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA
ED /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 sub
mul 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 3
mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx
sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul
add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add
y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul
mul 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 cleartomark
VPosEnd } def
/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
def grestore exec /LPutVar /SaveLPutVar load def } def
/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
GetEdgeA 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 pop
end } def
/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub
Atan /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 xA1
yA1 ] 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 -1
roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
begin 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 rotate
def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx
itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2
yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1
yB1 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 xB2
yB2 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 yA1
tx@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 def
xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx
transform 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 ArmB
0 ne { xB1 yB1 } if xB2 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
/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if
xB2 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 ED
GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin
false 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 rotate
def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2
mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3
mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2
xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false
Line 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 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 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 add
AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r
Div def /y ED /x ED } def
/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB
180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos
mul 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 dy
add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos
{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar
tx@Dict begin false Polygon end } def
/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan
def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2
mul 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 div
def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def
GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul
sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0
eq { 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 def
0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2
roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0
0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2
roll 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 add
add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub
mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t
sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse
y0 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 yB
sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
w 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 neg
exch X sub neg exch moveto setmatrix CP grestore } def
/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0
def } 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 } if
r 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 }
def
end
% 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 def
tx@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
} def
end
% END pst-text.pro
%%EndProcSet
%%BeginProcSet: special.pro
%!
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%%EndProcSet
%%BeginProcSet: color.pro
%!
TeXDict begin/setcmykcolor where{pop}{/setcmykcolor{dup 10 eq{pop
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/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
def } def
/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
def } def
/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos
abs 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 mul
m 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 def
n { 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 { pop
pop } 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 matrix
rotate matrix concatmatrix exch findfont exch makefont setfont } def
/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
x1 y1 lineto closepath } def
/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
exch { 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 arcto
x2 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 { 6
2 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 1
sub { 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 x1
sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
y0 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 div
round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div
round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub
0 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 add
exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n
div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1
dy 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 dup
stringwidth 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 i
w 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 mul
n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n
div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop
1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs
dup 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 g
exch 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 0
1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add
exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
mul 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 [ RAngle
dup 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 s
abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
div 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 s
mul 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 add
exch } 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 OLUnit
neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
/IfVisible true def } def
end
% 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, 1993
10 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 def
end
/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 begin
tx@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 end
grestore } 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 exch
Sin 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 } { dx
dup 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 dup
Cos mul exch Sin mul } def
/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h
mul 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 /d
ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d
sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan
sin def /NodePos { TriNodePos } def } def
/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos
hh 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 { Dist
Dist 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 idtransform
exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx
dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop
XYPos } ifelse } def
/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1
roll sin mul sub exch } ifelse } def
/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA
AddOffset yA add /yA1 ED xA add /xA1 ED } def
/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB
AddOffset yB add /yB1 ED xB add /xB1 ED } def
/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA
AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED
ArmA 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 ArmB
AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED
ArmB 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 b
known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA
ED /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 sub
mul 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 3
mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx
sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul
add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add
y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul
mul 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 cleartomark
VPosEnd } def
/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
def grestore exec /LPutVar /SaveLPutVar load def } def
/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
GetEdgeA 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 pop
end } def
/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub
Atan /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 xA1
yA1 ] 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 -1
roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
begin 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 rotate
def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx
itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2
yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1
yB1 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 xB2
yB2 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 yA1
tx@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 def
xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx
transform 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 ArmB
0 ne { xB1 yB1 } if xB2 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
/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if
xB2 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 ED
GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin
false 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 rotate
def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2
mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3
mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2
xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false
Line 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 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 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 add
AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r
Div def /y ED /x ED } def
/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB
180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos
mul 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 dy
add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos
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% PostScript prologue for pstricks.tex.
% Version 97 patch 3, 98/06/01
% For distribution, see pstricks.tex.
%
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/CP /currentpoint load def
/ED { exch def } bind def
/L /lineto load def
/T /translate load def
/TMatrix { } def
/RAngle { 0 } def
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/Pyth { dup mul exch dup mul add sqrt } def
/PtoC { 2 copy cos mul 3 1 roll sin mul } def
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/STV { SDict begin normalscale end STP } def
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/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
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/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }
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% DG modification begin - Jan. 15, 1997
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d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
% setmatrix } def
setmatrix pop } def
% DG/SR modification end
/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
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/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
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/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }
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/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
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/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
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/EAC { x2 y2 x y ArrowB curveto pop pop } def
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/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix
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% 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 mul
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/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
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/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]
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/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
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exch } def
/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
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/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
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/IfVisible true def } def
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%%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, 1993
10 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 {
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} 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 {
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} def
/SolidTriangle { TrianglePath fill } def
/Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def
/BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def
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} def
/SolidSquare { SquarePath fill } def
/Square { SquarePath .89 .89 scale SquarePath eofill } def
/BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def
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-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 {
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% END pst-dots.pro
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%!
% 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 begin
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/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }
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/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def
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/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
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/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h
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/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d
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sin def /NodePos { TriNodePos } def } def
/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos
hh 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 { Dist
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/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform
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XYPos } ifelse } def
/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1
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/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA
AddOffset yA add /yA1 ED xA add /xA1 ED } def
/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB
AddOffset yB add /yB1 ED xB add /xB1 ED } def
/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA
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ArmA 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 ArmB
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ArmB 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 b
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/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub
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/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt
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/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 cleartomark
VPosEnd } def
/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
def grestore exec /LPutVar /SaveLPutVar load def } def
/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
GetEdgeA 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 pop
end } def
/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub
Atan /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 xA1
yA1 ] 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 -1
roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
begin 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 rotate
def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx
itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2
yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1
yB1 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 xB2
yB2 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 yA1
tx@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 def
xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx
transform 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 ArmB
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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
/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if
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/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 ED
GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin
false 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 rotate
def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2
mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3
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xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false
Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]
cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {
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% DG/SR modification begin - May 9, 1997 - Patch 1
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%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 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 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 add
AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r
Div def /y ED /x ED } def
/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB
180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos
mul 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 dy
add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos
{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar
tx@Dict begin false Polygon end } def
/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan
def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2
mul 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 div
def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def
GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul
sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0
eq { 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 def
0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2
roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0
0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2
roll 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 add
add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub
mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t
sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse
y0 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 yB
sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
w 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 neg
exch X sub neg exch moveto setmatrix CP grestore } def
/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0
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/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 } if
r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop }
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def
end
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%%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 def
tx@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
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grestore
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/firstx newx def /firsty newy def
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/oldx newx def /oldy newy def
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/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
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Hoffset sub Sx add
Transform
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Char end tx@TextPathSavedShow
tx@TextPathDict begin
grestore
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} def
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/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 def
end
/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 begin
tx@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 end
grestore } 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 exch
Sin 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 } { dx
dup 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 dup
Cos mul exch Sin mul } def
/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h
mul 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 /d
ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d
sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan
sin def /NodePos { TriNodePos } def } def
/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos
hh 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 { Dist
Dist 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 idtransform
exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx
dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop
XYPos } ifelse } def
/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1
roll sin mul sub exch } ifelse } def
/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA
AddOffset yA add /yA1 ED xA add /xA1 ED } def
/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB
AddOffset yB add /yB1 ED xB add /xB1 ED } def
/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA
AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED
ArmA 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 ArmB
AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED
ArmB 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 b
known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA
ED /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 sub
mul 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 3
mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx
sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul
add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add
y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul
mul 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 cleartomark
VPosEnd } def
/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
def grestore exec /LPutVar /SaveLPutVar load def } def
/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
GetEdgeA 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 pop
end } def
/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub
Atan /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 xA1
yA1 ] 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 -1
roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
begin 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 rotate
def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx
itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2
yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1
yB1 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 xB2
yB2 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 yA1
tx@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 def
xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx
transform 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 ArmB
0 ne { xB1 yB1 } if xB2 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
/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if
xB2 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 ED
GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin
false 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 rotate
def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2
mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3
mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2
xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false
Line 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 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 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 add
AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r
Div def /y ED /x ED } def
/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB
180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos
mul 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 dy
add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos
{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar
tx@Dict begin false Polygon end } def
/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan
def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2
mul 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 div
def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def
GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul
sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0
eq { 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 def
0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2
roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0
0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2
roll 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 add
add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub
mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t
sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse
y0 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 yB
sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
w 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 neg
exch X sub neg exch moveto setmatrix CP grestore } def
/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0
def } 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 } if
r 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 }
def
end
% 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 def
tx@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
} def
end
% END pst-text.pro
%%EndProcSet
%%BeginProcSet: special.pro
%!
TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N
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%%EndProcSet
%%BeginProcSet: color.pro
%!
TeXDict begin/setcmykcolor where{pop}{/setcmykcolor{dup 10 eq{pop
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/TeXcolorrgb{setrgbcolor}def/TeXcolorgrey{setgray}def/TeXcolorgray{
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FV(=)f Ff(f2)p FZ(;)k Ff(2)l FZ(<)l Ff(3)p FC(^)q Ff(f2)d
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250 6 23 v 4182 241 25 3 v 67 w Ff(f1)d FV(=)f Ff(1)p
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3498 793 2094 4 v 3498 847 a FV(\()p Ff(f1)h FV(=)f Ff(1)p
FC(^)o Ff(f0)h FV(=)f Ff(1)p FV(\))p FC(\033)p Ff(f0)h
FV(=)f Ff(f1)p FZ(;)k(M)4129 857 y FP(1)4161 847 y FZ(;)f(M)4248
857 y FP(2)4281 847 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
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FZ(;)j(S)o(;)h(T)p 4878 835 6 23 v 4883 825 25 3 v 67
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FV(=)f Ff(fm)p FV(\))5591 802 y FC(\033)5639 813 y Fd(L)p
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FC(\033)p Ff(f0)h FV(=)f Ff(fy)q FV(\))p FZ(;)j(M)4185
943 y FP(1)4218 933 y FZ(;)g(M)4305 943 y FP(2)4337 933
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4934 921 6 23 v 4940 911 25 3 v 67 w Ff(f0)d FV(=)f Ff(f1)p
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FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p FV(\))5648
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Ff(fx)h FV(=)f Ff(fy)p FV(\))p FZ(;)k(M)4205 1029 y FP(1)4237
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23 v 4960 998 25 3 v 68 w Ff(f0)e FV(=)f Ff(f1)p FZ(;)p
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Ff(m)p FC(^)q Ff(fn)g FV(=)g Ff(fm)p FV(\))5667 977 y
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67 w Ff(f0)d FV(=)f Ff(f1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p
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FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p 4016 1180 6
23 v 4021 1170 25 3 v 67 w Ff(0)l FZ(<)l Ff(1)p FC(^)r
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FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)g FV(=)g
Ff(fm)p FV(\))5304 1146 y FC(^)5346 1158 y Fd(R)p 3126
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23 v 3939 1257 25 3 v 57 w FC(9)p Ff(m)p FZ(:)p FV(\()p
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FZ(;)k(S)o(;)f(T)p 4171 1353 6 23 v 4177 1343 25 3 v
57 w FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l
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y FV(1)2148 1612 y F9(=)20 b FX(8)p Fu(y)q Gc(:)p Fu(x)p
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FZ(;)p Ff(y)2626 1612 y F9(\))101 b Gc(T)30 b F9(=)19
b FX(8)p Fu(i)p Gc(:)p Fu(x)p Gc(:)p Fu(y)q Gc(:)m F9(\(\()p
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b FX(\033)g Fu(fx)19 b F9(=)g Fu(fy)p F9(\))2026 1738
y Gc(M)2094 1747 y FV(2)2148 1738 y F9(=)h FX(8)p Fu(y)q
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1714 y Ff(x)p FZ(;)p Ff(y)2627 1738 y F9(\))100 b Gc(S)23
b F9(=)d FX(8)p Fu(x)p Gc(:)p Fu(y)q Gc(:)m F9(\()p Fu(sx)8
b FX(\024)g Fu(y)k FX(\033)g Fu(x)c Gc(<)g Fu(y)q F9(\))6506
465 y
currentpoint grestore moveto
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Black Black eop end
%%Page: 133 145
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465 y
currentpoint grestore moveto
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5273 y Gg(.)p Black Black eop end
%%Page: 134 146
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25 3 v 59 w Ff(f0)h FV(=)f Ff(f1)p FZ(;)k Ff(f1)c FV(=)g
Ff(1)p FZ(;)k Ff(f0)d FV(=)f Ff(1)6358 -976 y FC(\033)6406
-965 y Fd(L)p 4618 -899 1623 4 v 4607 -845 a FC(8)p Ff(y)q
FZ(:)p FV(\(\()p Ff(fy)i FV(=)e Ff(0)p FC(^)o Ff(f0)h
FV(=)f Ff(0)p FV(\))p FC(\033)p Ff(f0)h FV(=)f Ff(fy)q
FV(\))p FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)h FV(=)f
Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p 5731 -857
6 23 v 5737 -867 25 3 v 59 w Ff(f0)h FV(=)f Ff(f1)p FZ(;)k
Ff(f1)c FV(=)g Ff(1)p FZ(;)k Ff(f0)d FV(=)f Ff(1)6240
-887 y FC(8)6275 -876 y Fd(L)p 4598 -813 1662 4 v 4588
-759 a FC(8)p Ff(x)p FZ(:)p Ff(y)q FZ(:)p FV(\(\()p Ff(fy)h
FV(=)f Ff(0)p FC(^)p Ff(fx)h FV(=)f Ff(0)p FV(\))p FC(\033)p
Ff(fx)g FV(=)g Ff(fy)q FV(\))p FZ(;)p FC(8)p Ff(x)p FZ(:)p
FV(\()p Ff(fx)h FV(=)f Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p
FV(\))p 5751 -771 6 23 v 5757 -781 25 3 v 59 w Ff(f0)g
FV(=)g Ff(f1)q FZ(;)j Ff(f1)e FV(=)f Ff(1)p FZ(;)j Ff(f0)e
FV(=)f Ff(1)6259 -801 y FC(8)6294 -790 y Fd(L)p 4598
-726 1662 4 v 4914 -672 a FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)g FV(=)g Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p
FZ(;)j(T)p 5425 -684 6 23 v 5431 -694 25 3 v 68 w Ff(f0)e
FV(=)f Ff(f1)p FZ(;)j Ff(f1)e FV(=)f Ff(1)p FZ(;)k Ff(f0)c
FV(=)g Ff(1)6259 -715 y FC(8)6294 -704 y Fd(L)p 3568
-640 2367 4 v 4085 -586 a FZ(M)4143 -576 y FP(1)4176
-586 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)g FV(=)g
Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p
4773 -598 6 23 v 4778 -608 25 3 v 67 w Ff(f1)d FV(=)f
Ff(1)p FZ(;)k Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)d FV(=)f
Ff(f1)p FZ(;)k Ff(f0)c FV(=)g Ff(1)5934 -632 y FC(^)5975
-621 y Fd(R)3275 -541 y Fc(|)p 3299 -541 1540 8 v 1540
w({z)p 4887 -541 V 1540 w(})4823 -480 y Fd(X)4869 -468
y FP(3)p 2885 -224 247 4 v 2885 -172 a Ff(1)l FC(\024)l
Ff(2)p 2993 -184 6 23 v 2999 -194 25 3 v 61 w(1)l FC(\024)l
Ff(2)p 2793 -142 431 4 v 2783 -77 a FC(8)p Ff(x)p FZ(:)p
FV(\()p Ff(x)l FC(\024)l Ff(m)2991 -98 y Fe(x)p Fd(;)p
Fe(2)3047 -77 y FV(\))p 3086 -89 6 23 v 3091 -99 25 3
v 59 w Ff(1)l FC(\024)l Ff(2)3223 -130 y FC(8)3258 -119
y Fd(L)p 2793 -45 431 4 v 2887 7 a FZ(M)2945 17 y FP(1)p
2992 -5 6 23 v 2997 -15 25 3 v 3036 7 a Ff(1)l FC(\024)l
Ff(2)3223 -33 y FC(8)3258 -22 y Fd(L)p 3352 -44 247 4
v 3352 7 a Ff(0)l FZ(<)l Ff(2)p 3460 -5 6 23 v 3466 -15
25 3 v 61 w(0)l FZ(<)l Ff(2)p 2887 37 712 4 v 2989 88
a(1)l FC(\024)l Ff(2)p FC(\033)r Ff(0)l FZ(<)l Ff(2)p
FZ(;)12 b(M)3312 98 y FP(1)p 3358 76 6 23 v 3364 66 25
3 v 3403 88 a Ff(0)l FZ(<)l Ff(2)3598 46 y FC(\033)3646
57 y Fd(L)p 2932 118 622 4 v 2921 172 a FC(8)p Ff(y)q
FZ(:)p FV(\()p Ff(1)l FC(\024)l Ff(y)q FC(\033)r Ff(0)l
FZ(<)l Ff(y)q FV(\))p FZ(;)g(M)3369 182 y FP(1)p 3415
160 6 23 v 3421 150 25 3 v 3460 172 a Ff(0)l FZ(<)l Ff(2)3553
130 y FC(8)3588 141 y Fd(L)p 2932 205 622 4 v 3086 255
a FZ(M)3144 265 y FP(1)3177 255 y FZ(;)e(S)p 3261 243
6 23 v 3266 233 25 3 v 61 w Ff(0)l FZ(<)l Ff(2)3553 216
y FC(8)3588 227 y Fd(L)p 3776 -382 319 4 v 3776 -331
a Ff(f2)e FV(=)f Ff(0)p 3920 -343 6 23 v 3926 -353 25
3 v 59 w(f2)h FV(=)f Ff(0)p 4144 -382 319 4 v 49 w(f2)h
FV(=)f Ff(1)p 4288 -343 6 23 v 4294 -353 25 3 v 59 w(f2)h
FV(=)f Ff(1)p 3776 -311 687 4 v 3795 -260 a(f2)h FV(=)f
Ff(0)p FC(_)o Ff(f2)h FV(=)f Ff(1)p 4110 -272 6 23 v
4116 -282 25 3 v 59 w(f2)h FV(=)f Ff(0)p FZ(;)j Ff(f2)e
FV(=)f Ff(1)4462 -303 y FC(_)4504 -292 y Fd(L)p 3739
-230 761 4 v 3729 -176 a FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)h FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p
4166 -188 6 23 v 4172 -198 25 3 v 59 w Ff(f2)h FV(=)f
Ff(0)p FZ(;)j Ff(f2)e FV(=)f Ff(1)4499 -219 y FC(8)4534
-208 y Fd(L)p 4665 -382 319 4 v 4665 -331 a Ff(f0)g FV(=)g
Ff(0)p 4809 -343 6 23 v 4814 -353 25 3 v 59 w(f0)h FV(=)f
Ff(0)p 5033 -382 319 4 v 50 w(f0)h FV(=)f Ff(1)p 5177
-343 6 23 v 5183 -353 25 3 v 59 w(f0)h FV(=)f Ff(1)p
4665 -311 687 4 v 4684 -260 a(f0)g FV(=)g Ff(0)p FC(_)p
Ff(f0)h FV(=)f Ff(1)p 4999 -272 6 23 v 5005 -282 25 3
v 59 w(f0)g FV(=)g Ff(0)p FZ(;)k Ff(f0)d FV(=)f Ff(1)5351
-303 y FC(_)5392 -292 y Fd(L)p 4628 -230 761 4 v 4617
-176 a FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)h FV(=)f Ff(0)p
FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p 5055 -188 6 23 v
5060 -198 25 3 v 59 w Ff(f0)h FV(=)f Ff(0)p FZ(;)k Ff(f0)c
FV(=)g Ff(1)5388 -219 y FC(8)5423 -208 y Fd(L)p 3739
-144 1650 4 v 4007 -90 a FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)h FV(=)f Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p
4445 -102 6 23 v 4451 -112 25 3 v 59 w Ff(f2)g FV(=)g
Ff(0)p FC(^)p Ff(f0)h FV(=)f Ff(0)p FZ(;)j Ff(f2)e FV(=)f
Ff(1)p FZ(;)k Ff(f0)c FV(=)g Ff(1)5388 -136 y FC(^)5429
-125 y Fd(R)p 5526 -141 351 4 v 5526 -90 a Ff(f0)h FV(=)f
Ff(f2)p 5686 -102 6 23 v 5692 -112 25 3 v 59 w(f0)h FV(=)f
Ff(f2)p 4018 -58 1859 4 v 4193 -4 a FV(\()p Ff(f2)h FV(=)f
Ff(0)p FC(^)o Ff(f0)h FV(=)f Ff(0)p FV(\))p FC(\033)p
Ff(f0)h FV(=)f Ff(f2)p FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)h FV(=)f Ff(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p
5192 -16 6 23 v 5198 -26 25 3 v 59 w Ff(f0)h FV(=)f Ff(f2)p
FZ(;)k Ff(f2)c FV(=)g Ff(1)p FZ(;)k Ff(f0)d FV(=)f Ff(1)5876
-49 y FC(\033)5924 -37 y Fd(L)p 4136 29 1623 4 v 4126
83 a FC(8)p Ff(y)q FZ(:)p FV(\(\()p Ff(fy)h FV(=)f Ff(0)p
FC(^)p Ff(f0)g FV(=)g Ff(0)p FV(\))p FC(\033)p Ff(f0)h
FV(=)f Ff(fy)q FV(\))p FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)h FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p
5249 71 6 23 v 5255 61 25 3 v 59 w Ff(f0)h FV(=)f Ff(f2)p
FZ(;)k Ff(f2)c FV(=)g Ff(1)p FZ(;)k Ff(f0)d FV(=)f Ff(1)5758
40 y FC(8)5793 51 y Fd(L)p 4117 115 1662 4 v 4106 169
a FC(8)p Ff(x)p FZ(:)p Ff(y)q FZ(:)p FV(\(\()p Ff(fy)i
FV(=)e Ff(0)p FC(^)o Ff(fx)h FV(=)f Ff(0)p FV(\))p FC(\033)p
Ff(fx)h FV(=)f Ff(fy)q FV(\))p FZ(;)p FC(8)p Ff(x)p FZ(:)p
FV(\()p Ff(fx)g FV(=)g Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p
FV(\))p 5269 157 6 23 v 5275 147 25 3 v 59 w Ff(f0)g
FV(=)g Ff(f2)q FZ(;)j Ff(f2)e FV(=)f Ff(1)p FZ(;)k Ff(f0)c
FV(=)g Ff(1)5777 127 y FC(8)5812 138 y Fd(L)p 4117 201
1662 4 v 4432 255 a FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)h
FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)k(T)p
4943 243 6 23 v 4949 233 25 3 v 67 w Ff(f0)d FV(=)f Ff(f2)p
FZ(;)j Ff(f2)e FV(=)f Ff(1)p FZ(;)k Ff(f0)d FV(=)f Ff(1)5777
213 y FC(8)5812 224 y Fd(L)p 3086 288 2367 4 v 3603 342
a FZ(M)3661 352 y FP(1)3694 342 y FZ(;)p FC(8)p Ff(x)p
FZ(:)p FV(\()p Ff(fx)h FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f
Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p 4291 330 6 23 v 4297
320 25 3 v 68 w Ff(f2)d FV(=)g Ff(1)p FZ(;)k Ff(0)l FZ(<)l
Ff(2)p FC(^)q Ff(f0)d FV(=)f Ff(f2)p FZ(;)k Ff(f0)c FV(=)g
Ff(1)5452 296 y FC(^)5493 307 y Fd(R)6070 191 y F3(.)6070
224 y(.)6070 257 y(.)6070 290 y(.)6035 342 y FZ(X)6085
352 y FP(3)p 3603 374 2532 4 v 3962 428 a FZ(M)4020 438
y FP(1)4052 428 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)h FV(=)f Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p
FZ(;)j(S)o(;)h(T)p 4649 416 6 23 v 4655 406 25 3 v 67
w Ff(f2)d FV(=)f Ff(1)p FC(^)p Ff(f1)g FV(=)g Ff(1)p
FZ(;)k Ff(0)l FZ(<)l Ff(2)p FC(^)q Ff(f0)d FV(=)f Ff(f2)p
FZ(;)k Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)d FV(=)f Ff(f1)p
FZ(;)k Ff(f0)c FV(=)g Ff(1)6134 382 y FC(^)6176 394 y
Fd(R)2793 473 y Fc(|)p 2817 473 1667 8 v 1667 w({z)p
4532 473 V 1667 w(})4469 534 y Fd(X)4515 546 y FP(4)p
2660 648 247 4 v 2660 699 a Ff(2)l FC(\024)l Ff(2)p 2768
687 6 23 v 2773 678 25 3 v 61 w(2)l FC(\024)l Ff(2)p
2567 729 433 4 v 2556 794 a FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(2)l FC(\024)l Ff(m)2766 773 y Fe(x)p Fd(;)p Fe(2)2823
794 y FV(\))p 2861 782 6 23 v 2867 772 25 3 v 59 w Ff(2)l
FC(\024)l Ff(2)2999 741 y FC(8)3034 752 y Fd(L)p 2567
827 433 4 v 2662 878 a FZ(M)2720 888 y FP(2)p 2766 866
6 23 v 2772 856 25 3 v 2811 878 a Ff(2)l FC(\024)l Ff(2)2999
838 y FC(8)3034 849 y Fd(L)p 3127 827 247 4 v 3127 878
a Ff(1)l FZ(<)l Ff(2)p 3235 866 6 23 v 3241 856 25 3
v 61 w(1)l FZ(<)l Ff(2)p 2662 908 713 4 v 2764 960 a(2)l
FC(\024)l Ff(2)p FC(\033)q Ff(1)l FZ(<)l Ff(2)p FZ(;)13
b(M)3087 970 y FP(2)p 3133 948 6 23 v 3139 938 25 3 v
3178 960 a Ff(1)l FZ(<)l Ff(2)3373 917 y FC(\033)3421
928 y Fd(L)p 2707 990 622 4 v 2696 1044 a FC(8)p Ff(y)q
FZ(:)p FV(\()p Ff(2)l FC(\024)l Ff(y)q FC(\033)r Ff(1)l
FZ(<)l Ff(y)q FV(\))p FZ(;)f(M)3144 1054 y FP(2)p 3190
1032 6 23 v 3196 1022 25 3 v 3235 1044 a Ff(1)l FZ(<)l
Ff(2)3328 1001 y FC(8)3363 1012 y Fd(L)p 2707 1076 622
4 v 2861 1127 a FZ(M)2919 1137 y FP(2)2951 1127 y FZ(;)f(S)p
3035 1115 6 23 v 3041 1105 25 3 v 61 w Ff(1)l FZ(<)l
Ff(2)3328 1088 y FC(8)3363 1099 y Fd(L)4500 634 y F3(.)4500
667 y(.)4500 700 y(.)4500 733 y(.)4465 784 y FZ(X)4515
794 y FP(4)p 4615 733 351 4 v 4615 784 a Ff(f1)d FV(=)f
Ff(f2)p 4775 772 6 23 v 4781 763 25 3 v 59 w(f1)h FV(=)f
Ff(f2)p 3591 814 2232 4 v 3591 868 a FV(\()p Ff(f2)h
FV(=)f Ff(1)p FC(^)o Ff(f1)h FV(=)f Ff(1)p FV(\))p FC(\033)p
Ff(f1)h FV(=)f Ff(f2)p FZ(;)k(M)4222 878 y FP(1)4254
868 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f
Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p
4851 856 6 23 v 4857 846 25 3 v 68 w Ff(f1)d FV(=)g Ff(f2)q
FZ(;)j Ff(0)l FZ(<)l Ff(2)p FC(^)q Ff(f0)e FV(=)f Ff(f2)p
FZ(;)k Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)d FV(=)f Ff(f1)p
FZ(;)k Ff(f0)d FV(=)f Ff(1)5822 823 y FC(\033)5870 834
y Fd(L)p 3534 900 2346 4 v 3523 954 a FC(8)p Ff(y)q FZ(:)p
FV(\(\()p Ff(fy)i FV(=)e Ff(1)p FC(^)o Ff(f1)h FV(=)f
Ff(1)p FV(\))p FC(\033)p Ff(f1)h FV(=)f Ff(fy)q FV(\))p
FZ(;)j(M)4278 964 y FP(1)4311 954 y FZ(;)p FC(8)p Ff(x)p
FZ(:)p FV(\()p Ff(fx)e FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f
Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p 4908 942 6 23 v 4913
932 25 3 v 67 w Ff(f1)d FV(=)f Ff(f2)p FZ(;)k Ff(0)l
FZ(<)l Ff(2)p FC(^)q Ff(f0)d FV(=)f Ff(f2)p FZ(;)k Ff(0)l
FZ(<)l Ff(1)p FC(^)q Ff(f0)d FV(=)f Ff(f1)p FZ(;)k Ff(f0)c
FV(=)g Ff(1)5879 912 y FC(8)5914 923 y Fd(L)p 3514 987
2385 4 v 3504 1041 a FC(8)p Ff(x)p FZ(:)p Ff(y)q FZ(:)p
FV(\(\()p Ff(fy)i FV(=)e Ff(1)p FC(^)o Ff(fx)h FV(=)f
Ff(1)p FV(\))p FC(\033)p Ff(fx)h FV(=)f Ff(fy)p FV(\))p
FZ(;)k(M)4298 1051 y FP(1)4330 1041 y FZ(;)p FC(8)p Ff(x)p
FZ(:)p FV(\()p Ff(fx)d FV(=)f Ff(0)p FC(_)p Ff(fx)g FV(=)g
Ff(1)p FV(\))p FZ(;)k(S)o(;)g(T)p 4927 1029 6 23 v 4933
1019 25 3 v 67 w Ff(f1)d FV(=)f Ff(f2)p FZ(;)k Ff(0)l
FZ(<)l Ff(2)p FC(^)q Ff(f0)d FV(=)f Ff(f2)p FZ(;)j Ff(0)l
FZ(<)l Ff(1)p FC(^)r Ff(f0)d FV(=)g Ff(f1)q FZ(;)j Ff(f0)e
FV(=)f Ff(1)5898 998 y FC(8)5933 1009 y Fd(L)p 3514 1073
2385 4 v 3877 1127 a FZ(M)3935 1137 y FP(1)3967 1127
y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)h FV(=)f
Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p
4565 1115 6 23 v 4570 1105 25 3 v 67 w Ff(f1)d FV(=)f
Ff(f2)p FZ(;)k Ff(0)l FZ(<)l Ff(2)p FC(^)q Ff(f0)d FV(=)f
Ff(f2)p FZ(;)k Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)d FV(=)f
Ff(f1)p FZ(;)k Ff(f0)c FV(=)g Ff(1)5898 1085 y FC(8)5933
1096 y Fd(L)p 2861 1159 2676 4 v 3242 1213 a FZ(M)3300
1223 y FP(1)3332 1213 y FZ(;)j(M)3419 1223 y FP(2)3452
1213 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)f
Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p
4049 1201 6 23 v 4054 1191 25 3 v 68 w Ff(0)l FZ(<)l
Ff(2)p FC(^)q Ff(f0)d FV(=)f Ff(f2)p FZ(;)j Ff(0)l FZ(<)l
Ff(1)p FC(^)r Ff(f0)d FV(=)g Ff(f1)q FZ(;)j Ff(1)l FZ(<)l
Ff(2)p FC(^)r Ff(f1)d FV(=)g Ff(f2)q FZ(;)j Ff(f0)e FV(=)f
Ff(1)5535 1168 y FC(^)5577 1179 y Fd(R)p 3159 1246 2079
4 v 3159 1300 a FZ(M)3217 1310 y FP(1)3250 1300 y FZ(;)j(M)3337
1310 y FP(2)3369 1300 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)e FV(=)f Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p
FZ(;)j(S)o(;)h(T)p 3966 1288 6 23 v 3972 1278 25 3 v
57 w FC(9)p Ff(m)p FZ(:)p FV(\()p Ff(0)l FZ(<)l Ff(m)p
FC(^)q Ff(f0)c FV(=)g Ff(fm)p FV(\))p FZ(;)k Ff(0)l FZ(<)l
Ff(1)p FC(^)q Ff(f0)d FV(=)f Ff(f1)p FZ(;)j Ff(1)l FZ(<)l
Ff(2)p FC(^)r Ff(f1)e FV(=)f Ff(f2)p FZ(;)j Ff(f0)e FV(=)f
Ff(1)5237 1257 y FC(9)5272 1268 y Fd(R)p 3135 1332 2127
4 v 3135 1386 a FZ(M)3193 1396 y FP(1)3226 1386 y FZ(;)j(M)3313
1396 y FP(2)3345 1386 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)e FV(=)f Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p
FZ(;)j(S)o(;)h(T)p 3943 1374 6 23 v 3948 1364 25 3 v
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FZ(;)k Ff(f0)d FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p
Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)g
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23 v 4104 1537 25 3 v 68 w Ff(1)l FZ(<)l Ff(2)p FC(^)q
Ff(f1)e FV(=)f Ff(f2)p FZ(;)k Ff(f0)c FV(=)g Ff(1)p FZ(;)p
FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l
Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p FV(\))5343 1516
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FZ(;)j(S)o(;)h(T)p 4016 1633 6 23 v 4021 1623 25 3 v
57 w FC(9)p Ff(m)p FZ(:)p FV(\()p Ff(1)l FZ(<)l Ff(m)p
FC(^)q Ff(f1)c FV(=)g Ff(fm)p FV(\))p FZ(;)k Ff(f0)d
FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p
FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)g FV(=)g Ff(fm)p
FV(\))5188 1603 y FC(9)5223 1614 y Fd(R)p 3209 1677 1981
4 v 3446 1731 a FZ(M)3504 1741 y FP(1)3537 1731 y FZ(;)j(M)3624
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FZ(;)k(S)o(;)g(T)p 4253 1719 6 23 v 4259 1709 25 3 v
67 w Ff(f0)d FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p
Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)g
FV(=)g Ff(fm)p FV(\))5188 1689 y FC(9)5223 1700 y Fd(R)2567
1776 y Fc(|)p 2591 1776 1658 8 v 1658 w({z)p 4297 1776
V 1658 w(})4233 1838 y Fd(X)4279 1850 y FP(5)2259 1970
y Gc(M)2327 1979 y FV(1)2381 1970 y F9(=)19 b FX(8)p
Fu(y)q Gc(:)p Fu(x)p Gc(:)n F9(\()p Fu(x)8 b FX(\024)g
Fu(m)2788 1947 y Ff(x)p FZ(;)p Ff(y)2859 1970 y F9(\))101
b Gc(T)30 b F9(=)19 b FX(8)p Fu(i)p Gc(:)p Fu(x)p Gc(:)p
Fu(y)q Gc(:)m F9(\(\()p Fu(fy)h F9(=)g Fu(i)p FX(^)p
Fu(fx)f F9(=)g Fu(i)p F9(\))12 b FX(\033)g Fu(fx)18 b
F9(=)i Fu(fy)p F9(\))2259 2097 y Gc(M)2327 2106 y FV(2)2381
2097 y F9(=)f FX(8)p Fu(y)q Gc(:)p Fu(x)p Gc(:)n F9(\()p
Fu(y)9 b FX(\024)f Fu(m)2789 2073 y Ff(x)p FZ(;)p Ff(y)2860
2097 y F9(\))100 b Gc(S)23 b F9(=)d FX(8)p Fu(x)p Gc(:)p
Fu(y)q Gc(:)m F9(\()p Fu(sx)8 b FX(\024)g Fu(y)k FX(\033)g
Fu(x)c Gc(<)g Fu(y)q F9(\))6739 408 y
currentpoint grestore moveto
6739 408 a 4009
5012 4 4630 v 321 5015 3691 4 v Black 1262 5283 a Gg(Figure)24
b(3:)29 b(Subproofs)c Ga(X)2092 5297 y F9(3)2132 5283
y Gg(,)d Ga(X)2252 5297 y F9(4)2315 5283 y Gg(and)i Ga(X)2544
5297 y F9(5)2583 5283 y Gg(.)p Black Black eop end
%%Page: 135 147
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FV(=)f Ff(0)p FC(^)p Ff(f1)g FV(=)g Ff(0)4134 -949 y
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Ff(f1)h FV(=)f Ff(fy)q FV(\))p FZ(;)k Ff(f2)c FV(=)g
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465 y
currentpoint grestore moveto
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FC(_)p Ff(f1)h FV(=)f Ff(1)p FZ(;)j Ff(1)l FC(\024)l
Ff(1)p FZ(;)j Ff(f0)7 b FV(=)g Ff(0)p FZ(;)k(M)3558 -325
y FP(1)3590 -335 y FZ(;)g(M)3678 -325 y FP(2)3710 -335
y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f
Ff(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p
4307 -347 6 23 v 4313 -357 25 3 v 68 w Ff(0)l FZ(<)l
Ff(1)p FC(^)q Ff(f0)e FV(=)f Ff(f1)p FZ(;)k Ff(1)l FZ(<)l
Ff(2)p FC(^)q Ff(f1)d FV(=)f Ff(f2)p FZ(;)k Ff(f0)c FV(=)g
Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p
Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p FV(\))5626
-381 y FC(_)5667 -370 y Fd(L)p 2887 -303 2741 4 v 3052
-249 a Ff(1)l FC(\024)l Ff(1)p FZ(;)12 b Ff(f0)c FV(=)f
Ff(0)p FZ(;)k(M)3393 -239 y FP(1)3425 -249 y FZ(;)f(M)3512
-239 y FP(2)3545 -249 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)e FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p
FZ(;)j(S)o(;)h(T)p 4142 -261 6 23 v 4147 -271 25 3 v
67 w Ff(0)l FZ(<)l Ff(1)p FC(^)r Ff(f0)d FV(=)f Ff(f1)p
FZ(;)j Ff(1)l FZ(<)l Ff(2)p FC(^)r Ff(f1)d FV(=)g Ff(f2)q
FZ(;)j Ff(f0)e FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p
Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)g
FV(=)g Ff(fm)p FV(\))5626 -291 y FC(8)5661 -280 y Fd(L)p
2960 -216 2594 4 v 2949 -152 a FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(x)l FC(\024)l Ff(m)3157 -173 y Fe(x)p Fd(;)p Fe(0)3214
-152 y FV(\))p FZ(;)j Ff(f0)e FV(=)f Ff(0)p FZ(;)k(M)3485
-142 y FP(1)3517 -152 y FZ(;)f(M)3604 -142 y FP(2)3637
-152 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)f
Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p
4234 -164 6 23 v 4240 -174 25 3 v 68 w Ff(0)l FZ(<)l
Ff(1)p FC(^)q Ff(f0)e FV(=)f Ff(f1)p FZ(;)j Ff(1)l FZ(<)l
Ff(2)p FC(^)r Ff(f1)d FV(=)g Ff(f2)q FZ(;)j Ff(f0)e FV(=)f
Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p
Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)o FV(\))5552
-205 y FC(8)5587 -194 y Fd(L)p 2960 -119 2594 4 v 3114
-65 a Ff(f0)g FV(=)g Ff(0)p FZ(;)k(M)3331 -55 y FP(1)3363
-65 y FZ(;)g(M)3451 -55 y FP(2)3483 -65 y FZ(;)p FC(8)p
Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f Ff(0)p FC(_)p Ff(fx)g
FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p 4080 -77 6 23
v 4086 -87 25 3 v 68 w Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)e
FV(=)f Ff(f1)p FZ(;)k Ff(1)l FZ(<)l Ff(2)p FC(^)q Ff(f1)d
FV(=)f Ff(f2)p FZ(;)k Ff(f0)c FV(=)g Ff(1)p FZ(;)p FC(9)p
Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p
FC(^)q Ff(fn)h FV(=)f Ff(fm)p FV(\))5552 -108 y FC(8)5587
-97 y Fd(L)2887 -21 y Fc(|)p 2911 -21 1365 8 v 1365 w({z)p
4324 -21 V 1365 w(})4266 41 y Fd(Y)4300 53 y FP(6)p 2180
995 247 4 v 2180 1047 a Ff(1)l FC(\024)l Ff(2)p 2288
1035 6 23 v 2294 1025 25 3 v 61 w(1)l FC(\024)l Ff(2)p
2476 996 247 4 v 51 w(0)l FZ(<)l Ff(2)p 2584 1035 6 23
v 2590 1025 25 3 v 61 w(0)l FZ(<)l Ff(2)p 2180 1077 543
4 v 2196 1128 a(1)l FC(\024)l Ff(2)p FC(\033)q Ff(0)l
FZ(<)l Ff(2)p FZ(;)13 b Ff(1)l FC(\024)l Ff(2)p 2569
1116 6 23 v 2574 1106 25 3 v 60 w(0)l FZ(<)l Ff(2)2722
1086 y FC(\033)2770 1097 y Fd(L)p 2139 1158 626 4 v 2128
1212 a FC(8)p Ff(y)q FZ(:)p FV(\()p Ff(1)l FC(\024)l
Ff(y)q FC(\033)r Ff(0)l FZ(<)l Ff(y)q FV(\))p FZ(;)f
Ff(1)l FC(\024)l Ff(2)p 2626 1200 6 23 v 2631 1190 25
3 v 60 w(0)l FZ(<)l Ff(2)2763 1170 y FC(8)2798 1181 y
Fd(L)p 2139 1244 626 4 v 2293 1296 a Ff(1)l FC(\024)l
Ff(2)p FZ(;)h(S)p 2471 1284 6 23 v 2477 1274 25 3 v 61
w Ff(0)l FZ(<)l Ff(2)2763 1256 y FC(8)2798 1267 y Fd(L)p
2892 813 319 4 v 2892 864 a Ff(f2)8 b FV(=)f Ff(1)p 3036
852 6 23 v 3042 842 25 3 v 59 w(f2)g FV(=)g Ff(1)4299
198 y F3(.)4299 231 y(.)4299 265 y(.)4299 298 y(.)4270
349 y FZ(Y)4306 359 y FP(6)p 4407 298 319 4 v 4407 349
a Ff(f0)g FV(=)g Ff(1)p 4551 337 6 23 v 4556 327 25 3
v 59 w(f0)h FV(=)f Ff(1)p 3260 379 2458 4 v 3260 433
a(f0)h FV(=)f Ff(0)p FC(_)p Ff(f0)g FV(=)g Ff(1)p FZ(;)k(M)3649
443 y FP(1)3681 433 y FZ(;)g(M)3769 443 y FP(2)3801 433
y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f
Ff(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p
4398 421 6 23 v 4404 411 25 3 v 68 w Ff(0)l FZ(<)l Ff(1)p
FC(^)q Ff(f0)e FV(=)f Ff(f1)p FZ(;)k Ff(1)l FZ(<)l Ff(2)p
FC(^)q Ff(f1)d FV(=)f Ff(f2)p FZ(;)k Ff(f0)c FV(=)g Ff(1)p
FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l
FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p FV(\))5717
387 y FC(_)5758 398 y Fd(L)p 3260 465 2458 4 v 3426 519
a FZ(M)3484 529 y FP(1)3516 519 y FZ(;)j(M)3603 529 y
FP(2)3636 519 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e
FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p
4233 507 6 23 v 4238 497 25 3 v 67 w Ff(0)l FZ(<)l Ff(1)p
FC(^)r Ff(f0)d FV(=)f Ff(f1)p FZ(;)j Ff(1)l FZ(<)l Ff(2)p
FC(^)r Ff(f1)d FV(=)g Ff(f2)q FZ(;)j Ff(f0)e FV(=)f Ff(1)p
FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l
FZ(<)l Ff(m)p FC(^)q Ff(fn)g FV(=)g Ff(fm)p FV(\))5717
477 y FC(8)5752 488 y Fd(L)p 3343 551 2292 4 v 3343 605
a FZ(M)3401 615 y FP(1)3434 605 y FZ(;)j(M)3521 615 y
FP(2)3553 605 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e
FV(=)f Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p
4150 593 6 23 v 4156 583 25 3 v 57 w FC(9)p Ff(m)p FZ(:)p
FV(\()p Ff(0)l FZ(<)l Ff(m)p FC(^)q Ff(f0)c FV(=)g Ff(fm)p
FV(\))p FZ(;)k Ff(1)l FZ(<)l Ff(2)p FC(^)q Ff(f1)d FV(=)f
Ff(f2)p FZ(;)j Ff(f0)e FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p
FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q
Ff(fn)h FV(=)f Ff(fm)p FV(\))5634 563 y FC(9)5669 574
y Fd(R)p 3343 638 2292 4 v 3581 692 a FZ(M)3639 702 y
FP(1)3671 692 y FZ(;)k(M)3759 702 y FP(2)3791 692 y FZ(;)p
FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f Ff(0)p FC(_)p
Ff(fx)g FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p 4388
680 6 23 v 4394 670 25 3 v 68 w Ff(1)l FZ(<)l Ff(2)p
FC(^)q Ff(f1)e FV(=)f Ff(f2)p FZ(;)k Ff(f0)c FV(=)g Ff(1)p
FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l
FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p FV(\))5634
649 y FC(9)5669 660 y Fd(R)p 3499 724 1981 4 v 3499 778
a FZ(M)3557 788 y FP(1)3589 778 y FZ(;)k(M)3677 788 y
FP(2)3709 778 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d
FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p
4306 766 6 23 v 4312 756 25 3 v 57 w FC(9)p Ff(m)p FZ(:)p
FV(\()p Ff(1)l FZ(<)l Ff(m)p FC(^)q Ff(f1)e FV(=)f Ff(fm)p
FV(\))p FZ(;)j Ff(f0)e FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p
FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q
Ff(fn)g FV(=)g Ff(fm)p FV(\))5478 736 y FC(9)5513 747
y Fd(R)p 3499 810 1981 4 v 3736 864 a FZ(M)3794 874 y
FP(1)3827 864 y FZ(;)j(M)3914 874 y FP(2)3947 864 y FZ(;)p
FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)g Ff(0)p FC(_)p
Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p 4544
852 6 23 v 4549 842 25 3 v 67 w Ff(f0)d FV(=)f Ff(1)p
FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l
FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)o FV(\))5478
822 y FC(9)5513 833 y Fd(R)p 2892 897 2350 4 v 3149 951
a Ff(f2)h FV(=)f Ff(1)p FZ(;)j(M)3366 961 y FP(1)3398
951 y FZ(;)h(M)3486 961 y FP(2)3518 951 y FZ(;)p FC(8)p
Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f Ff(0)p FC(_)p Ff(fx)g
FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)g(T)p 4115 939 6 23
v 4121 929 25 3 v 67 w Ff(f2)d FV(=)f Ff(1)p FC(^)o Ff(f0)h
FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p
FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p
FV(\))5241 905 y FC(^)5282 916 y Fd(R)p 5852 899 351
4 v 5852 951 a Ff(f0)h FV(=)f Ff(f2)p 6012 939 6 23 v
6018 929 25 3 v 59 w(f0)h FV(=)f Ff(f2)p 3149 983 3054
4 v 3549 1037 a FV(\()p Ff(f2)h FV(=)f Ff(1)p FC(^)p
Ff(f0)g FV(=)g Ff(1)p FV(\))p FC(\033)p Ff(f0)h FV(=)f
Ff(f2)p FZ(;)k Ff(f2)d FV(=)f Ff(1)p FZ(;)j(M)4339 1047
y FP(1)4371 1037 y FZ(;)h(M)4459 1047 y FP(2)4491 1037
y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f
Ff(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)g(T)p
5088 1025 6 23 v 5094 1015 25 3 v 67 w Ff(f0)d FV(=)f
Ff(f2)p FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p
Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)o FV(\))6202
992 y FC(\033)6250 1003 y Fd(L)p 3492 1069 2367 4 v 3482
1123 a FC(8)p Ff(y)q FZ(:)p FV(\(\()p Ff(fy)h FV(=)f
Ff(1)p FC(^)p Ff(f0)h FV(=)f Ff(1)p FV(\))p FC(\033)p
Ff(f0)g FV(=)g Ff(fy)q FV(\))p FZ(;)k Ff(f2)c FV(=)g
Ff(1)p FZ(;)k(M)4396 1133 y FP(1)4428 1123 y FZ(;)g(M)4516
1133 y FP(2)4548 1123 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)d FV(=)f Ff(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p
FZ(;)k(S)o(;)g(T)p 5145 1111 6 23 v 5151 1101 25 3 v
67 w Ff(f0)d FV(=)f Ff(f2)p FZ(;)p FC(9)p Ff(n)p FZ(:)p
Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)g
FV(=)g Ff(fm)p FV(\))5858 1081 y FC(8)5893 1092 y Fd(L)p
3473 1156 2407 4 v 3462 1210 a FC(8)p Ff(x)p FZ(:)p Ff(y)q
FZ(:)p FV(\(\()p Ff(fy)i FV(=)e Ff(1)p FC(^)p Ff(fx)g
FV(=)g Ff(1)p FV(\))p FC(\033)p Ff(fx)h FV(=)f Ff(fy)q
FV(\))p FZ(;)j Ff(f2)e FV(=)f Ff(1)p FZ(;)k(M)4416 1220
y FP(1)4448 1210 y FZ(;)f(M)4535 1220 y FP(2)4568 1210
y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)f
Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p
5165 1198 6 23 v 5170 1188 25 3 v 68 w Ff(f0)c FV(=)g
Ff(f2)q FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p
Ff(n)l FZ(<)l Ff(m)p FC(^)p Ff(fn)h FV(=)f Ff(fm)p FV(\))5878
1167 y FC(8)5913 1178 y Fd(L)p 3473 1242 2407 4 v 3836
1296 a Ff(f2)g FV(=)g Ff(1)p FZ(;)k(M)4053 1306 y FP(1)4085
1296 y FZ(;)g(M)4173 1306 y FP(2)4205 1296 y FZ(;)p FC(8)p
Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f Ff(0)p FC(_)o Ff(fx)h
FV(=)f Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p 4802 1284 6
23 v 4808 1274 25 3 v 68 w Ff(f0)d FV(=)g Ff(f2)q FZ(;)p
FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l
Ff(m)p FC(^)q Ff(fn)g FV(=)g Ff(fm)p FV(\))5878 1254
y FC(8)5913 1265 y Fd(L)p 2293 1328 3223 4 v 2935 1382
a Ff(f2)h FV(=)f Ff(1)p FZ(;)j Ff(1)l FC(\024)l Ff(2)p
FZ(;)j(M)3276 1392 y FP(1)3308 1382 y FZ(;)e(M)3396 1392
y FP(2)3428 1382 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)d FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p
FZ(;)k(S)o(;)f(T)p 4025 1370 6 23 v 4031 1360 25 3 v
68 w Ff(0)l FZ(<)l Ff(2)p FC(^)q Ff(f0)e FV(=)f Ff(f2)p
FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l
FZ(<)l Ff(m)p FC(^)q Ff(fn)g FV(=)g Ff(fm)p FV(\))5515
1337 y FC(^)5557 1348 y Fd(R)2139 1427 y Fc(|)p 2163
1427 2030 8 v 2030 w({z)p 4241 1427 V 2030 w(})4183 1489
y Fd(Y)4217 1501 y FP(7)2026 1738 y Gc(M)2094 1747 y
FV(1)2148 1738 y F9(=)20 b FX(8)p Fu(y)q Gc(:)p Fu(x)p
Gc(:)m F9(\()p Fu(x)8 b FX(\024)g Fu(m)2555 1714 y Ff(x)p
FZ(;)p Ff(y)2626 1738 y F9(\))101 b Gc(T)30 b F9(=)19
b FX(8)p Fu(i)p Gc(:)p Fu(x)p Gc(:)p Fu(y)q Gc(:)m F9(\(\()p
Fu(fy)i F9(=)e Fu(i)p FX(^)p Fu(fx)g F9(=)g Fu(i)p F9(\))12
b FX(\033)g Fu(fx)19 b F9(=)g Fu(fy)p F9(\))2026 1864
y Gc(M)2094 1873 y FV(2)2148 1864 y F9(=)h FX(8)p Fu(y)q
Gc(:)p Fu(x)p Gc(:)m F9(\()p Fu(y)9 b FX(\024)f Fu(m)2556
1840 y Ff(x)p FZ(;)p Ff(y)2627 1864 y F9(\))100 b Gc(S)23
b F9(=)d FX(8)p Fu(x)p Gc(:)p Fu(y)q Gc(:)m F9(\()p Fu(sx)8
b FX(\024)g Fu(y)k FX(\033)g Fu(x)c Gc(<)g Fu(y)q F9(\))6506
465 y
currentpoint grestore moveto
6506 465 a 3543 5116 4 4724 v 321 5119 3226 4 v
Black 1364 5273 a Gg(Figure)24 b(5:)29 b(Subproofs)d
Ga(Y)2173 5287 y F9(6)2235 5273 y Gg(and)e Ga(Y)2442
5287 y F9(7)2481 5273 y Gg(.)p Black Black eop end
%%Page: 137 149
TeXDict begin 137 148 bop Black 3831 51 a Gb(137)p 277
88 3691 4 v Black Black 277 393 3226 4 v 277 5116 4 4724
v 1882 465 a
gsave currentpoint currentpoint translate -90 neg rotate neg exch
neg exch translate
1882 465 a 2724 -693 247 4 v 2724 -641 a
Ff(1)l FC(\024)l Ff(1)p 2832 -653 6 23 v 2837 -663 25
3 v 60 w(1)l FC(\024)l Ff(1)p 3020 -692 247 4 v 52 w(0)l
FZ(<)l Ff(1)p 3128 -653 6 23 v 3134 -663 25 3 v 61 w(0)l
FZ(<)l Ff(1)p 2724 -611 543 4 v 2739 -559 a(1)l FC(\024)l
Ff(1)p FC(\033)r Ff(0)l FZ(<)l Ff(1)p FZ(;)12 b Ff(1)l
FC(\024)l Ff(1)p 3112 -571 6 23 v 3118 -581 25 3 v 61
w(0)l FZ(<)l Ff(1)3266 -602 y FC(\033)3314 -591 y Fd(L)p
2682 -529 626 4 v 2672 -475 a FC(8)p Ff(y)q FZ(:)p FV(\()p
Ff(1)l FC(\024)l Ff(y)q FC(\033)q Ff(0)l FZ(<)l Ff(y)q
FV(\))p FZ(;)g Ff(1)l FC(\024)l Ff(1)p 3169 -487 6 23
v 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)l
Ff(1)p FZ(;)g(S)p 3015 -404 6 23 v 3020 -413 25 3 v 61
w Ff(0)l FZ(<)l Ff(1)3307 -431 y FC(8)3342 -420 y Fd(L)p
3448 -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)p
3817 -854 319 4 v 50 w(f0)g FV(=)g Ff(0)p 3961 -814 6
23 v 3966 -824 25 3 v 59 w(f0)h FV(=)f Ff(0)p 3448 -783
687 4 v 3467 -731 a(f1)h FV(=)f Ff(0)p FZ(;)k Ff(f0)c
FV(=)g Ff(0)p 3770 -743 6 23 v 3776 -753 25 3 v 59 w(f1)h
FV(=)f Ff(0)p FC(^)p Ff(f0)g FV(=)g Ff(0)4134 -774 y
FC(^)4176 -763 y Fd(R)p 4273 -783 351 4 v 4273 -731 a
Ff(f0)g FV(=)g Ff(f1)p 4433 -743 6 23 v 4439 -753 25
3 v 60 w(f0)g FV(=)g Ff(f1)p 3467 -702 1157 4 v 3512
-648 a FV(\()p Ff(f1)h FV(=)f Ff(0)p FC(^)o Ff(f0)h FV(=)f
Ff(0)p FV(\))p FC(\033)p Ff(f0)h FV(=)f Ff(f1)p FZ(;)k
Ff(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 v
3445 -561 a FC(8)p Ff(y)q FZ(:)p FV(\(\()p Ff(fy)h FV(=)f
Ff(0)p FC(^)p Ff(f0)g FV(=)g Ff(0)p FV(\))p FC(\033)p
Ff(f0)h FV(=)f Ff(fy)q FV(\))p FZ(;)k Ff(f1)c FV(=)g
Ff(0)p FZ(;)k Ff(f0)d FV(=)f Ff(0)p 4445 -573 6 23 v
4451 -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)p
FZ(:)p Ff(y)q FZ(:)p FV(\(\()p Ff(fy)i FV(=)e Ff(0)p
FC(^)o Ff(fx)h FV(=)f Ff(0)p FV(\))p FC(\033)p Ff(fx)h
FV(=)f Ff(fy)q FV(\))p FZ(;)j Ff(f1)e FV(=)f Ff(0)p FZ(;)j
Ff(f0)e FV(=)f Ff(0)p 4464 -487 6 23 v 4470 -497 25 3
v 59 w(f0)h FV(=)f Ff(f1)4654 -517 y FC(8)4689 -506 y
Fd(L)p 3436 -443 1220 4 v 3761 -392 a Ff(f1)h FV(=)f
Ff(0)p FZ(;)k Ff(f0)c FV(=)g Ff(0)p FZ(;)k(T)p 4139 -404
6 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)l
Ff(1)p FZ(;)h Ff(f0)c FV(=)f Ff(0)p FZ(;)j(S)o(;)h(T)p
3704 -322 6 23 v 3709 -332 25 3 v 68 w Ff(0)l FZ(<)l
Ff(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 -394
y(.)4829 -361 y(.)4801 -310 y FZ(Y)4837 -300 y FP(3)p
2425 -280 3175 4 v 2425 -226 a Ff(f1)g FV(=)g Ff(0)p
FC(_)p Ff(f1)h FV(=)f Ff(1)p FZ(;)j Ff(1)l FC(\024)l
Ff(1)p FZ(;)j Ff(f0)7 b FV(=)g Ff(0)p FZ(;)k Ff(2)l FC(\024)l
Ff(2)p FZ(;)h Ff(f1)c FV(=)f Ff(1)p FZ(;)k(M)3379 -216
y FP(1)3411 -226 y FZ(;)f(M)3498 -216 y FP(2)3531 -226
y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)f
Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p
4128 -238 6 23 v 4133 -248 25 3 v 67 w Ff(0)l FZ(<)l
Ff(1)p FC(^)r Ff(f0)d FV(=)f Ff(f1)p FZ(;)j Ff(1)l FZ(<)l
Ff(3)p FC(^)r Ff(f1)d FV(=)g Ff(f3)q FZ(;)j Ff(1)l FZ(<)l
Ff(2)p FC(^)r Ff(f1)d FV(=)g Ff(f2)q FZ(;)p FC(9)p Ff(n)p
FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)p
Ff(fn)h FV(=)f Ff(fm)p FV(\))5598 -272 y FC(_)5639 -261
y Fd(L)p 2425 -194 3175 4 v 2590 -140 a Ff(1)l FC(\024)l
Ff(1)p FZ(;)12 b Ff(f0)c FV(=)f Ff(0)p FZ(;)k Ff(2)l
FC(\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(\()p Ff(fx)e FV(=)f
Ff(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)g(T)p
3962 -152 6 23 v 3968 -162 25 3 v 67 w Ff(0)l FZ(<)l
Ff(1)p FC(^)q Ff(f0)d FV(=)f Ff(f1)p FZ(;)k Ff(1)l FZ(<)l
Ff(3)p FC(^)q Ff(f1)d FV(=)f Ff(f3)p FZ(;)k Ff(1)l FZ(<)l
Ff(2)p FC(^)q Ff(f1)d FV(=)f Ff(f2)p FZ(;)p FC(9)p Ff(n)p
FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q
Ff(fn)h FV(=)f Ff(fm)o FV(\))5598 -182 y FC(8)5633 -171
y Fd(L)p 2498 -107 3028 4 v 2487 -43 a FC(8)p Ff(x)p
FZ(:)p FV(\()p Ff(x)l FC(\024)l Ff(m)2695 -63 y Fe(x)p
Fd(;)p Fe(0)2752 -43 y FV(\))p FZ(;)j Ff(f0)e FV(=)f
Ff(0)p FZ(;)k Ff(2)l FC(\024)l Ff(2)p FZ(;)h Ff(f1)c
FV(=)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(\()p
Ff(fx)e FV(=)f Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p
FZ(;)j(S)o(;)h(T)p 4054 -55 6 23 v 4060 -64 25 3 v 67
w Ff(0)l FZ(<)l Ff(1)p FC(^)r Ff(f0)c FV(=)g Ff(f1)q
FZ(;)j Ff(1)l FZ(<)l Ff(3)p FC(^)q Ff(f1)e FV(=)f Ff(f3)p
FZ(;)k Ff(1)l FZ(<)l Ff(2)p FC(^)q Ff(f1)d FV(=)f Ff(f2)p
FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l
FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p FV(\))5525
-96 y FC(8)5560 -85 y Fd(L)p 2498 -10 3028 4 v 2652 44
a Ff(f0)g FV(=)g Ff(0)p FZ(;)k Ff(2)l FC(\024)l Ff(2)p
FZ(;)h Ff(f1)c FV(=)f Ff(1)p FZ(;)k(M)3152 54 y FP(1)3184
44 y FZ(;)f(M)3271 54 y FP(2)3304 44 y FZ(;)p FC(8)p
Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)f Ff(0)p FC(_)o Ff(fx)h
FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p 3901 32 6 23
v 3906 22 25 3 v 67 w Ff(0)l FZ(<)l Ff(1)p FC(^)r Ff(f0)c
FV(=)g Ff(f1)q FZ(;)j Ff(1)l FZ(<)l Ff(3)p FC(^)r Ff(f1)d
FV(=)g Ff(f3)q FZ(;)j Ff(1)l FZ(<)l Ff(2)p FC(^)q Ff(f1)e
FV(=)f Ff(f2)p FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p
FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p
FV(\))5525 2 y FC(8)5560 13 y Fd(L)2425 88 y Fc(|)p 2449
88 1582 8 v 1582 w({z)p 4079 88 V 1582 w(})4021 150 y
Fd(Y)4055 162 y FP(4)4057 424 y F3(.)4057 457 y(.)4057
490 y(.)4057 523 y(.)4029 575 y FZ(Y)4065 585 y FP(4)p
4165 523 319 4 v 4165 575 a Ff(f0)h FV(=)f Ff(1)p 4309
563 6 23 v 4315 553 25 3 v 59 w(f0)h FV(=)f Ff(1)p 2722
604 3051 4 v 2722 658 a(f0)h FV(=)f Ff(0)p FC(_)p Ff(f0)g
FV(=)g Ff(1)p FZ(;)k Ff(2)l FC(\024)l Ff(2)p FZ(;)h Ff(f1)c
FV(=)f Ff(1)p FZ(;)k(M)3394 668 y FP(1)3426 658 y FZ(;)g(M)3514
668 y FP(2)3546 658 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)d FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p
FZ(;)k(S)o(;)f(T)p 4143 646 6 23 v 4149 636 25 3 v 68
w Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)e FV(=)f Ff(f1)p
FZ(;)k Ff(1)l FZ(<)l Ff(3)p FC(^)q Ff(f1)d FV(=)f Ff(f3)p
FZ(;)j Ff(1)l FZ(<)l Ff(2)p FC(^)r Ff(f1)d FV(=)g Ff(f2)q
FZ(;)j Ff(f0)e FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p
Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)h
FV(=)f Ff(fm)o FV(\))5772 612 y FC(_)5814 623 y Fd(L)p
2722 690 3051 4 v 2888 744 a Ff(2)l FC(\024)l Ff(2)p
FZ(;)12 b Ff(f1)c FV(=)f Ff(1)p FZ(;)j(M)3228 754 y FP(1)3261
744 y FZ(;)g(M)3348 754 y FP(2)3381 744 y FZ(;)p FC(8)p
Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)g Ff(0)p FC(_)p Ff(fx)h
FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p 3978 732 6 23
v 3983 722 25 3 v 67 w Ff(0)l FZ(<)l Ff(1)p FC(^)r Ff(f0)c
FV(=)g Ff(f1)q FZ(;)j Ff(1)l FZ(<)l Ff(3)p FC(^)r Ff(f1)d
FV(=)g Ff(f3)q FZ(;)j Ff(1)l FZ(<)l Ff(2)p FC(^)q Ff(f1)e
FV(=)f Ff(f2)p FZ(;)k Ff(f0)d FV(=)f Ff(1)p FZ(;)p FC(9)p
Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p
FC(^)q Ff(fn)g FV(=)g Ff(fm)p FV(\))5772 702 y FC(8)5807
713 y Fd(L)p 2806 777 2885 4 v 2806 831 a Ff(2)l FC(\024)l
Ff(2)p FZ(;)12 b Ff(f1)c FV(=)f Ff(1)p FZ(;)j(M)3146
841 y FP(1)3178 831 y FZ(;)h(M)3266 841 y FP(2)3298 831
y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f
Ff(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)g(T)p
3895 819 6 23 v 3901 809 25 3 v 56 w FC(9)p Ff(m)p FZ(:)p
FV(\()p Ff(0)l FZ(<)l Ff(m)p FC(^)q Ff(f0)d FV(=)f Ff(fm)p
FV(\))p FZ(;)j Ff(1)l FZ(<)l Ff(3)p FC(^)r Ff(f1)d FV(=)g
Ff(f3)q FZ(;)j Ff(1)l FZ(<)l Ff(2)p FC(^)r Ff(f1)d FV(=)g
Ff(f2)q FZ(;)j Ff(f0)e FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p
FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q
Ff(fn)g FV(=)g Ff(fm)p FV(\))5689 788 y FC(9)5724 799
y Fd(R)p 2806 863 2885 4 v 3043 917 a Ff(2)l FC(\024)l
Ff(2)p FZ(;)13 b Ff(f1)7 b FV(=)g Ff(1)p FZ(;)k(M)3384
927 y FP(1)3416 917 y FZ(;)g(M)3504 927 y FP(2)3536 917
y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f
Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p
4133 905 6 23 v 4139 895 25 3 v 68 w Ff(1)l FZ(<)l Ff(3)p
FC(^)q Ff(f1)e FV(=)f Ff(f3)p FZ(;)k Ff(1)l FZ(<)l Ff(2)p
FC(^)q Ff(f1)d FV(=)f Ff(f2)p FZ(;)j Ff(f0)e FV(=)f Ff(1)p
FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l
FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p FV(\))5689
875 y FC(9)5724 886 y Fd(R)p 2961 949 2574 4 v 2961 1003
a Ff(2)l FC(\024)l Ff(2)p FZ(;)12 b Ff(f1)c FV(=)f Ff(1)p
FZ(;)k(M)3302 1013 y FP(1)3334 1003 y FZ(;)f(M)3421 1013
y FP(2)3454 1003 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)e FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p
FZ(;)j(S)o(;)h(T)p 4051 991 6 23 v 4056 981 25 3 v 57
w FC(9)p Ff(m)p FZ(:)p FV(\()p Ff(1)l FZ(<)l Ff(m)p FC(^)q
Ff(f1)c FV(=)g Ff(fm)p FV(\))p FZ(;)k Ff(1)l FZ(<)l Ff(2)p
FC(^)q Ff(f1)d FV(=)f Ff(f2)p FZ(;)k Ff(f0)c FV(=)g Ff(1)p
FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l
FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p FV(\))5534
961 y FC(9)5569 972 y Fd(R)p 2961 1036 2574 4 v 3199
1090 a Ff(2)l FC(\024)l Ff(2)p FZ(;)12 b Ff(f1)c FV(=)f
Ff(1)p FZ(;)j(M)3539 1100 y FP(1)3572 1090 y FZ(;)g(M)3659
1100 y FP(2)3691 1090 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)e FV(=)f Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p
FZ(;)j(S)o(;)h(T)p 4288 1078 6 23 v 4294 1068 25 3 v
67 w Ff(1)l FZ(<)l Ff(2)p FC(^)r Ff(f1)c FV(=)g Ff(f2)q
FZ(;)j Ff(f0)e FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p
Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)g
FV(=)g Ff(fm)p FV(\))5534 1047 y FC(9)5569 1058 y Fd(R)p
3106 1122 2285 4 v 3095 1187 a FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(2)l FC(\024)l Ff(m)3305 1166 y Fe(x)p Fd(;)p Fe(2)3362
1187 y FV(\))p FZ(;)j Ff(f1)e FV(=)f Ff(1)p FZ(;)j(M)3632
1197 y FP(1)3665 1187 y FZ(;)g(M)3752 1197 y FP(2)3784
1187 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)f
Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p
4382 1175 6 23 v 4387 1165 25 3 v 67 w Ff(1)l FZ(<)l
Ff(2)p FC(^)r Ff(f1)c FV(=)g Ff(f2)q FZ(;)j Ff(f0)e FV(=)f
Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p
Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)g FV(=)g Ff(fm)p FV(\))5389
1134 y FC(8)5424 1145 y Fd(L)p 3106 1219 2285 4 v 3260
1273 a Ff(f1)h FV(=)f Ff(1)p FZ(;)k(M)3478 1283 y FP(1)3510
1273 y FZ(;)f(M)3597 1283 y FP(2)3630 1273 y FZ(;)p FC(8)p
Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)f Ff(0)p FC(_)o Ff(fx)h
FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p 4227 1261 6
23 v 4232 1251 25 3 v 68 w Ff(1)l FZ(<)l Ff(2)p FC(^)q
Ff(f1)d FV(=)f Ff(f2)p FZ(;)j Ff(f0)e FV(=)f Ff(1)p FZ(;)p
FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l
Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p FV(\))5389 1231
y FC(8)5424 1242 y Fd(L)2722 1318 y Fc(|)p 2746 1318
1520 8 v 1520 w({z)p 4314 1318 V 1520 w(})4257 1379 y
Fd(Y)4291 1391 y FP(5)1982 1629 y Gc(M)2050 1638 y FV(1)2104
1629 y F9(=)19 b FX(8)p Fu(y)q Gc(:)p Fu(x)p Gc(:)n F9(\()p
Fu(x)8 b FX(\024)g Fu(m)2511 1605 y Ff(x)p FZ(;)p Ff(y)2582
1629 y F9(\))101 b Gc(T)30 b F9(=)19 b FX(8)p Fu(i)p
Gc(:)p Fu(x)p Gc(:)p Fu(y)q Gc(:)m F9(\(\()p Fu(fy)h
F9(=)g Fu(i)p FX(^)p Fu(fx)e F9(=)i Fu(i)p F9(\))12 b
FX(\033)g Fu(fx)18 b F9(=)i Fu(fy)p F9(\))1982 1755 y
Gc(M)2050 1764 y FV(2)2104 1755 y F9(=)f FX(8)p Fu(y)q
Gc(:)p Fu(x)p Gc(:)n F9(\()p Fu(y)9 b FX(\024)f Fu(m)2512
1731 y Ff(x)p FZ(;)p Ff(y)2583 1755 y F9(\))100 b Gc(S)23
b F9(=)d FX(8)p Fu(x)p Gc(:)p Fu(y)q Gc(:)m F9(\()p Fu(sx)8
b FX(\024)g Fu(y)k FX(\033)g Fu(x)c Gc(<)g Fu(y)q F9(\))6462
465 y
currentpoint grestore moveto
6462 465 a 3499 5116 4 4724 v 277 5119 3226 4 v
Black 1320 5273 a Gg(Figure)24 b(6:)29 b(Subproofs)c
Ga(Y)2128 5287 y F9(4)2190 5273 y Gg(and)f Ga(Y)2397
5287 y F9(5)2437 5273 y Gg(.)p Black Black eop end
%%Page: 138 150
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4451 724 6 23 v 4456 714 25 3 v 67 w Ff(2)l FZ(<)l Ff(3)p
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Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p 4344
1069 6 23 v 4349 1060 25 3 v 57 w FC(9)p Ff(m)p FZ(:)p
FV(\()p Ff(2)l FZ(<)l Ff(m)p FC(^)q Ff(f2)c FV(=)g Ff(fm)p
FV(\))p FZ(;)k Ff(1)l FZ(<)l Ff(3)p FC(^)q Ff(f1)d FV(=)f
Ff(f3)p FZ(;)k Ff(1)l FZ(<)l Ff(2)p FC(^)q Ff(f1)d FV(=)f
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FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)f Ff(0)p FC(_)o
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1156 6 23 v 4325 1146 25 3 v 67 w Ff(1)l FZ(<)l Ff(3)p
FC(^)r Ff(f1)c FV(=)g Ff(f3)q FZ(;)j Ff(1)l FZ(<)l Ff(2)p
FC(^)r Ff(f1)d FV(=)g Ff(f2)q FZ(;)p FC(9)p Ff(n)p FZ(:)p
Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)g
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1265 y FV(\))p FZ(;)j Ff(f1)e FV(=)f Ff(1)p FZ(;)k Ff(2)l
FC(\024)l Ff(2)p FZ(;)h Ff(f1)c FV(=)f Ff(1)p FZ(;)j(M)3783
1275 y FP(1)3816 1265 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)e FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p
FZ(;)k(S)o(;)f(T)p 4413 1253 6 23 v 4418 1243 25 3 v
68 w Ff(1)l FZ(<)l Ff(3)p FC(^)q Ff(f1)e FV(=)f Ff(f3)p
FZ(;)j Ff(1)l FZ(<)l Ff(2)p FC(^)r Ff(f1)d FV(=)g Ff(f2)q
FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l
FZ(<)l Ff(m)p FC(^)q Ff(fn)g FV(=)g Ff(fm)p FV(\))5572
1212 y FC(8)5607 1223 y Fd(L)p 2974 1297 2600 4 v 3069
1351 a Ff(f1)g FV(=)g Ff(1)p FZ(;)k Ff(2)l FC(\024)l
Ff(2)p FZ(;)h Ff(f1)c FV(=)f Ff(1)p FZ(;)k(M)3569 1361
y FP(1)3601 1351 y FZ(;)g(M)3689 1361 y FP(2)3721 1351
y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f
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4318 1339 6 23 v 4324 1329 25 3 v 68 w Ff(1)l FZ(<)l
Ff(3)p FC(^)q Ff(f1)e FV(=)f Ff(f3)p FZ(;)k Ff(1)l FZ(<)l
Ff(2)p FC(^)q Ff(f1)d FV(=)f Ff(f2)p FZ(;)p FC(9)p Ff(n)p
FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q
Ff(fn)g FV(=)g Ff(fm)p FV(\))5572 1309 y FC(8)5607 1320
y Fd(L)2781 1396 y Fc(|)p 2805 1396 1387 8 v 1387 w({z)p
4240 1396 V 1387 w(})4183 1457 y Fd(Y)4217 1469 y FP(3)2026
1707 y Gc(M)2094 1716 y FV(1)2148 1707 y F9(=)20 b FX(8)p
Fu(y)q Gc(:)p Fu(x)p Gc(:)m F9(\()p Fu(x)8 b FX(\024)g
Fu(m)2555 1683 y Ff(x)p FZ(;)p Ff(y)2626 1707 y F9(\))101
b Gc(T)30 b F9(=)19 b FX(8)p Fu(i)p Gc(:)p Fu(x)p Gc(:)p
Fu(y)q Gc(:)m F9(\(\()p Fu(fy)i F9(=)e Fu(i)p FX(^)p
Fu(fx)g F9(=)g Fu(i)p F9(\))12 b FX(\033)g Fu(fx)19 b
F9(=)g Fu(fy)p F9(\))2026 1833 y Gc(M)2094 1842 y FV(2)2148
1833 y F9(=)h FX(8)p Fu(y)q Gc(:)p Fu(x)p Gc(:)m F9(\()p
Fu(y)9 b FX(\024)f Fu(m)2556 1809 y Ff(x)p FZ(;)p Ff(y)2627
1833 y F9(\))100 b Gc(S)23 b F9(=)d FX(8)p Fu(x)p Gc(:)p
Fu(y)q Gc(:)m F9(\()p Fu(sx)8 b FX(\024)g Fu(y)k FX(\033)g
Fu(x)c Gc(<)g Fu(y)q F9(\))6506 465 y
currentpoint grestore moveto
6506 465 a 3543
5116 4 4724 v 321 5119 3226 4 v Black 1295 5273 a Gg(Figure)24
b(7:)29 b(Subproofs)d Ga(Y)2104 5287 y F9(1)2143 5273
y Gg(,)c Ga(Y)2241 5287 y F9(2)2303 5273 y Gg(and)i Ga(Y)2510
5287 y F9(3)2550 5273 y Gg(.)p Black Black eop end
%%Page: 139 151
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v 1882 465 a
gsave currentpoint currentpoint translate -90 neg rotate neg exch
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Ff(1)p 3588 -614 6 23 v 3594 -624 25 3 v 61 w(0)l FZ(<)l
Ff(1)p 3015 -572 712 4 v 3117 -520 a(1)l FC(\024)l Ff(1)p
FC(\033)r Ff(0)l FZ(<)l Ff(1)p FZ(;)12 b(M)3440 -510
y FP(1)p 3486 -532 6 23 v 3492 -542 25 3 v 3531 -520
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FV(=)f Ff(1)p 3904 -920 687 4 v 3923 -868 a(f1)h FV(=)f
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4244 -890 25 3 v 59 w(f1)h FV(=)f Ff(0)p FZ(;)j Ff(f1)e
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4294 -797 6 23 v 4300 -807 25 3 v 59 w Ff(f1)h FV(=)f
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5188 -807 25 3 v 59 w Ff(f0)h FV(=)f Ff(0)p FZ(;)k Ff(f0)c
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Ff(0)p FC(^)p Ff(f0)h FV(=)f Ff(0)p FZ(;)j Ff(f1)e FV(=)f
Ff(1)p FZ(;)k Ff(f0)d FV(=)f Ff(1)5516 -744 y FC(^)5557
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Ff(f1)p 5814 -710 6 23 v 5820 -720 25 3 v 59 w(f0)h FV(=)f
Ff(f1)p 4146 -666 1859 4 v 4321 -612 a FV(\()p Ff(f1)h
FV(=)f Ff(0)p FC(^)o Ff(f0)h FV(=)f Ff(0)p FV(\))p FC(\033)p
Ff(f0)h FV(=)f Ff(f1)p FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)h FV(=)f Ff(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p
5321 -624 6 23 v 5326 -634 25 3 v 59 w Ff(f0)h FV(=)f
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Ff(1)6004 -657 y FC(\033)6052 -646 y Fd(L)p 4264 -580
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Ff(f0)h FV(=)f Ff(fy)q FV(\))p FZ(;)p FC(8)p Ff(x)p FZ(:)p
FV(\()p Ff(fx)h FV(=)f Ff(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p
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FV(=)f Ff(0)p FV(\))p FC(\033)p Ff(fx)h FV(=)f Ff(fy)q
FV(\))p FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)g FV(=)g
Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p 5397 -451
6 23 v 5403 -461 25 3 v 59 w Ff(f0)g FV(=)g Ff(f1)q FZ(;)j
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FV(=)e Ff(1)p FC(^)p Ff(fx)g FV(=)g Ff(1)p FV(\))p FC(\033)p
Ff(fx)h FV(=)f Ff(fy)q FV(\))p FZ(;)j(M)3802 442 y FP(1)3835
432 y FZ(;)g(M)3922 442 y FP(2)3955 432 y FZ(;)p FC(8)p
Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)g Ff(0)p FC(_)p Ff(fx)h
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v 4557 410 25 3 v 67 w Ff(f1)d FV(=)f Ff(f2)p FZ(;)k
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Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)d FV(=)f Ff(f1)p FZ(;)k
Ff(1)l FZ(<)l Ff(3)p FC(^)q Ff(f1)d FV(=)f Ff(f3)p FZ(;)j
Ff(0)l FZ(<)l Ff(1)p FC(^)r Ff(f0)d FV(=)g Ff(f1)q FZ(;)j
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v 4195 497 25 3 v 68 w Ff(f1)d FV(=)g Ff(f2)q FZ(;)j
Ff(2)l FZ(<)l Ff(3)p FC(^)q Ff(f2)e FV(=)f Ff(f3)p FZ(;)k
Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)d FV(=)f Ff(f1)p FZ(;)k
Ff(1)l FZ(<)l Ff(3)p FC(^)q Ff(f1)d FV(=)f Ff(f3)p FZ(;)k
Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)d FV(=)f Ff(f1)p FZ(;)j
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605 y FZ(;)k(M)2984 615 y FP(2)3016 605 y FZ(;)p FC(8)p
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FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p 3613 593 6 23
v 3619 583 25 3 v 68 w Ff(2)l FZ(<)l Ff(3)p FC(^)q Ff(f2)e
FV(=)f Ff(f3)p FZ(;)k Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)d
FV(=)f Ff(f1)p FZ(;)k Ff(1)l FZ(<)l Ff(3)p FC(^)q Ff(f1)d
FV(=)f Ff(f3)p FZ(;)j Ff(0)l FZ(<)l Ff(1)p FC(^)r Ff(f0)d
FV(=)g Ff(f1)q FZ(;)j Ff(1)l FZ(<)l Ff(2)p FC(^)r Ff(f1)d
FV(=)g Ff(f2)q FZ(;)j Ff(f0)e FV(=)f Ff(1)5781 559 y
FC(^)5823 570 y Fd(R)p 2724 637 2701 4 v 2724 691 a FZ(M)2782
701 y FP(1)2814 691 y FZ(;)k(M)2902 701 y FP(2)2934 691
y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f
Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p
3531 679 6 23 v 3537 669 25 3 v 57 w FC(9)p Ff(m)p FZ(:)p
FV(\()p Ff(2)l FZ(<)l Ff(m)p FC(^)q Ff(f2)e FV(=)f Ff(fm)o
FV(\))p FZ(;)k Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)d FV(=)f
Ff(f1)p FZ(;)k Ff(1)l FZ(<)l Ff(3)p FC(^)q Ff(f1)d FV(=)f
Ff(f3)p FZ(;)k Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)d FV(=)f
Ff(f1)p FZ(;)k Ff(1)l FZ(<)l Ff(2)p FC(^)q Ff(f1)d FV(=)f
Ff(f2)p FZ(;)j Ff(f0)e FV(=)f Ff(1)5423 649 y FC(9)5458
660 y Fd(R)p 2700 724 2749 4 v 2700 778 a FZ(M)2758 788
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FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f Ff(0)p
FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p
3507 766 6 23 v 3513 756 25 3 v 68 w Ff(0)l FZ(<)l Ff(1)p
FC(^)q Ff(f0)e FV(=)f Ff(f1)p FZ(;)k Ff(1)l FZ(<)l Ff(3)p
FC(^)q Ff(f1)d FV(=)f Ff(f3)p FZ(;)j Ff(0)l FZ(<)l Ff(1)p
FC(^)r Ff(f0)d FV(=)g Ff(f1)q FZ(;)j Ff(1)l FZ(<)l Ff(2)p
FC(^)r Ff(f1)d FV(=)g Ff(f2)q FZ(;)j Ff(f0)e FV(=)f Ff(1)p
FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l
FZ(<)l Ff(m)p FC(^)q Ff(fn)g FV(=)g Ff(fm)p FV(\))5447
735 y FC(9)5482 746 y Fd(R)p 2618 810 2913 4 v 2618 864
a FZ(M)2676 874 y FP(1)2708 864 y FZ(;)j(M)2795 874 y
FP(2)2828 864 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e
FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p
3425 852 6 23 v 3430 842 25 3 v 57 w FC(9)p Ff(m)p FZ(:)p
FV(\()p Ff(0)l FZ(<)l Ff(m)p FC(^)q Ff(f0)c FV(=)g Ff(fm)p
FV(\))p FZ(;)k Ff(1)l FZ(<)l Ff(3)p FC(^)q Ff(f1)d FV(=)f
Ff(f3)p FZ(;)k Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)d FV(=)f
Ff(f1)p FZ(;)j Ff(1)l FZ(<)l Ff(2)p FC(^)r Ff(f1)e FV(=)f
Ff(f2)p FZ(;)j Ff(f0)e FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p
FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q
Ff(fn)h FV(=)f Ff(fm)o FV(\))5530 822 y FC(9)5565 833
y Fd(R)p 2618 896 2913 4 v 2855 950 a FZ(M)2913 960 y
FP(1)2946 950 y FZ(;)j(M)3033 960 y FP(2)3065 950 y FZ(;)p
FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)f Ff(0)p FC(_)p
Ff(fx)g FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)g(T)p 3662
938 6 23 v 3668 928 25 3 v 67 w Ff(1)l FZ(<)l Ff(3)p
FC(^)q Ff(f1)d FV(=)f Ff(f3)p FZ(;)k Ff(0)l FZ(<)l Ff(1)p
FC(^)q Ff(f0)d FV(=)f Ff(f1)p FZ(;)k Ff(1)l FZ(<)l Ff(2)p
FC(^)q Ff(f1)d FV(=)f Ff(f2)p FZ(;)k Ff(f0)c FV(=)g Ff(1)p
FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l
FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p FV(\))5530
908 y FC(9)5565 919 y Fd(R)p 2773 983 2603 4 v 2773 1037
a FZ(M)2831 1047 y FP(1)2863 1037 y FZ(;)k(M)2951 1047
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Ff(fx)d FV(=)f Ff(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p
FZ(;)k(S)o(;)f(T)p 3580 1025 6 23 v 3586 1015 25 3 v
57 w FC(9)p Ff(m)p FZ(:)p FV(\()p Ff(1)l FZ(<)l Ff(m)p
FC(^)q Ff(f1)e FV(=)f Ff(fm)p FV(\))p FZ(;)j Ff(0)l FZ(<)l
Ff(1)p FC(^)r Ff(f0)d FV(=)g Ff(f1)q FZ(;)j Ff(1)l FZ(<)l
Ff(2)p FC(^)q Ff(f1)e FV(=)f Ff(f2)p FZ(;)k Ff(f0)d FV(=)f
Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p
Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)g FV(=)g Ff(fm)p FV(\))5374
994 y FC(9)5409 1005 y Fd(R)p 2773 1069 2603 4 v 3011
1123 a FZ(M)3069 1133 y FP(1)3101 1123 y FZ(;)j(M)3188
1133 y FP(2)3221 1123 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)e FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p
FZ(;)j(S)o(;)h(T)p 3818 1111 6 23 v 3823 1101 25 3 v
68 w Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)d FV(=)f Ff(f1)p
FZ(;)j Ff(1)l FZ(<)l Ff(2)p FC(^)r Ff(f1)d FV(=)g Ff(f2)q
FZ(;)j Ff(f0)e FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p
Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)h
FV(=)f Ff(fm)o FV(\))5374 1081 y FC(9)5409 1092 y Fd(R)p
2928 1155 2292 4 v 2928 1209 a FZ(M)2986 1219 y FP(1)3019
1209 y FZ(;)j(M)3106 1219 y FP(2)3138 1209 y FZ(;)p FC(8)p
Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)f Ff(0)p FC(_)p Ff(fx)h
FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p 3735 1197 6
23 v 3741 1187 25 3 v 57 w FC(9)p Ff(m)p FZ(:)p FV(\()p
Ff(0)l FZ(<)l Ff(m)p FC(^)q Ff(f0)c FV(=)g Ff(fm)p FV(\))p
FZ(;)k Ff(1)l FZ(<)l Ff(2)p FC(^)q Ff(f1)d FV(=)f Ff(f2)p
FZ(;)j Ff(f0)e FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p
Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)h
FV(=)f Ff(fm)p FV(\))5219 1167 y FC(9)5254 1178 y Fd(R)p
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Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f Ff(0)p FC(_)p Ff(fx)g
FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)g(T)p 3973 1284 6
23 v 3979 1274 25 3 v 67 w Ff(1)l FZ(<)l Ff(2)p FC(^)q
Ff(f1)d FV(=)f Ff(f2)p FZ(;)k Ff(f0)d FV(=)f Ff(1)p FZ(;)p
FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l
Ff(m)p FC(^)q Ff(fn)g FV(=)g Ff(fm)p FV(\))5219 1253
y FC(9)5254 1264 y Fd(R)p 3084 1328 1981 4 v 3084 1382
a FZ(M)3142 1392 y FP(1)3174 1382 y FZ(;)k(M)3262 1392
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FZ(;)k(S)o(;)f(T)p 3891 1370 6 23 v 3897 1360 25 3 v
57 w FC(9)p Ff(m)p FZ(:)p FV(\()p Ff(1)l FZ(<)l Ff(m)p
FC(^)q Ff(f1)e FV(=)f Ff(fm)p FV(\))p FZ(;)j Ff(f0)e
FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p
FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)g FV(=)g Ff(fm)p
FV(\))5063 1340 y FC(9)5098 1351 y Fd(R)p 3084 1414 1981
4 v 3322 1468 a FZ(M)3380 1478 y FP(1)3412 1468 y FZ(;)j(M)3499
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Ff(fx)d FV(=)g Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p
FZ(;)j(S)o(;)h(T)p 4129 1456 6 23 v 4134 1446 25 3 v
67 w Ff(f0)d FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p
Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)h
FV(=)f Ff(fm)p FV(\))5063 1426 y FC(9)5098 1437 y Fd(R)2071
1513 y Fc(|)p 2095 1513 2028 8 v 2028 w({z)p 4171 1513
V 2028 w(})4100 1574 y Fd(Y)4134 1586 y FP(13)1982 1765
y Gc(M)2050 1774 y FV(1)2104 1765 y F9(=)19 b FX(8)p
Fu(y)q Gc(:)p Fu(x)p Gc(:)n F9(\()p Fu(x)8 b FX(\024)g
Fu(m)2511 1742 y Ff(x)p FZ(;)p Ff(y)2582 1765 y F9(\))101
b Gc(T)30 b F9(=)19 b FX(8)p Fu(i)p Gc(:)p Fu(x)p Gc(:)p
Fu(y)q Gc(:)m F9(\(\()p Fu(fy)h F9(=)g Fu(i)p FX(^)p
Fu(fx)e F9(=)i Fu(i)p F9(\))12 b FX(\033)g Fu(fx)18 b
F9(=)i Fu(fy)p F9(\))1982 1892 y Gc(M)2050 1901 y FV(2)2104
1892 y F9(=)f FX(8)p Fu(y)q Gc(:)p Fu(x)p Gc(:)n F9(\()p
Fu(y)9 b FX(\024)f Fu(m)2512 1868 y Ff(x)p FZ(;)p Ff(y)2583
1892 y F9(\))100 b Gc(S)23 b F9(=)d FX(8)p Fu(x)p Gc(:)p
Fu(y)q Gc(:)m F9(\()p Fu(sx)8 b FX(\024)g Fu(y)k FX(\033)g
Fu(x)c Gc(<)g Fu(y)q F9(\))6462 465 y
currentpoint grestore moveto
6462 465 a 3499
5116 4 4724 v 277 5119 3226 4 v Black 1285 5273 a Gg(Figure)24
b(8:)29 b(Subproofs)c Ga(Y)2093 5287 y F9(12)2190 5273
y Gg(and)f Ga(Y)2397 5287 y F9(13)2472 5273 y Gg(.)p
Black Black eop end
%%Page: 140 152
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gsave currentpoint currentpoint translate -90 neg rotate neg exch
neg exch translate
1927 465
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Ff(f3)h FV(=)f Ff(0)p FZ(;)j Ff(f3)e FV(=)f Ff(1)3896
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3848 -752 25 3 v 59 w Ff(f3)h FV(=)f Ff(0)p FC(^)o Ff(f2)h
FV(=)f Ff(0)p FZ(;)k Ff(f3)c FV(=)g Ff(1)p FZ(;)k Ff(f2)d
FV(=)f Ff(1)4785 -776 y FC(^)4826 -765 y Fd(R)p 4923
-782 351 4 v 4923 -731 a Ff(f2)h FV(=)f Ff(f3)p 5083
-743 6 23 v 5089 -752 25 3 v 59 w(f2)h FV(=)f Ff(f3)p
3415 -698 1859 4 v 3590 -644 a FV(\()p Ff(f3)h FV(=)f
Ff(0)p FC(^)p Ff(f2)g FV(=)g Ff(0)p FV(\))p FC(\033)p
Ff(f2)h FV(=)f Ff(f3)p FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)h FV(=)f Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p
4590 -656 6 23 v 4596 -666 25 3 v 59 w Ff(f2)g FV(=)g
Ff(f3)q FZ(;)j Ff(f3)e FV(=)f Ff(1)p FZ(;)j Ff(f2)e FV(=)f
Ff(1)5273 -689 y FC(\033)5321 -678 y Fd(L)p 3533 -612
1623 4 v 3523 -558 a FC(8)p Ff(y)q FZ(:)p FV(\(\()p Ff(fy)h
FV(=)f Ff(0)p FC(^)p Ff(f2)h FV(=)f Ff(0)p FV(\))p FC(\033)p
Ff(f2)g FV(=)g Ff(fy)q FV(\))p FZ(;)p FC(8)p Ff(x)p FZ(:)p
FV(\()p Ff(fx)h FV(=)f Ff(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p
FV(\))p 4647 -570 6 23 v 4652 -580 25 3 v 59 w Ff(f2)h
FV(=)f Ff(f3)p FZ(;)k Ff(f3)d FV(=)f Ff(1)p FZ(;)j Ff(f2)e
FV(=)f Ff(1)5155 -600 y FC(8)5190 -589 y Fd(L)p 3514
-526 1662 4 v 3503 -472 a FC(8)p Ff(x)p FZ(:)p Ff(y)q
FZ(:)p FV(\(\()p Ff(fy)i FV(=)e Ff(0)p FC(^)p Ff(fx)g
FV(=)g Ff(0)p FV(\))p FC(\033)p Ff(fx)h FV(=)f Ff(fy)q
FV(\))p FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)h FV(=)f
Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p 4666 -484
6 23 v 4672 -493 25 3 v 59 w Ff(f2)h FV(=)f Ff(f3)p FZ(;)k
Ff(f3)c FV(=)g Ff(1)p FZ(;)k Ff(f2)d FV(=)f Ff(1)5175
-514 y FC(8)5210 -503 y Fd(L)p 3514 -439 1662 4 v 3829
-385 a FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)h FV(=)f Ff(0)p
FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p FZ(;)k(T)p 4340
-397 6 23 v 4346 -407 25 3 v 67 w Ff(f2)d FV(=)f Ff(f3)p
FZ(;)k Ff(f3)c FV(=)g Ff(1)p FZ(;)k Ff(f2)d FV(=)f Ff(1)5175
-427 y FC(8)5210 -416 y Fd(L)p 2484 -353 2367 4 v 3001
-299 a FZ(M)3059 -289 y FP(1)3091 -299 y FZ(;)p FC(8)p
Ff(x)p FZ(:)p FV(\()p Ff(fx)h FV(=)f Ff(0)p FC(_)p Ff(fx)g
FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p 3688 -311 6
23 v 3694 -321 25 3 v 68 w Ff(f3)e FV(=)f Ff(1)p FZ(;)j
Ff(f2)e FV(=)f Ff(1)p FZ(;)k Ff(2)l FZ(<)l Ff(3)p FC(^)q
Ff(f2)d FV(=)f Ff(f3)4849 -345 y FC(^)4891 -333 y Fd(R)2191
-254 y Fc(|)p 2215 -254 1540 8 v 1540 w({z)p 3803 -254
V 1540 w(})3745 -193 y Fd(Y)3779 -181 y FP(9)2786 478
y F3(.)2786 511 y(.)2786 544 y(.)2786 578 y(.)2758 629
y FZ(Y)2794 639 y FP(9)p 2986 64 247 4 v 2986 115 a Ff(1)l
FC(\024)l Ff(1)p 3094 103 6 23 v 3099 93 25 3 v 60 w(1)l
FC(\024)l Ff(1)p 2894 145 431 4 v 2883 210 a FC(8)p Ff(x)p
FZ(:)p FV(\()p Ff(x)l FC(\024)l Ff(m)3091 189 y Fe(x)p
Fd(;)p Fe(0)3148 210 y FV(\))p 3186 198 6 23 v 3191 188
25 3 v 58 w Ff(1)l FC(\024)l Ff(1)3323 157 y FC(8)3358
168 y Fd(L)p 2894 242 431 4 v 2987 294 a FZ(M)3045 304
y FP(1)p 3092 282 6 23 v 3098 272 25 3 v 3137 294 a Ff(1)l
FC(\024)l Ff(1)3323 254 y FC(8)3358 265 y Fd(L)p 3452
243 247 4 v 3452 294 a Ff(0)l FZ(<)l Ff(1)p 3560 282
6 23 v 3566 272 25 3 v 61 w(0)l FZ(<)l Ff(1)p 2987 324
712 4 v 3089 375 a(1)l FC(\024)l Ff(1)p FC(\033)r Ff(0)l
FZ(<)l Ff(1)p FZ(;)12 b(M)3412 385 y FP(1)p 3459 363
6 23 v 3464 353 25 3 v 3503 375 a Ff(0)l FZ(<)l Ff(1)3698
333 y FC(\033)3746 344 y Fd(L)p 3032 405 622 4 v 3021
459 a FC(8)p Ff(y)q FZ(:)p FV(\()p Ff(1)l FC(\024)l Ff(y)q
FC(\033)r Ff(0)l FZ(<)l Ff(y)q FV(\))p FZ(;)g(M)3469
469 y FP(1)p 3515 447 6 23 v 3521 437 25 3 v 3560 459
a Ff(0)l FZ(<)l Ff(1)3653 417 y FC(8)3688 428 y Fd(L)p
3032 492 622 4 v 3187 543 a FZ(M)3245 553 y FP(1)3277
543 y FZ(;)e(S)p 3361 531 6 23 v 3367 521 25 3 v 62 w
Ff(0)l FZ(<)l Ff(1)3653 503 y FC(8)3688 514 y Fd(L)p
3876 -95 319 4 v 3876 -44 a Ff(f1)e FV(=)f Ff(0)p 4020
-56 6 23 v 4026 -66 25 3 v 59 w(f1)h FV(=)f Ff(0)p 4245
-95 319 4 v 50 w(f1)g FV(=)g Ff(1)p 4389 -56 6 23 v 4394
-66 25 3 v 59 w(f1)h FV(=)f Ff(1)p 3876 -24 687 4 v 3895
27 a(f1)h FV(=)f Ff(0)p FC(_)o Ff(f1)h FV(=)f Ff(1)p
4210 15 6 23 v 4216 5 25 3 v 59 w(f1)h FV(=)f Ff(0)p
FZ(;)k Ff(f1)c FV(=)g Ff(1)4562 -16 y FC(_)4604 -5 y
Fd(L)p 3839 57 761 4 v 3829 111 a FC(8)p Ff(x)p FZ(:)p
FV(\()p Ff(fx)h FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p
FV(\))p 4266 99 6 23 v 4272 89 25 3 v 59 w Ff(f1)h FV(=)f
Ff(0)p FZ(;)j Ff(f1)e FV(=)f Ff(1)4599 69 y FC(8)4634
80 y Fd(L)p 4765 -95 319 4 v 4765 -44 a Ff(f0)h FV(=)f
Ff(0)p 4909 -56 6 23 v 4915 -66 25 3 v 59 w(f0)g FV(=)g
Ff(0)p 5133 -95 319 4 v 50 w(f0)h FV(=)f Ff(1)p 5277
-56 6 23 v 5283 -66 25 3 v 59 w(f0)h FV(=)f Ff(1)p 4765
-24 687 4 v 4784 27 a(f0)g FV(=)g Ff(0)p FC(_)p Ff(f0)h
FV(=)f Ff(1)p 5099 15 6 23 v 5105 5 25 3 v 59 w(f0)g
FV(=)g Ff(0)p FZ(;)k Ff(f0)d FV(=)f Ff(1)5451 -16 y FC(_)5492
-5 y Fd(L)p 4728 57 761 4 v 4717 111 a FC(8)p Ff(x)p
FZ(:)p FV(\()p Ff(fx)h FV(=)f Ff(0)p FC(_)p Ff(fx)h FV(=)f
Ff(1)p FV(\))p 5155 99 6 23 v 5161 89 25 3 v 59 w Ff(f0)g
FV(=)g Ff(0)p FZ(;)k Ff(f0)d FV(=)f Ff(1)5488 69 y FC(8)5523
80 y Fd(L)p 3839 143 1650 4 v 4108 197 a FC(8)p Ff(x)p
FZ(:)p FV(\()p Ff(fx)h FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f
Ff(1)p FV(\))p 4545 185 6 23 v 4551 175 25 3 v 59 w Ff(f1)h
FV(=)f Ff(0)p FC(^)o Ff(f0)h FV(=)f Ff(0)p FZ(;)k Ff(f1)c
FV(=)g Ff(1)p FZ(;)k Ff(f0)d FV(=)f Ff(1)5488 151 y FC(^)5529
163 y Fd(R)p 5626 146 351 4 v 5626 197 a Ff(f0)h FV(=)f
Ff(f1)p 5786 185 6 23 v 5792 175 25 3 v 59 w(f0)h FV(=)f
Ff(f1)p 4118 230 1859 4 v 4293 284 a FV(\()p Ff(f1)h
FV(=)f Ff(0)p FC(^)o Ff(f0)h FV(=)f Ff(0)p FV(\))p FC(\033)p
Ff(f0)h FV(=)f Ff(f1)p FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)h FV(=)f Ff(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p
5293 272 6 23 v 5298 262 25 3 v 59 w Ff(f0)h FV(=)f Ff(f1)p
FZ(;)k Ff(f1)d FV(=)f Ff(1)p FZ(;)j Ff(f0)e FV(=)f Ff(1)5976
239 y FC(\033)6024 250 y Fd(L)p 4236 316 1623 4 v 4226
370 a FC(8)p Ff(y)q FZ(:)p FV(\(\()p Ff(fy)h FV(=)f Ff(0)p
FC(^)p Ff(f0)g FV(=)g Ff(0)p FV(\))p FC(\033)q Ff(f0)g
FV(=)g Ff(fy)q FV(\))p FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)h FV(=)f Ff(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p
5350 358 6 23 v 5355 348 25 3 v 59 w Ff(f0)h FV(=)f Ff(f1)p
FZ(;)k Ff(f1)d FV(=)f Ff(1)p FZ(;)j Ff(f0)e FV(=)f Ff(1)5858
328 y FC(8)5893 339 y Fd(L)p 4217 402 1662 4 v 4206 456
a FC(8)p Ff(x)p FZ(:)p Ff(y)q FZ(:)p FV(\(\()p Ff(fy)i
FV(=)e Ff(0)p FC(^)o Ff(fx)h FV(=)f Ff(0)p FV(\))p FC(\033)p
Ff(fx)h FV(=)f Ff(fy)q FV(\))p FZ(;)p FC(8)p Ff(x)p FZ(:)p
FV(\()p Ff(fx)h FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p
FV(\))p 5369 444 6 23 v 5375 434 25 3 v 59 w Ff(f0)h
FV(=)f Ff(f1)p FZ(;)j Ff(f1)e FV(=)f Ff(1)p FZ(;)k Ff(f0)c
FV(=)g Ff(1)5878 414 y FC(8)5913 425 y Fd(L)p 4217 489
1662 4 v 4532 543 a FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)h
FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)k(T)p
5043 531 6 23 v 5049 521 25 3 v 67 w Ff(f0)d FV(=)f Ff(f1)p
FZ(;)k Ff(f1)c FV(=)g Ff(1)p FZ(;)k Ff(f0)d FV(=)f Ff(1)5878
500 y FC(8)5913 511 y Fd(L)p 3187 575 2367 4 v 3704 629
a FZ(M)3762 639 y FP(1)3794 629 y FZ(;)p FC(8)p Ff(x)p
FZ(:)p FV(\()p Ff(fx)h FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f
Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p 4391 617 6 23 v 4397
607 25 3 v 68 w Ff(f1)d FV(=)g Ff(1)p FZ(;)k Ff(0)l FZ(<)l
Ff(1)p FC(^)q Ff(f0)d FV(=)f Ff(f1)p FZ(;)k Ff(f0)d FV(=)f
Ff(1)5552 583 y FC(^)5593 594 y Fd(R)p 2740 661 2296
4 v 2901 715 a FZ(M)2959 725 y FP(1)2991 715 y FZ(;)p
FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)h FV(=)f Ff(0)p FC(_)p
Ff(fx)g FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)g(T)p 3588
703 6 23 v 3594 693 25 3 v 67 w Ff(f3)d FV(=)f Ff(1)p
FC(^)o Ff(f1)h FV(=)f Ff(1)p FZ(;)k Ff(f2)c FV(=)g Ff(1)p
FZ(;)k Ff(2)l FZ(<)l Ff(3)p FC(^)q Ff(f2)d FV(=)f Ff(f3)p
FZ(;)k Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)d FV(=)f Ff(f1)p
FZ(;)k Ff(f0)c FV(=)g Ff(1)5035 669 y FC(^)5076 681 y
Fd(R)2740 760 y Fc(|)p 2764 760 1617 8 v 1617 w({z)p
4429 760 V 1617 w(})4356 821 y Fd(Y)4390 833 y FP(10)p
2500 935 247 4 v 2500 987 a Ff(2)l FC(\024)l Ff(3)p 2607
975 6 23 v 2613 965 25 3 v 60 w(2)l FC(\024)l Ff(3)p
2406 1017 433 4 v 2396 1081 a FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(2)l FC(\024)l Ff(m)2606 1061 y Fe(x)p Fd(;)p Fe(2)2662
1081 y FV(\))p 2701 1069 6 23 v 2706 1060 25 3 v 59 w
Ff(2)l FC(\024)l Ff(3)2838 1028 y FC(8)2873 1039 y Fd(L)p
2406 1114 433 4 v 2501 1165 a FZ(M)2559 1175 y FP(2)p
2606 1153 6 23 v 2611 1143 25 3 v 2650 1165 a Ff(2)l
FC(\024)l Ff(3)2838 1125 y FC(8)2873 1136 y Fd(L)p 2967
1115 247 4 v 2967 1165 a Ff(1)l FZ(<)l Ff(3)p 3075 1153
6 23 v 3081 1143 25 3 v 61 w(1)l FZ(<)l Ff(3)p 2501 1195
713 4 v 2603 1247 a(2)l FC(\024)l Ff(3)p FC(\033)r Ff(1)l
FZ(<)l Ff(3)p FZ(;)12 b(M)2926 1257 y FP(2)p 2973 1235
6 23 v 2979 1225 25 3 v 3018 1247 a Ff(1)l FZ(<)l Ff(3)3213
1204 y FC(\033)3261 1216 y Fd(L)p 2546 1277 622 4 v 2536
1331 a FC(8)p Ff(y)q FZ(:)p FV(\()p Ff(2)l FC(\024)l
Ff(y)q FC(\033)q Ff(1)l FZ(<)l Ff(y)q FV(\))p FZ(;)g(M)2983
1341 y FP(2)p 3030 1319 6 23 v 3035 1309 25 3 v 3075
1331 a Ff(1)l FZ(<)l Ff(3)3167 1289 y FC(8)3202 1300
y Fd(L)p 2546 1363 622 4 v 2701 1414 a FZ(M)2759 1424
y FP(2)2791 1414 y FZ(;)f(S)p 2875 1402 6 23 v 2881 1392
25 3 v 61 w Ff(1)l FZ(<)l Ff(3)3167 1375 y FC(8)3202
1386 y Fd(L)4420 921 y F3(.)4420 954 y(.)4420 987 y(.)4420
1020 y(.)4377 1072 y FZ(Y)4413 1082 y FP(10)p 4542 1020
351 4 v 4542 1072 a Ff(f1)c FV(=)g Ff(f3)p 4702 1060
6 23 v 4708 1050 25 3 v 60 w(f1)g FV(=)g Ff(f3)p 3431
1101 2392 4 v 3431 1155 a FV(\()p Ff(f3)g FV(=)g Ff(1)p
FC(^)p Ff(f1)h FV(=)f Ff(1)p FV(\))p FC(\033)p Ff(f1)g
FV(=)g Ff(f3)q FZ(;)j(M)4061 1165 y FP(1)4094 1155 y
FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)g Ff(0)p
FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p
4691 1143 6 23 v 4696 1133 25 3 v 67 w Ff(f1)d FV(=)f
Ff(f3)p FZ(;)k Ff(f2)d FV(=)f Ff(1)p FZ(;)j Ff(2)l FZ(<)l
Ff(3)p FC(^)r Ff(f2)d FV(=)g Ff(f3)q FZ(;)j Ff(0)l FZ(<)l
Ff(1)p FC(^)q Ff(f0)e FV(=)f Ff(f1)p FZ(;)k Ff(f0)d FV(=)f
Ff(1)5821 1110 y FC(\033)5869 1121 y Fd(L)p 3374 1187
2505 4 v 3363 1241 a FC(8)p Ff(y)q FZ(:)p FV(\(\()p Ff(fy)i
FV(=)e Ff(1)p FC(^)o Ff(f1)h FV(=)f Ff(1)p FV(\))p FC(\033)p
Ff(f1)h FV(=)f Ff(fy)q FV(\))p FZ(;)j(M)4118 1251 y FP(1)4150
1241 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)f
Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p
4747 1229 6 23 v 4753 1220 25 3 v 67 w Ff(f1)d FV(=)f
Ff(f3)p FZ(;)k Ff(f2)c FV(=)g Ff(1)p FZ(;)k Ff(2)l FZ(<)l
Ff(3)p FC(^)q Ff(f2)d FV(=)f Ff(f3)p FZ(;)k Ff(0)l FZ(<)l
Ff(1)p FC(^)q Ff(f0)d FV(=)f Ff(f1)p FZ(;)k Ff(f0)c FV(=)g
Ff(1)5878 1199 y FC(8)5913 1210 y Fd(L)p 3354 1274 2544
4 v 3344 1328 a FC(8)p Ff(x)p FZ(:)p Ff(y)q FZ(:)p FV(\(\()p
Ff(fy)h FV(=)f Ff(1)p FC(^)p Ff(fx)h FV(=)f Ff(1)p FV(\))p
FC(\033)p Ff(fx)g FV(=)g Ff(fy)q FV(\))p FZ(;)k(M)4138
1338 y FP(1)4170 1328 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)d FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p
FZ(;)k(S)o(;)f(T)p 4767 1316 6 23 v 4773 1306 25 3 v
68 w Ff(f1)d FV(=)g Ff(f3)q FZ(;)j Ff(f2)e FV(=)f Ff(1)p
FZ(;)k Ff(2)l FZ(<)l Ff(3)p FC(^)q Ff(f2)d FV(=)f Ff(f3)p
FZ(;)k Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)d FV(=)f Ff(f1)p
FZ(;)j Ff(f0)e FV(=)f Ff(1)5897 1285 y FC(8)5932 1296
y Fd(L)p 3354 1360 2544 4 v 3717 1414 a FZ(M)3775 1424
y FP(1)3807 1414 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p
Ff(fx)h FV(=)f Ff(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p
FZ(;)k(S)o(;)g(T)p 4404 1402 6 23 v 4410 1392 25 3 v
67 w Ff(f1)d FV(=)f Ff(f3)p FZ(;)k Ff(f2)c FV(=)g Ff(1)p
FZ(;)k Ff(2)l FZ(<)l Ff(3)p FC(^)q Ff(f2)d FV(=)f Ff(f3)p
FZ(;)k Ff(0)l FZ(<)l Ff(1)p FC(^)q Ff(f0)d FV(=)f Ff(f1)p
FZ(;)k Ff(f0)c FV(=)g Ff(1)5897 1372 y FC(8)5932 1383
y Fd(L)p 2701 1446 2835 4 v 3081 1500 a FZ(M)3139 1510
y FP(1)3172 1500 y FZ(;)j(M)3259 1510 y FP(2)3291 1500
y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)f
Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p
3888 1488 6 23 v 3894 1479 25 3 v 67 w Ff(f2)d FV(=)f
Ff(1)p FZ(;)k Ff(2)l FZ(<)l Ff(3)p FC(^)q Ff(f2)d FV(=)f
Ff(f3)p FZ(;)j Ff(0)l FZ(<)l Ff(1)p FC(^)r Ff(f0)d FV(=)g
Ff(f1)q FZ(;)j Ff(1)l FZ(<)l Ff(3)p FC(^)r Ff(f1)d FV(=)g
Ff(f3)q FZ(;)j Ff(f0)e FV(=)f Ff(1)5534 1455 y FC(^)5576
1466 y Fd(R)2406 1545 y Fc(|)p 2430 1545 1737 8 v 1737
w({z)p 4215 1545 V 1737 w(})4144 1607 y Fd(Y)4178 1619
y FP(11)2026 1798 y Gc(M)2094 1807 y FV(1)2148 1798 y
F9(=)20 b FX(8)p Fu(y)q Gc(:)p Fu(x)p Gc(:)m F9(\()p
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465 y
currentpoint grestore moveto
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%%Page: 141 153
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%%Page: 142 154
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y(possible)36 b(sets)f(\(generated)h(by)e(the)g(set)g(operators\))j
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Ga(M)1826 4953 y FX(0)1845 4986 y F6(f)-7 b Ga(a)25 b
F4(:=)2077 4974 y F9(\()2105 4986 y Ga(x)r F4(:)r Ga(B)2260
4974 y F9(\))2287 4986 y Ga(P)t F6(g)511 b Gg(by)24 b(Lemma)e(2.3.11)
549 5104 y(\(4\))100 b Ga(M)852 5071 y FX(0)871 5104
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b FB(J)p F4(\()p Ga(B)5 b F4(\))p FB(K)381 b Gg(by)24
b(\(2\))f(and)h(\(3\))549 5223 y(\(5\))754 5211 y FX(h)782
5223 y Ga(a)r F4(:)r Ga(B)933 5211 y FX(i)960 5223 y
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1530 5241 y FX(h)p Gc(B)s FX(i)1646 5223 y F4(\()p FB(J)p
F4(\()p Ga(B)5 b F4(\))q FB(K)o F4(\))925 b Gg(by)24
b(De\002nition)h(2.3.3)549 5341 y(\(6\))754 5329 y FX(h)782
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Ga(M)1058 5308 y FX(0)1107 5341 y F6(2)g FB(J)p F6(h)p
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Black Black eop end
%%Page: 143 155
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b F6(\021)c(:)p Ga(C)7 b Gg(:)504 544 y(\(1\))101 b Ga(M)35
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532 y F9(\()1193 544 y Ga(x)1245 532 y F9(\))1272 544
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1006 y F9(\()737 1018 y Ga(x)r F4(:)r Ga(C)890 1006 y
F9(\))918 1018 y Ga(S)979 985 y FX(0)1027 1018 y F6(2)j
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F4(\()p FB(J)p F4(\()p Ga(C)i F4(\))p FB(K)o F4(\))323
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1581 y Ga(T)2618 1548 y FX(0)2641 1581 y Ga(;)15 b(a)p
F4(\))24 b Gg(and)710 1687 y FX(h)737 1699 y Ga(a)r F4(:)r
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b F6(2)26 b FW(A)t(N)t(D)t(R)t(I)t(G)t(H)t(T)1675 1718
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1818 y(\(2\))101 b Ga(S)816 1781 y Gc(aux)796 1818 y
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2055 y(\(4\))101 b Ga(M)808 2022 y FX(0)854 2055 y Gg(freshly)25
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2173 y(\(5\))710 2161 y FX(h)737 2173 y Ga(d)r F4(:)r
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2173 y F6(2)i FB(J)p F6(h)p Ga(C)7 b F6(i)p FB(K)1721
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2292 y Ga(a)r F4(:)r Ga(C)7 b F6(^)p Ga(D)1025 2280 y
FX(i)1052 2292 y Ga(M)1150 2259 y FX(0)1199 2292 y F6(2)27
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F6(i)q FB(K)o F4(\))122 b Gg(by)23 b(\(4\),)h(\(5\))g(and)g(Def.)e
(2.3.3)504 2411 y(\(7\))710 2399 y FX(h)737 2411 y Ga(a)r
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y Ga(M)1150 2378 y FX(0)1199 2411 y F6(2)25 b FB(J)p
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48 w FW(O)t(R)t(R)t(I)t(G)t(H)t(T)862 2556 y Gc(i)862
2621 y FX(h)p Gc(C)939 2630 y FV(1)976 2621 y FX(_)p
Gc(C)1073 2630 y FV(2)1108 2621 y FX(i)1140 2589 y F4(\()p
FB(J)p F6(h)p Ga(C)1312 2603 y Gc(i)1340 2589 y F6(i)q
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2603 y F9(1)1792 2589 y F6(_)p Ga(C)1918 2603 y F9(2)1957
2589 y Gg(,)e F4(\()p Ga(i)j F4(=)f(1)p Ga(;)15 b F4(2\))p
Gg(:)504 2758 y(\(1\))101 b Ga(M)35 b F6(\021)25 b FL(Or)1029
2721 y Gc(i)1029 2781 y(R)1086 2758 y F4(\()1121 2746
y FX(h)1149 2758 y Ga(d)1196 2746 y FX(i)1224 2758 y
Ga(S)5 b(;)15 b(a)p F4(\))p Gg(,)48 b Ga(M)1577 2725
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2781 y(R)1879 2758 y F4(\()1914 2746 y FX(h)1942 2758
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FX(0)2101 2758 y Ga(;)15 b(a)p F4(\))p Gg(,)48 b Ga(S)2402
2721 y Gc(aux)2382 2758 y F6(\000)-32 b(\000)h(!)25 b
Ga(S)2638 2725 y FX(0)2684 2758 y Gg(and)710 2864 y FX(h)737
2876 y Ga(a)r F4(:)r Ga(C)879 2890 y F9(1)919 2876 y
F6(_)p Ga(C)1045 2890 y F9(2)1084 2864 y FX(i)1112 2876
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2876 y F4(\()p FB(J)p F6(h)p Ga(C)2123 2890 y Gc(i)2152
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3007 y(\(2\))101 b Ga(M)33 b Gg(freshly)25 b(introduces)h
Ga(a)d Gg(and)1732 2995 y FX(h)1760 3007 y Ga(d)r F4(:)r
Ga(C)1901 3021 y Gc(i)1930 2995 y FX(i)1957 3007 y Ga(S)30
b F6(2)25 b FB(J)p F6(h)p Ga(C)2266 3021 y Gc(i)2294
3007 y F6(i)q FB(K)448 b Gg(by)24 b(De\002nition)g(2.3.3)504
3126 y(\(3\))101 b Ga(M)808 3093 y FX(0)854 3126 y Gg(freshly)25
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3363 y(\(5\))710 3351 y FX(h)737 3363 y Ga(a)r F4(:)r
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y Ga(S)5 b(;)2033 2746 y FX(h)2061 2758 y Ga(b)2100 2746
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2746 y F9(\()2376 2758 y Ga(y)2424 2746 y F9(\))2451
2758 y Ga(N)10 b F4(\))1213 2895 y F6(\021)30 b FL(Cut)p
F4(\()1487 2883 y FX(h)1514 2895 y Ga(c)1553 2883 y FX(i)1581
2895 y Ga(M)10 b(;)1719 2883 y F9(\()1747 2895 y Ga(y)1795
2883 y F9(\))1822 2895 y Ga(N)g F4(\))1106 3002 y F9(\()p
FX(\003)p F9(\))1314 3035 y Gg(because)25 b Ga(M)33 b
Gg(freshly)25 b(introduces)i Ga(c)p Gg(.)549 3192 y(If)h
FL(Cut)p F4(\()810 3180 y FX(h)838 3192 y Ga(c)877 3180
y FX(i)905 3192 y Ga(M)10 b(;)1043 3180 y F9(\()1071
3192 y Ga(y)1119 3180 y F9(\))1146 3192 y Ga(N)g F4(\))29
b Gg(is)g(strongly)i(normalising,)i(then)d(its)f(reduct)h
FL(Cut)p F4(\()2922 3180 y FX(h)2950 3192 y Ga(a)2998
3180 y FX(i)3026 3192 y Ga(S)5 b(;)3127 3180 y F9(\()3154
3192 y Ga(x)3206 3180 y F9(\))3234 3192 y Ga(U)10 b F4(\))29
b Gg(must)549 3305 y(be)d(strongly)j(normalising)h(too.)38
b(In)27 b(case)1906 3293 y F9(\()1933 3305 y Ga(y)5 b
F4(:)r Ga(C)i F6(^)o Ga(D)2220 3293 y F9(\))2247 3305
y Ga(N)36 b Gg(is)27 b(in)i FW(B)t(I)t(N)t(D)t(I)t(N)t(G)2877
3324 y F9(\()p Gc(C)5 b FX(^)r Gc(D)r F9(\))3099 3305
y F4(\()p FB(J)p F6(h)p Ga(C)i F6(^)o Ga(D)s F6(i)q FB(K)o
F4(\))q Gg(,)549 3418 y(we)22 b(reason)j(analogous.)549
3571 y(If)c(neither)902 3559 y FX(h)930 3571 y Ga(c)r
F4(:)r Ga(C)7 b F6(^)p Ga(D)1209 3559 y FX(i)1236 3571
y Ga(M)30 b Gg(nor)1496 3559 y F9(\()1523 3571 y Ga(y)5
b F4(:)r Ga(C)i F6(^)p Ga(D)1811 3559 y F9(\))1838 3571
y Ga(N)30 b Gg(are)21 b(in)j FW(B)t(I)t(N)t(D)t(I)t(N)t(G)r
Gg(,)e(then)g(we)e(proceed)j(as)e(follo)n(ws.)549 3725
y(\(3.1\))822 3713 y FX(h)850 3725 y Ga(c)r F4(:)r Ga(C)7
b F6(^)p Ga(D)1129 3713 y FX(i)1156 3725 y Ga(M)35 b
F6(2)27 b FW(A)t(N)t(D)t(R)t(I)t(G)t(H)t(T)1779 3744
y FX(h)p Gc(C)5 b FX(^)r Gc(D)r FX(i)2002 3725 y F4(\()p
FB(J)p F6(h)p Ga(C)i F6(i)p FB(K)o Ga(;)15 b FB(J)p F6(h)p
Ga(D)s F6(i)q FB(K)o F4(\))q Gg(,)822 3838 y F9(\()850
3850 y Ga(y)5 b F4(:)r Ga(C)i F6(^)o Ga(D)1137 3838 y
F9(\))1164 3850 y Ga(N)36 b F6(2)26 b FW(A)t(N)t(D)t(L)t(E)t(F)t(T)1717
3817 y F9(1)1717 3881 y(\()p Gc(C)5 b FX(^)t Gc(D)r F9(\))1942
3850 y F4(\()p FB(J)p F4(\()p Ga(C)i F4(\))p FB(K)p F4(\))732
b Gg(ne)n(w)23 b(assumption)549 3984 y(\(3.2\))822 3972
y FX(h)850 3984 y Ga(a)17 b F4(:)h Ga(C)1030 3972 y FX(i)1056
3984 y Ga(S)31 b F6(2)25 b FB(J)p F6(h)p Ga(C)7 b F6(i)o
FB(K)23 b Gg(and)1621 3972 y F9(\()1648 3984 y Ga(x)17
b F4(:)h Ga(C)1832 3972 y F9(\))1859 3984 y Ga(U)35 b
F6(2)25 b FB(J)p F4(\()p Ga(C)7 b F4(\))p FB(K)601 b
Gg(by)24 b(De\002nition)h(2.3.3)549 4109 y(\(3.3\))100
b Ga(S;)15 b(U)36 b F6(2)25 b Ga(S)5 b(N)1236 4123 y
Gc(aux)2905 4109 y Gg(by)24 b(Lemma)e(2.3.13)549 4233
y(\(3.4\))100 b FL(Cut)p F4(\()995 4221 y FX(h)1023 4233
y Ga(a)r F4(:)r Ga(C)1172 4221 y FX(i)1199 4233 y Ga(S)5
b(;)1300 4221 y F9(\()1328 4233 y Ga(x)r F4(:)r Ga(C)1481
4221 y F9(\))1508 4233 y Ga(U)10 b F4(\))26 b F6(2)f
Ga(S)5 b(N)1861 4247 y Gc(aux)2250 4233 y Gg(by)24 b(induction)i(\(the)
e(de)o(gree)h(decreased\))p Black 321 4426 a Gb(Logical)g(Reduction)e
Fb(\033)1135 4440 y Fy(R)1200 4426 y FO(=)p Fb(\033)1334
4440 y Fy(L)1391 4426 y Gb(,)g FO(B)33 b Fb(\021)d FO(C)6
b Fb(\033)p FO(D)s Gb(:)p Black 549 4583 a Gg(\(1\))100
b Ga(M)36 b F6(\021)25 b FL(Imp)1118 4605 y Gc(R)1176
4583 y F4(\()1211 4571 y F9(\()1238 4583 y Ga(x)1290
4571 y F9(\))q FX(h)1345 4583 y Ga(a)1393 4571 y FX(i)1421
4583 y Ga(S)5 b(;)15 b(b)p F4(\))p Gg(,)23 b Ga(N)60
b F6(\021)25 b FL(Imp)2016 4605 y Gc(L)2068 4583 y F4(\()2103
4571 y FX(h)2131 4583 y Ga(c)2170 4571 y FX(i)2198 4583
y Ga(T)12 b(;)2303 4571 y F9(\()2331 4583 y Ga(y)2379
4571 y F9(\))2407 4583 y Ga(U)d(;)15 b(z)t F4(\))p Gg(,)754
4708 y Ga(M)33 b Gg(and)24 b Ga(N)33 b Gg(freshly)25
b(introduce)h Ga(b)d Gg(and)h Ga(z)t Gg(,)e(respecti)n(v)o(ely)-6
b(,)754 4820 y FX(h)782 4832 y Ga(c)r F4(:)r Ga(C)7 b
F6(\033)p Ga(D)1071 4820 y FX(i)1098 4832 y Ga(M)35 b
F6(2)25 b FB(J)p F6(h)p Ga(C)7 b F6(\033)o Ga(D)s F6(i)p
FB(K)23 b Gg(and)1848 4820 y F9(\()1875 4832 y Ga(y)5
b F4(:)r Ga(C)i F6(\033)o Ga(D)2172 4820 y F9(\))2200
4832 y Ga(N)35 b F6(2)25 b FB(J)p F4(\()p Ga(C)7 b F6(\033)o
Ga(D)s F4(\))p FB(K)261 b Gg(by)23 b(assumption)549 4985
y(The)g(term)g FL(Cut)p F4(\()1075 4973 y FX(h)1103 4985
y Ga(b)1142 4973 y FX(i)1169 4985 y Ga(M)10 b(;)1307
4973 y F9(\()1335 4985 y Ga(z)1381 4973 y F9(\))1409
4985 y Ga(N)g F4(\))23 b Gg(reduces)i(to)f(either:)p
Black Black 757 5216 a FL(Cut)p F4(\()930 5204 y FX(h)958
5216 y Ga(a)1006 5204 y FX(i)1059 5216 y FL(Cut)p F4(\()1232
5204 y FX(h)1259 5216 y Ga(c)1298 5204 y FX(i)1326 5216
y Ga(T)13 b(;)1432 5204 y F9(\()1460 5216 y Ga(x)1512
5204 y F9(\))1539 5216 y Ga(S)5 b F4(\))q Ga(;)1676 5204
y F9(\()1703 5216 y Ga(y)1751 5204 y F9(\))1779 5216
y Ga(U)10 b F4(\))100 b Gg(or)g FL(Cut)p F4(\()2334 5204
y FX(h)2362 5216 y Ga(c)2401 5204 y FX(i)2428 5216 y
Ga(T)13 b(;)2534 5204 y F9(\()2562 5216 y Ga(x)2614 5204
y F9(\))2667 5216 y FL(Cut)p F4(\()2840 5204 y FX(h)2867
5216 y Ga(a)2915 5204 y FX(i)2943 5216 y Ga(S)5 b(;)3044
5204 y F9(\()3072 5216 y Ga(y)3120 5204 y F9(\))3147
5216 y Ga(U)10 b F4(\)\))26 b Gg(.)p Black Black eop
end
%%Page: 147 159
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(Chapter)f(2)2639 b(147)p 277 88 3691 4 v Black 504 388
a Gg(W)-7 b(e)34 b(ha)n(v)o(e)i(to)e(sho)n(w)h(that)g(both)h(reducts)g
(are)f(strongly)i(normalising.)65 b(W)-7 b(e)34 b(shall)h(gi)n(v)o(e)g
(the)504 501 y(details)25 b(for)f(the)g(\002rst)f(case.)504
659 y(Since)h Ga(M)33 b Gg(and)24 b Ga(N)33 b Gg(are)23
b(not)h(axioms,)g(it)g(follo)n(ws)g(from)f(Lemma)g(2.3.6\(i\))h(that)
504 812 y FX(h)532 824 y Ga(b)r F4(:)r Ga(C)7 b F6(\033)o
Ga(D)820 812 y FX(i)848 824 y Ga(M)35 b F6(2)27 b FW(B)t(I)t(N)t(D)t(I)
t(N)t(G)1394 842 y FX(h)p Gc(C)5 b FX(\033)r Gc(D)r FX(i)1624
824 y F4(\()p FB(J)p F4(\()p Ga(C)i F6(\033)p Ga(D)s
F4(\))p FB(K)o F4(\))46 b F6([)h FW(I)t(M)t(P)t(R)t(I)t(G)t(H)t(T)2594
842 y FX(h)p Gc(C)5 b FX(\033)t Gc(D)r FX(i)2826 824
y F4(\()p FB(J)p F4(\()p Ga(C)i F4(\))q FB(K)o Ga(;)15
b FB(J)p F6(h)p Ga(D)s F6(i)q FB(K)o F4(\))504 947 y
F9(\()532 959 y Ga(z)6 b F4(:)r Ga(C)h F6(\033)p Ga(D)828
947 y F9(\))855 959 y Ga(N)35 b F6(2)27 b FW(B)t(I)t(N)t(D)t(I)t(N)t(G)
1386 978 y F9(\()p Gc(C)5 b FX(\033)r Gc(D)r F9(\))1616
959 y F4(\()p FB(J)p F6(h)p Ga(C)i F6(\033)p Ga(D)s F6(i)p
FB(K)o F4(\))46 b F6([)h FW(I)t(M)t(P)t(L)t(E)t(F)t(T)2531
978 y F9(\()p Gc(C)5 b FX(\033)h Gc(D)r F9(\))2766 959
y F4(\()p FB(J)p F6(h)p Ga(C)h F6(i)p FB(K)o Ga(;)15
b FB(J)p F4(\()p Ga(D)s F4(\))q FB(K)o F4(\))504 1115
y Gg(Again)35 b(the)g(proof)h(splits)g(into)g(tw)o(o)e(cases)i
(depending)i(on)d(whether)h(the)f(co-named)i(term)504
1216 y FX(h)532 1228 y Ga(b)17 b F4(:)g Ga(C)7 b F6(\033)p
Ga(D)851 1216 y FX(i)878 1228 y Ga(M)38 b Gg(or)28 b(the)g(named)h
(term)1709 1216 y F9(\()1737 1228 y Ga(z)21 b F4(:)d
Ga(C)7 b F6(\033)o Ga(D)2063 1216 y F9(\))2090 1228 y
Ga(N)38 b Gg(belong)30 b(to)g FW(B)t(I)t(N)t(D)t(I)t(N)t(G)r
Gg(.)44 b(Let)27 b(us)i(assume)504 1329 y FX(h)532 1341
y Ga(b)r F4(:)r Ga(C)7 b F6(\033)o Ga(D)820 1329 y FX(i)848
1341 y Ga(M)32 b Gg(is)24 b(an)f(element)i(in)g FW(B)t(I)t(N)t(D)t(I)t
(N)t(G)1901 1360 y FX(h)p Gc(C)5 b FX(\033)r Gc(D)r FX(i)2132
1341 y F4(\()p FB(J)p F4(\()p Ga(C)i F6(\033)o Ga(D)s
F4(\))p FB(K)p F4(\))p Gg(.)504 1517 y(\(2.1\))778 1505
y FX(h)806 1517 y Ga(b)r F4(:)r Ga(C)g F6(\033)o Ga(D)1094
1505 y FX(i)1121 1517 y Ga(M)36 b F6(2)27 b FW(B)t(I)t(N)t(D)t(I)t(N)t
(G)1668 1535 y FX(h)p Gc(C)5 b FX(\033)q Gc(D)r FX(i)1898
1517 y F4(\()p FB(J)p F4(\()p Ga(C)i F6(\033)o Ga(D)s
F4(\))q FB(K)o F4(\))584 b Gg(ne)n(w)23 b(assumption)504
1641 y(\(2.2\))101 b Ga(M)5 b F6(f)-7 b Ga(b)26 b F4(:=)1095
1629 y F9(\()1123 1641 y Ga(v)1170 1629 y F9(\))1198
1641 y Ga(P)s F6(g)g(2)f Ga(S)5 b(N)1550 1655 y Gc(aux)1695
1641 y Gg(for)23 b(all)1937 1629 y F9(\()1965 1641 y
Ga(v)5 b F4(:)r Ga(C)i F6(\033)o Ga(D)2261 1629 y F9(\))2289
1641 y Ga(P)38 b F6(2)25 b FB(J)p F4(\()p Ga(C)7 b F6(\033)o
Ga(D)s F4(\))p FB(K)190 b Gg(by)24 b(Def.)e(2.3.3)504
1765 y(\(2.3\))101 b Ga(M)5 b F6(f)-7 b Ga(b)26 b F4(:=)1095
1753 y F9(\()1123 1765 y Ga(z)1169 1753 y F9(\))1197
1765 y Ga(N)p F6(g)g(2)f Ga(S)5 b(N)1561 1779 y Gc(aux)2408
1765 y Gg(by)23 b(\(1\),)h(\(2.2\))g(and)3024 1753 y
F9(\()3051 1765 y Ga(v)3098 1753 y F9(\))3126 1765 y
Ga(P)38 b F6(\021)3318 1753 y F9(\()3345 1765 y Ga(z)3391
1753 y F9(\))3419 1765 y Ga(N)504 1889 y Gg(\(2.4\))101
b(The)23 b(follo)n(wing)i(calculation)i(sho)n(ws)d(that)g
FL(Cut)p F4(\()2318 1877 y FX(h)2345 1889 y Ga(c)2384
1877 y FX(i)2412 1889 y Ga(M)10 b(;)2550 1877 y F9(\()2578
1889 y Ga(z)2624 1877 y F9(\))2652 1889 y Ga(N)g F4(\))25
b F6(2)g Ga(S)5 b(N)3015 1903 y Gc(aux)3138 1889 y Gg(.)p
Black Black 874 2104 a Ga(M)g F6(f)-7 b Ga(b)26 b F4(:=)1192
2092 y F9(\()1219 2104 y Ga(z)1265 2092 y F9(\))1293
2104 y Ga(N)p F6(g)31 b(\021)f FL(Imp)1687 2125 y Gc(R)1745
2104 y F4(\()1780 2092 y F9(\()1808 2104 y Ga(x)1860
2092 y F9(\))p FX(h)1915 2104 y Ga(a)1963 2092 y FX(i)1990
2104 y Ga(S)5 b(;)15 b(b)p F4(\))-5 b F6(f)e Ga(b)27
b F4(:=)2385 2092 y F9(\()2413 2104 y Ga(z)2459 2092
y F9(\))2486 2104 y Ga(N)q F6(g)1442 2240 y F4(=)j FL(Cut)p
F4(\()1716 2228 y FX(h)1744 2240 y Ga(b)1783 2228 y FX(i)1810
2240 y FL(Imp)1954 2262 y Gc(R)2012 2240 y F4(\()2047
2228 y F9(\()2075 2240 y Ga(x)2127 2228 y F9(\))p FX(h)2182
2240 y Ga(a)2230 2228 y FX(i)2257 2240 y Ga(S)q F6(f)-7
b Ga(b)25 b F4(:=)2537 2228 y F9(\()2565 2240 y Ga(z)2611
2228 y F9(\))2639 2240 y Ga(N)p F6(g)q Ga(;)15 b(b)p
F4(\))p Ga(;)2912 2228 y F9(\()2940 2240 y Ga(z)2986
2228 y F9(\))3014 2240 y Ga(N)10 b F4(\))1435 2320 y
FV(\()p FC(\003)p FV(\))1442 2404 y F6(\021)30 b FL(Cut)p
F4(\()1716 2392 y FX(h)1744 2404 y Ga(b)1783 2392 y FX(i)1810
2404 y FL(Imp)1954 2426 y Gc(R)2012 2404 y F4(\()2047
2392 y F9(\()2075 2404 y Ga(x)2127 2392 y F9(\))p FX(h)2182
2404 y Ga(a)2230 2392 y FX(i)2257 2404 y Ga(S)5 b(;)15
b(b)p F4(\))q Ga(;)2473 2392 y F9(\()2501 2404 y Ga(z)2547
2392 y F9(\))2575 2404 y Ga(N)10 b F4(\))1442 2541 y
F6(\021)30 b FL(Cut)p F4(\()1716 2529 y FX(h)1744 2541
y Ga(b)1783 2529 y FX(i)1810 2541 y Ga(M)10 b(;)1948
2529 y F9(\()1976 2541 y Ga(z)2022 2529 y F9(\))2050
2541 y Ga(N)g F4(\))1336 2672 y F9(\()p FX(\003)p F9(\))1543
2705 y Gg(because)25 b Ga(M)33 b Gg(freshly)25 b(introduces)i
Ga(b)p Gg(.)504 2905 y(Therefore)37 b(we)e(kno)n(w)g(that)h(the)f(term)
g FL(Cut)p F4(\()1962 2893 y FX(h)1990 2905 y Ga(b)2029
2893 y FX(i)2056 2905 y Ga(M)11 b(;)2195 2893 y F9(\()2222
2905 y Ga(z)2268 2893 y F9(\))2296 2905 y Ga(N)f F4(\))35
b Gg(is)g(strongly)i(normalising,)k(and)504 3018 y(hence)26
b(its)e(reduct)i FL(Cut)p F4(\()1273 3006 y FX(h)1300
3018 y Ga(a)1348 3006 y FX(i)1401 3018 y FL(Cut)p F4(\()1574
3006 y FX(h)1602 3018 y Ga(c)1641 3006 y FX(i)1669 3018
y Ga(T)12 b(;)1774 3006 y F9(\()1802 3018 y Ga(x)1854
3006 y F9(\))1882 3018 y Ga(S)5 b F4(\))p Ga(;)2018 3006
y F9(\()2046 3018 y Ga(y)2094 3006 y F9(\))2121 3018
y 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 y
F9(\()3096 3130 y Ga(z)6 b F4(:)r Ga(C)h F6(\033)p Ga(D)3392
3118 y F9(\))3419 3130 y Ga(N)504 3243 y Gg(belongs)26
b(to)f FW(B)t(I)t(N)t(D)t(I)t(N)t(G)1240 3262 y F9(\()p
Gc(C)5 b FX(\033)r Gc(D)r F9(\))1471 3243 y F4(\()p FB(J)p
F6(h)p Ga(C)i F6(\033)o Ga(D)s F6(i)p FB(K)p F4(\))23
b 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)17
b F4(:)g Ga(C)7 b F6(\033)p Ga(D)851 3502 y FX(i)878
3514 y Ga(M)45 b Gg(and)1178 3502 y F9(\()1205 3514 y
Ga(z)22 b F4(:)17 b Ga(C)7 b F6(\033)o Ga(D)1531 3502
y F9(\))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)r
FX(i)2681 3514 y F4(\()p FB(J)p F4(\()p Ga(C)i F4(\))q
FB(K)o Ga(;)15 b FB(J)p F6(h)p Ga(D)s F6(i)q FB(K)o F4(\))36
b Gg(and)g(to)506 3627 y FW(I)t(M)t(P)t(L)t(E)t(F)t(T)833
3646 y F9(\()p Gc(C)6 b FX(\033)f Gc(D)r F9(\))1068 3627
y F4(\()p FB(J)p F6(h)p Ga(C)i F6(i)p FB(K)o Ga(;)15
b FB(J)p F4(\()p Ga(D)s F4(\))q FB(K)p F4(\))p Gg(,)22
b(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)806
3945 y Ga(b)17 b F4(:)g Ga(C)7 b F6(\033)o Ga(D)1124
3933 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)1977
3945 y F4(\()p FB(J)p F4(\()p Ga(C)i F4(\))p FB(K)p Ga(;)15
b FB(J)p F6(h)p Ga(D)s F6(i)p FB(K)p F4(\))p Gg(,)778
4058 y F9(\()806 4070 y Ga(z)21 b F4(:)d Ga(C)7 b F6(\033)o
Ga(D)1132 4058 y F9(\))1159 4070 y Ga(N)35 b F6(2)27
b FW(I)t(M)t(P)t(L)t(E)t(F)t(T)1682 4088 y F9(\()p Gc(C)5
b FX(\033)h Gc(D)r F9(\))1916 4070 y F4(\()p FB(J)p F6(h)p
Ga(C)h F6(i)p FB(K)p Ga(;)15 b FB(J)p F4(\()p Ga(D)s
F4(\))q FB(K)o F4(\))452 b Gg(ne)n(w)23 b(assumption)504
4194 y(\(3.2\))778 4182 y F9(\()806 4194 y Ga(x)17 b
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%%Page: 151 163
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b(induction)k(and)d(Lem)e(2.3.11)504 5394 y(\(4\))101
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%%Page: 152 164
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b(Details)24 b(f)n(or)g(some)g(Pr)n(oofs)p -144 88 3691
4 v Black Black 321 388 a(Commuting)f(Reduction:)p Black
45 w Gg(W)-7 b(e)23 b(gi)n(v)o(e)h(one)g(case.)549 562
y Ga(M)35 b F6(\021)25 b FL(Cut)p F4(\()941 550 y FX(h)969
562 y Ga(a)1017 550 y FX(i)1044 562 y Ga(S)5 b(;)1145
550 y F9(\()1173 562 y Ga(x)1225 550 y F9(\))1252 562
y Ga(T)13 b F4(\))23 b Gg(and)h Ga(N)35 b F6(\021)25
b FL(Cut)1813 515 y FC( )1874 562 y F4(\()1909 550 y
FX(h)1937 562 y Ga(a)1985 550 y FX(i)2012 562 y Ga(S)5
b(;)2113 550 y F9(\()2141 562 y Ga(x)2193 550 y F9(\))2221
562 y Ga(T)12 b F4(\))549 686 y Gg(\(1\))100 b F6(j)p
Ga(M)10 b F6(j)902 700 y Gc(x)972 686 y F6(\021)25 b
FL(Cut)p F4(\()1241 674 y FX(h)1269 686 y Ga(a)1317 674
y FX(i)1344 686 y F6(j)p Ga(S)5 b F6(j)1455 700 y Gc(x)1499
686 y Ga(;)1539 674 y F9(\()1567 686 y Ga(x)1619 674
y F9(\))1647 686 y F6(j)p Ga(T)13 b F6(j)1763 700 y Gc(x)1807
686 y F4(\))1108 b Gg(by)24 b(Lemma)f(2.6.7)549 810 y(\(2\))100
b FL(Cut)p F4(\()927 798 y FX(h)955 810 y Ga(a)1003 798
y FX(i)1030 810 y F6(j)p Ga(S)5 b F6(j)1141 824 y Gc(x)1186
810 y Ga(;)1226 798 y F9(\()1254 810 y Ga(x)1306 798
y F9(\))1333 810 y F6(j)p Ga(T)13 b F6(j)1449 824 y Gc(x)1493
810 y F4(\))1574 773 y Gc(aux)1554 810 y F6(\000)-31
b(\000)f(!)1724 777 y F9(0)p Gc(=)p F9(1)1859 810 y F6(j)p
Ga(S)5 b F6(j)1970 824 y Gc(x)2010 810 y F6(f)-7 b Ga(a)26
b F4(:=)2243 798 y F9(\()2270 810 y Ga(x)2322 798 y F9(\))2365
810 y F6(j)p Ga(T)13 b F6(j)2481 824 y Gc(x)2515 810
y F6(g)2219 935 y Gg(`0'-case:)31 b(if)24 b F6(j)p Ga(S)5
b F6(j)2755 949 y Gc(x)2822 935 y Gg(freshly)25 b(introduces)h
Ga(a)549 1059 y Gg(\(3\))100 b F6(j)p Ga(S)5 b F6(j)865
1073 y Gc(x)905 1059 y F6(f)-7 b Ga(a)26 b F4(:=)1138
1047 y F9(\()1165 1059 y Ga(x)1217 1047 y F9(\))1260
1059 y F6(j)p Ga(T)13 b F6(j)1376 1073 y Gc(x)1410 1059
y F6(g)26 b(\021)f(j)p Ga(N)10 b F6(j)1710 1073 y Gc(x)2905
1059 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)f
Ga(M)2161 1253 y Gc(x)2096 1290 y F6(\000)-32 b(\000)h(!)-5
b Ga(N)10 b Gg(,)22 b(we)h(ha)n(v)o(e)h F6(j)p Ga(M)10
b F6(j)2857 1304 y Gc(x)2927 1290 y F6(\021)25 b(j)p
Ga(N)10 b F6(j)3156 1304 y Gc(x)3200 1290 y Gg(.)p Black
321 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 1751
a Gb(Garbage)i(Reduction:)p Black 46 w Gg(T)-7 b(ak)o(e)22
b(for)h(e)o(xample)h Ga(M)35 b F6(\021)25 b FL(Cut)2107
1704 y FC( )2168 1751 y F4(\()2203 1739 y FX(h)2231 1751
y Ga(a)2279 1739 y FX(i)2306 1751 y Ga(S)5 b(;)2407 1739
y F9(\()2435 1751 y Ga(x)2487 1739 y F9(\))2514 1751
y Ga(T)13 b F4(\))22 b Gg(with)h Ga(a)e Gg(not)i(free)h(in)e
Ga(S)5 b Gg(,)22 b(then)549 1864 y(by)h(Lemma)g(2.6.10)h
F6(j)p Ga(M)10 b F6(j)1361 1878 y Gc(x)1430 1864 y F6(\021)25
b(j)p Ga(N)10 b F6(j)1659 1878 y Gc(x)1704 1864 y Gg(.)p
3480 1864 4 62 v 3484 1806 55 4 v 3484 1864 V 3538 1864
4 62 v Black 321 2077 a Gb(Pr)n(oof)33 b(of)f(Lemma)g(2.6.16.)p
Black 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)-31
b(\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)20
b F6(\021)10 b FL(Cut)1318 2383 y FC( )1379 2431 y F4(\()1414
2419 y FX(h)1442 2431 y Ga(a)1490 2419 y FX(i)1518 2431
y FL(Not)1660 2445 y Gc(R)1718 2431 y F4(\()1753 2419
y F9(\()1781 2431 y Ga(x)1833 2419 y F9(\))1860 2431
y Ga(S)5 b(;)15 b(a)p F4(\))q Ga(;)2085 2419 y F9(\()2113
2431 y Ga(y)2161 2419 y F9(\))2188 2431 y Ga(T)e F4(\))48
b Gg(and)1051 2567 y Ga(N)20 b F6(\021)10 b FL(Cut)o
F4(\()1397 2555 y FX(h)1425 2567 y Ga(a)1473 2555 y FX(i)1501
2567 y FL(Not)1643 2581 y Gc(R)1701 2567 y F4(\()1736
2555 y F9(\()1764 2567 y Ga(x)1816 2555 y F9(\))1843
2567 y FL(Cut)1922 2520 y FC( )1983 2567 y F4(\()2018
2555 y FX(h)2046 2567 y Ga(a)2094 2555 y FX(i)2121 2567
y Ga(S)5 b(;)2222 2555 y F9(\()2250 2567 y Ga(y)2298
2555 y F9(\))2325 2567 y Ga(T)13 b F4(\))p Ga(;)i(a)p
F4(\))q Ga(;)2590 2555 y F9(\()2618 2567 y Ga(y)2666
2555 y F9(\))2693 2567 y Ga(T)e F4(\))p Gg(.)321 2806
y(Hence)24 b(we)f(ha)n(v)o(e)h Ga(M)1085 2769 y Gc(x)1019
2806 y F6(\000)-31 b(\000)g(!)25 b Ga(N)10 b Gg(.)28
b(The)23 b(subterms)i(of)e Ga(N)33 b Gg(are:)p Black
Black 944 3064 a(\(1\))101 b(all)23 b(subterms)i(of)f
Ga(S)j Gg(and)d Ga(T)13 b Gg(,)944 3177 y(\(2\))101 b
FL(Cut)1228 3130 y FC( )1289 3177 y F4(\()1324 3165 y
FX(h)1352 3177 y Ga(a)1400 3165 y FX(i)1428 3177 y Ga(S)5
b(;)1529 3165 y F9(\()1556 3177 y Ga(y)1604 3165 y F9(\))1632
3177 y Ga(T)12 b F4(\))p Gg(,)944 3290 y(\(3\))101 b
FL(Not)1292 3304 y Gc(R)1350 3290 y F4(\()1385 3278 y
F9(\()1413 3290 y Ga(x)1465 3278 y F9(\))1492 3290 y
FL(Cut)1571 3243 y FC( )1632 3290 y F4(\()1667 3278 y
FX(h)1695 3290 y Ga(a)1743 3278 y FX(i)1770 3290 y Ga(S)5
b(;)1871 3278 y F9(\()1899 3290 y Ga(y)1947 3278 y F9(\))1974
3290 y Ga(T)13 b F4(\))p Ga(;)i(a)p F4(\))24 b Gg(and)944
3403 y(\(4\))101 b Ga(N)35 b F6(\021)25 b FL(Cut)p F4(\()1527
3391 y FX(h)1554 3403 y Ga(a)1602 3391 y FX(i)1630 3403
y FL(Not)1773 3417 y Gc(R)1830 3403 y F4(\()1865 3391
y F9(\()1893 3403 y Ga(x)1945 3391 y F9(\))1972 3403
y FL(Cut)2051 3355 y FC( )2112 3403 y F4(\()2147 3391
y FX(h)2175 3403 y Ga(a)2223 3391 y FX(i)2250 3403 y
Ga(S)5 b(;)2351 3391 y F9(\()2379 3403 y Ga(y)2427 3391
y F9(\))2455 3403 y Ga(T)12 b F4(\))q Ga(;)j(a)p F4(\))p
Ga(;)2719 3391 y F9(\()2747 3403 y Ga(y)2795 3391 y F9(\))2823
3403 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)e
Ga(S)5 b(N)2723 3691 y Gc(aux)2846 3677 y Gg(.)58 b(Case)34
b(\(1\))g(follo)n(ws)321 3790 y(by)28 b(assumption:)40
b(the)27 b Ga(x)p Gg(-normal)i(form)e(of)h(e)n(v)o(ery)g(subterm)g(of)g
Ga(M)37 b Gg(is)27 b(an)g(element)i(in)e Ga(S)5 b(N)3242
3804 y Gc(aux)3365 3790 y Gg(,)27 b(and)321 3903 y(therefore)j(the)e
Ga(x)p Gg(-normal)g(form)g(of)f(e)n(v)o(ery)h(subterm)g(of)g
Ga(S)j Gg(and)d Ga(T)40 b Gg(must)27 b(be)h(in)f Ga(S)5
b(N)3018 3917 y Gc(aux)3140 3903 y Gg(,)28 b(too.)41
b(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)2223
3978 y(aux)2203 4016 y F6(\000)-31 b(\000)f(!)2373 3983
y FX(\003)2438 4016 y F6(j)p Ga(N)10 b F6(j)2571 4030
y Gc(x)2615 4016 y Gg(,)20 b(and)g(thus)h F6(j)p Ga(N)10
b F6(j)3112 4030 y Gc(x)3181 4016 y F6(2)25 b Ga(S)5
b(N)3401 4030 y Gc(aux)3524 4016 y Gg(.)321 4128 y(By)23
b(Lemma)g(2.6.7)g(we)g(ha)n(v)o(e)h(the)g(identities)p
Black Black 1140 4370 a F6(j)p FL(Cut)p F4(\()1338 4358
y FX(h)1366 4370 y Ga(a)1414 4358 y FX(i)1441 4370 y
FL(Not)1584 4384 y Gc(R)1641 4370 y F4(\()1676 4358 y
F9(\()1704 4370 y Ga(x)1756 4358 y F9(\))1784 4370 y
FL(Cut)1862 4322 y FC( )1923 4370 y F4(\()1958 4358 y
FX(h)1986 4370 y Ga(a)2034 4358 y FX(i)2062 4370 y Ga(S)5
b(;)2163 4358 y F9(\()2190 4370 y Ga(y)2238 4358 y F9(\))2266
4370 y Ga(T)12 b F4(\))q Ga(;)j(a)p F4(\))q Ga(;)2531
4358 y F9(\()2558 4370 y Ga(y)2606 4358 y F9(\))2634
4370 y Ga(T)e F4(\))p F6(j)2760 4384 y Gc(x)969 4483
y F6(\021)100 b FL(Cut)o F4(\()1312 4471 y FX(h)1340
4483 y Ga(a)1388 4471 y FX(i)1416 4483 y F6(j)p FL(Not)1584
4497 y Gc(R)1641 4483 y F4(\()1676 4471 y F9(\()1704
4483 y Ga(x)1756 4471 y F9(\))1784 4483 y FL(Cut)1862
4435 y FC( )1923 4483 y F4(\()1958 4471 y FX(h)1986 4483
y Ga(a)2034 4471 y FX(i)2062 4483 y Ga(S)5 b(;)2163 4471
y F9(\()2190 4483 y Ga(y)2238 4471 y F9(\))2266 4483
y Ga(T)12 b F4(\))q Ga(;)j(a)p F4(\))p F6(j)2515 4497
y Gc(x)2560 4483 y Ga(;)2600 4471 y F9(\()2628 4483 y
Ga(y)2676 4471 y F9(\))2703 4483 y F6(j)p Ga(T)e F6(j)2819
4497 y Gc(x)2863 4483 y F4(\))969 4595 y F6(\021)100
b FL(Cut)o F4(\()1312 4583 y FX(h)1340 4595 y Ga(a)1388
4583 y FX(i)1416 4595 y FL(Not)1558 4609 y Gc(R)1616
4595 y F4(\()1651 4583 y F9(\()1679 4595 y Ga(x)1731
4583 y F9(\))1758 4595 y F6(j)p FL(Cut)1862 4548 y FC( )1923
4595 y F4(\()1958 4583 y FX(h)1986 4595 y Ga(a)2034 4583
y FX(i)2062 4595 y Ga(S)5 b(;)2163 4583 y F9(\()2190
4595 y Ga(y)2238 4583 y F9(\))2266 4595 y Ga(T)12 b F4(\))p
F6(j)2391 4609 y Gc(x)2436 4595 y Ga(;)j(a)p F4(\))q
Ga(;)2600 4583 y F9(\()2628 4595 y Ga(y)2676 4583 y F9(\))2703
4595 y F6(j)p Ga(T)e F6(j)2819 4609 y Gc(x)2863 4595
y F4(\))321 4834 y Gg(and)24 b(therefore)i(the)e Ga(x)p
Gg(-normal)g(form)g(of)f(\(2\))h(and)g(\(3\))g(are)g(in)f
Ga(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 3538
4834 4 62 v Black 321 5046 a Gb(Pr)n(oof)34 b(of)f(Lemma)f(2.6.20.)p
Black 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)27
b(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(.)31
b(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)23
b(of)c(them.)27 b(W)-7 b(e)19 b(write)g(rpo)h(as)f(shorthand)321
5385 y(for)24 b(De\002nition)g(2.6.12.)p Black Black
eop end
%%Page: 153 165
TeXDict 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 Black
277 388 a(Inner)23 b(Reduction:)p Black 46 w Gg(W)-7
b(e)22 b(gi)n(v)o(e)i(one)g(case.)504 533 y Ga(M)36 b
F6(\021)25 b FL(Cut)p F4(\()897 521 y FX(h)924 533 y
Ga(a)972 521 y FX(i)1000 533 y Ga(S)5 b(;)1101 521 y
F9(\()1129 533 y Ga(x)1181 521 y F9(\))1208 533 y Ga(T)13
b F4(\))1376 496 y Gc(l)q(oc)1334 533 y F6(\000)-31 b(\000)g(!)25
b FL(Cut)p F4(\()1703 521 y FX(h)1731 533 y Ga(a)1779
521 y FX(i)1806 533 y Ga(S)1867 500 y FX(0)1890 533 y
Ga(;)1930 521 y F9(\()1958 533 y Ga(x)2010 521 y F9(\))2038
533 y Ga(T)12 b F4(\))26 b F6(\021)f Ga(N)504 646 y Gg(\(1\))101
b Ga(S)838 608 y Gc(l)q(oc)796 646 y F6(\000)-31 b(\000)g(!)25
b Ga(S)1053 613 y FX(0)1099 646 y Gg(and)f Ga(S)p 1253
661 61 4 v 30 w(>)1410 613 y Gc(r)r(po)1543 646 y Ga(S)1604
613 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 4
v 35 w F4(=)25 b Ga(S)p 929 773 61 4 v 26 w F6(\001)1036
772 y Gc(m)1123 758 y Ga(T)p 1123 773 66 4 v 60 w Gg(and)50
b Ga(N)p 1416 773 83 4 v 35 w F4(=)25 b Ga(S)1681 725
y FX(0)p 1620 773 85 4 v 1724 758 a F6(\001)1749 772
y 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)1809
b Gg(by)24 b(Lemma)e(2.6.19\(i\))504 984 y(\(4\))101
b Ga(S)p 710 999 61 4 v 25 w F6(\001)816 998 y Gc(m)903
984 y Ga(T)p 903 999 66 4 v 38 w(>)1065 951 y Gc(r)r(po)1198
984 y Ga(S)1259 951 y FX(0)p 1198 999 85 4 v 1330 984
a Gg(and)49 b Ga(S)p 1509 999 61 4 v 25 w F6(\001)1615
998 y Gc(m)1703 984 y Ga(T)p 1703 999 66 4 v 38 w(>)1865
951 y Gc(r)r(po)1997 984 y Ga(T)p 1997 999 V 849 w Gg(by)23
b(\(1\))h(and)g(rpo\(i\))504 1097 y(\(5\))101 b F6(f)-24
b(j)p Ga(S)p 756 1112 61 4 v 6 w(;)15 b(T)p 858 1112
66 4 v 13 w F6(j)-24 b(g)27 b Ga(>)1068 1053 y Gc(r)r(po)1068
1127 y(mul)q(t)1247 1097 y F6(f)-24 b(j)p Ga(S)1354 1064
y FX(0)p 1293 1112 85 4 v 1379 1097 a Ga(;)15 b(T)p 1419
1112 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(>)904
1177 y Gc(r)r(po)1037 1210 y Ga(N)p 1037 1225 83 4 v
1180 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:)p
Black 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)800
1608 y FC( )861 1655 y F4(\()896 1643 y FX(h)924 1655
y Ga(c)963 1643 y FX(i)990 1655 y FL(And)1145 1669 y
Gc(R)1203 1655 y F4(\()1238 1643 y FX(h)1266 1655 y Ga(a)1314
1643 y FX(i)1341 1655 y Ga(S)5 b(;)1442 1643 y FX(h)1470
1655 y Ga(b)1509 1643 y FX(i)1536 1655 y Ga(T)13 b(;)i(c)p
F4(\))q Ga(;)1757 1643 y F9(\()1785 1655 y Ga(x)1837
1643 y F9(\))1864 1655 y Ga(U)10 b F4(\))782 1742 y Gc(x)717
1779 y F6(\000)-31 b(\000)f(!)26 b FL(Cut)o F4(\()1085
1767 y FX(h)1113 1779 y Ga(c)1152 1767 y FX(i)1180 1779
y FL(And)1335 1793 y Gc(R)1392 1779 y F4(\()1427 1767
y FX(h)1455 1779 y Ga(a)1503 1767 y FX(i)1531 1779 y
FL(Cut)1609 1732 y FC( )1670 1779 y F4(\()1705 1767 y
FX(h)1733 1779 y Ga(c)1772 1767 y FX(i)1800 1779 y Ga(S)5
b(;)1901 1767 y F9(\()1929 1779 y Ga(x)1981 1767 y F9(\))2008
1779 y Ga(U)10 b F4(\))p Ga(;)2155 1767 y FX(h)2183 1779
y Ga(b)2222 1767 y FX(i)2250 1779 y FL(Cut)2329 1732
y FC( )2389 1779 y F4(\()2424 1767 y FX(h)2452 1779 y
Ga(c)2491 1767 y FX(i)2519 1779 y Ga(T)j(;)2625 1767
y F9(\()2653 1779 y Ga(x)2705 1767 y F9(\))2732 1779
y Ga(U)d F4(\))p Ga(;)15 b(c)p F4(\))q Ga(;)2994 1767
y F9(\()3022 1779 y Ga(x)3074 1767 y F9(\))3102 1779
y Ga(U)10 b F4(\))25 b F6(\021)g Ga(N)504 1903 y Gg(\(1\))146
b Ga(M)p 755 1918 99 4 v 36 w F4(=)25 b FB(L)p Ga(S)p
1010 1918 61 4 v 5 w(;)15 b(T)p 1111 1918 66 4 v 13 w
FB(M)g F6(h)p Ga(U)p 1262 1918 72 4 v 11 w F6(i)1370
1917 y Gc(m)1485 1903 y Gg(and)49 b Ga(N)p 1664 1918
83 4 v 36 w F4(=)24 b FB(L)p Ga(S)p 1903 1918 61 4 v
6 w F6(h)p Ga(U)p 2000 1918 72 4 v 10 w F6(i)2107 1917
y Gc(r)2145 1903 y Ga(;)15 b(T)p 2185 1918 66 4 v 14
w F6(h)p Ga(U)p 2287 1918 72 4 v 10 w F6(i)2394 1917
y Gc(s)2431 1903 y FB(M)21 b F6(\001)2512 1917 y Gc(t)2562
1903 y Ga(U)p 2562 1918 V 146 w Gg(by)i(De\002nition)i(2.6.17)504
2027 y(\(2\))146 b Ga(m)26 b F6(\025)f Ga(t;)15 b(r)m(;)g(s)1551
b Gg(by)23 b(Lemma)g(2.6.19\(i,ii\))504 2152 y(\(3\))p
758 2152 28 4 v 775 2152 V 793 2152 V 211 w F6(h)p 857
2152 V 875 2152 V 893 2152 V 65 w(i)955 2166 y Gc(m)1047
2152 y F6(\035)p 1165 2152 V 1183 2152 V 1201 2152 V
110 w(\001)1273 2166 y Gc(t)p 1325 2152 V 1343 2152 V
1360 2152 V 2487 2152 a Gg(by)h(\(2\))f(and)h(De\002nition)h(2.6.14)504
2276 y(\(4\))146 b FB(L)p Ga(S)p 790 2291 61 4 v 6 w(;)15
b(T)p 892 2291 66 4 v 13 w FB(M)p F6(h)p Ga(U)p 1028
2291 72 4 v 11 w F6(i)1136 2290 y Gc(m)1228 2276 y Ga(>)1299
2243 y Gc(r)r(po)1431 2276 y Ga(S)p 1431 2291 61 4 v
53 w Gg(and)50 b FB(L)p Ga(S)p 1755 2291 V 5 w(;)15 b(T)p
1856 2291 66 4 v 13 w FB(M)p F6(h)p Ga(U)p 1992 2291
72 4 v 11 w F6(i)2100 2290 y Gc(m)2192 2276 y Ga(>)2263
2243 y Gc(r)r(po)2396 2276 y Ga(U)p 2396 2291 V 724 w
Gg(by)23 b(rpo\(i\))504 2400 y(\(5\))146 b F6(f)-24 b(j)p
FB(L)p Ga(S)p 836 2415 61 4 v 7 w(;)15 b(T)p 939 2415
66 4 v 13 w FB(M)p Ga(;)g(U)p 1080 2415 72 4 v 11 w F6(j)-24
b(g)26 b Ga(>)1296 2356 y Gc(r)r(po)1296 2429 y(mul)q(t)1476
2400 y F6(f)-24 b(j)p Ga(S)p 1522 2415 61 4 v 6 w(;)15
b(U)p 1624 2415 72 4 v 10 w F6(j)-24 b(g)1440 b Gg(by)23
b(rpo\(i\))504 2524 y(\(6\))146 b FB(L)p Ga(S)p 790 2539
61 4 v 6 w(;)15 b(T)p 892 2539 66 4 v 13 w FB(M)p F6(h)p
Ga(U)p 1028 2539 72 4 v 11 w F6(i)1136 2538 y Gc(m)1228
2524 y Ga(>)1299 2491 y Gc(r)r(po)1431 2524 y Ga(S)p
1431 2539 61 4 v 5 w F6(h)p Ga(U)p 1527 2539 72 4 v 11
w F6(i)1635 2538 y Gc(r)2301 2524 y Gg(if)23 b Ga(m)i
F4(=)g Ga(r)s Gg(,)d(then)i(by)g(\(5\))g(and)g(rpo\(iii\))2326
2648 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 v
6 w(;)15 b(T)p 892 2788 66 4 v 13 w FB(M)p F6(h)p Ga(U)p
1028 2788 72 4 v 11 w F6(i)1136 2787 y Gc(m)1228 2773
y Ga(>)1299 2740 y Gc(r)r(po)1431 2773 y Ga(T)p 1431
2788 66 4 v 13 w F6(h)p Ga(U)p 1532 2788 72 4 v 10 w
F6(i)1639 2787 y Gc(s)2775 2773 y Gg(analogous)26 b(to)e(\(4,5,6\))504
2897 y(\(8\))146 b FB(L)p Ga(S)p 790 2912 61 4 v 6 w(;)15
b(T)p 892 2912 66 4 v 13 w FB(M)p F6(h)p Ga(U)p 1028
2912 72 4 v 11 w F6(i)1136 2911 y Gc(m)1228 2897 y Ga(>)1299
2864 y Gc(r)r(po)1431 2897 y FB(L)p Ga(S)p 1466 2912
61 4 v 6 w F6(h)p Ga(U)p 1563 2912 72 4 v 10 w F6(i)1670
2911 y Gc(r)1708 2897 y Ga(;)g(T)p 1748 2912 66 4 v 14
w F6(h)p Ga(U)p 1850 2912 72 4 v 10 w F6(i)1957 2911
y Gc(s)1994 2897 y FB(M)776 b Gg(by)24 b(\(6,7\))g(and)g(rpo\(ii\))504
3021 y(\(9\))146 b FB(L)p Ga(S)p 790 3036 61 4 v 6 w(;)15
b(T)p 892 3036 66 4 v 13 w FB(M)p F6(h)p Ga(U)p 1028
3036 72 4 v 11 w F6(i)1136 3035 y Gc(m)1228 3021 y Ga(>)1299
2988 y Gc(r)r(po)1431 3021 y Ga(U)p 1431 3036 V 1689
w Gg(by)23 b(rpo\(i\))504 3145 y(\(10\))101 b Ga(M)p
755 3160 99 4 v 36 w(>)950 3112 y Gc(r)r(po)1082 3145
y 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)803
3339 y FC( )863 3386 y F4(\()898 3374 y FX(h)926 3386
y Ga(d)973 3374 y FX(i)1001 3386 y FL(And)1156 3400 y
Gc(R)1213 3386 y F4(\()1248 3374 y FX(h)1276 3386 y Ga(a)1324
3374 y FX(i)1352 3386 y Ga(S)5 b(;)1453 3374 y FX(h)1480
3386 y Ga(b)1519 3374 y FX(i)1547 3386 y Ga(T)13 b(;)i(c)p
F4(\))q Ga(;)1768 3374 y F9(\()1796 3386 y Ga(x)1848
3374 y F9(\))1875 3386 y Ga(U)10 b F4(\))782 3473 y Gc(x)717
3510 y F6(\000)-31 b(\000)f(!)26 b FL(And)1067 3524 y
Gc(R)1125 3510 y F4(\()1160 3498 y FX(h)1188 3510 y Ga(a)1236
3498 y FX(i)1263 3510 y FL(Cut)1342 3463 y FC( )1403
3510 y F4(\()1438 3498 y FX(h)1466 3510 y Ga(d)1513 3498
y FX(i)1540 3510 y Ga(S)5 b(;)1641 3498 y F9(\()1669
3510 y Ga(x)1721 3498 y F9(\))1749 3510 y Ga(U)10 b F4(\))p
Ga(;)1896 3498 y FX(h)1924 3510 y Ga(b)1963 3498 y FX(i)1990
3510 y FL(Cut)2069 3463 y FC( )2130 3510 y F4(\()2165
3498 y FX(h)2193 3510 y Ga(d)2240 3498 y FX(i)2267 3510
y Ga(T)j(;)2373 3498 y F9(\()2401 3510 y Ga(x)2453 3498
y F9(\))2480 3510 y Ga(U)d F4(\))q Ga(;)15 b(c)p F4(\))26
b F6(\021)f Ga(N)504 3634 y Gg(\(1\))101 b Ga(M)p 710
3649 99 4 v 35 w F4(=)25 b FB(L)p Ga(S)p 964 3649 61
4 v 6 w(;)15 b(T)p 1066 3649 66 4 v 13 w FB(M)g F6(h)p
Ga(U)p 1217 3649 72 4 v 11 w F6(i)1325 3648 y Gc(m)1440
3634 y Gg(and)49 b Ga(N)p 1619 3649 83 4 v 35 w F4(=)25
b FB(L)p Ga(S)p 1858 3649 61 4 v 5 w F6(h)p Ga(U)p 1954
3649 72 4 v 11 w F6(i)2062 3648 y Gc(r)2100 3634 y Ga(;)15
b(T)p 2140 3649 66 4 v 13 w F6(h)p Ga(U)p 2241 3649 72
4 v 10 w F6(i)2348 3648 y Gc(s)2386 3634 y FB(M)349 b
Gg(by)23 b(De\002nition)i(2.6.17)504 3759 y(\(2\))101
b Ga(m)25 b F6(\025)g Ga(r)m(;)15 b(s)1670 b Gg(by)23
b(Lemma)g(2.6.19\(i,ii\))504 3883 y(\(3\))101 b FB(L)p
Ga(S)p 745 3898 61 4 v 5 w(;)15 b(T)p 846 3898 66 4 v
14 w FB(M)p F6(h)p Ga(U)p 983 3898 72 4 v 10 w F6(i)1090
3897 y Gc(m)1182 3883 y Ga(>)1253 3850 y Gc(r)r(po)1386
3883 y Ga(S)p 1386 3898 61 4 v 53 w Gg(and)49 b FB(L)p
Ga(S)p 1709 3898 V 5 w(;)15 b(T)p 1810 3898 66 4 v 14
w FB(M)p F6(h)p Ga(U)p 1947 3898 72 4 v 10 w F6(i)2054
3897 y Gc(m)2147 3883 y Ga(>)2218 3850 y Gc(r)r(po)2350
3883 y Ga(U)p 2350 3898 V 770 w Gg(by)23 b(rpo\(i\))504
4007 y(\(4\))101 b F6(f)-24 b(j)p FB(L)p Ga(S)p 791 4022
61 4 v 6 w(;)15 b(T)p 893 4022 66 4 v 14 w FB(M)p Ga(;)g(U)p
1035 4022 72 4 v 10 w F6(j)-24 b(g)27 b Ga(>)1251 3963
y Gc(r)r(po)1251 4036 y(mul)q(t)1430 4007 y F6(f)-24
b(j)p Ga(S)p 1476 4022 61 4 v 6 w(;)15 b(U)p 1578 4022
72 4 v 11 w F6(j)-24 b(g)1485 b Gg(by)23 b(rpo\(i\))504
4131 y(\(5\))101 b FB(L)p Ga(S)p 745 4146 61 4 v 5 w(;)15
b(T)p 846 4146 66 4 v 14 w FB(M)p F6(h)p Ga(U)p 983 4146
72 4 v 10 w F6(i)1090 4145 y Gc(m)1182 4131 y Ga(>)1253
4098 y Gc(r)r(po)1386 4131 y Ga(S)p 1386 4146 61 4 v
5 w F6(h)p Ga(U)p 1482 4146 72 4 v 10 w F6(i)1589 4145
y 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)s
Gg(,)d(then)j(by)e(\(3\))h(and)g(rpo\(ii\))504 4380 y(\(6\))101
b FB(L)p Ga(S)p 745 4395 61 4 v 5 w(;)15 b(T)p 846 4395
66 4 v 14 w FB(M)p F6(h)p Ga(U)p 983 4395 72 4 v 10 w
F6(i)1090 4394 y Gc(m)1182 4380 y Ga(>)1253 4347 y Gc(r)r(po)1386
4380 y Ga(T)p 1386 4395 66 4 v 13 w F6(h)p Ga(U)p 1487
4395 72 4 v 10 w F6(i)1594 4394 y Gc(s)2775 4380 y Gg(analogous)26
b(to)e(\(3,4,5\))504 4504 y(\(7\))101 b Ga(M)p 710 4519
99 4 v 35 w(>)904 4471 y Gc(r)r(po)1037 4504 y Ga(N)p
1037 4519 83 4 v 1695 w Gg(by)24 b(\(5,6\))g(and)g(rpo\(ii\))504
4745 y Ga(M)36 b F6(\021)25 b FL(Cut)803 4697 y FC( )863
4745 y F4(\()898 4733 y FX(h)926 4745 y Ga(a)974 4733
y FX(i)1002 4745 y FL(Cut)p F4(\()1175 4733 y FX(h)1202
4745 y Ga(b)1241 4733 y FX(i)1269 4745 y Ga(S)5 b(;)1370
4733 y F9(\()1398 4745 y Ga(x)1450 4733 y F9(\))1477
4745 y Ga(T)13 b F4(\))p Ga(;)1618 4733 y F9(\()1646
4745 y Ga(y)1694 4733 y F9(\))1721 4745 y Ga(U)d F4(\))782
4832 y Gc(x)717 4869 y F6(\000)-31 b(\000)f(!)26 b FL(Cut)o
F4(\()1085 4857 y FX(h)1113 4869 y Ga(b)1152 4857 y FX(i)1180
4869 y FL(Cut)1258 4821 y FC( )1319 4869 y F4(\()1354
4857 y FX(h)1382 4869 y Ga(a)1430 4857 y FX(i)1458 4869
y Ga(S)5 b(;)1559 4857 y F9(\()1586 4869 y Ga(y)1634
4857 y F9(\))1662 4869 y Ga(U)10 b F4(\))p Ga(;)1809
4857 y F9(\()1837 4869 y Ga(x)1889 4857 y F9(\))1916
4869 y FL(Cut)1995 4821 y FC( )2056 4869 y F4(\()2091
4857 y FX(h)2119 4869 y Ga(a)2167 4857 y FX(i)2194 4869
y Ga(T)j(;)2300 4857 y F9(\()2328 4869 y Ga(y)2376 4857
y F9(\))2403 4869 y Ga(U)d F4(\))q(\))25 b F6(\021)g
Ga(N)504 4993 y Gg(\(1\))101 b Ga(M)p 710 5008 99 4 v
35 w F4(=)25 b(\()p Ga(S)p 964 5008 61 4 v 26 w F6(\001)1071
5007 y Gc(m)1158 4993 y Ga(T)p 1158 5008 66 4 v 13 w
F4(\))p F6(h)p Ga(U)p 1294 5008 72 4 v 10 w F6(i)1401
5007 y Gc(n)1497 4993 y Gg(and)49 b Ga(N)p 1676 5008
83 4 v 35 w F4(=)25 b Ga(S)p 1880 5008 61 4 v 5 w F6(h)p
Ga(U)p 1976 5008 72 4 v 10 w F6(i)2083 5007 y Gc(r)2142
4993 y F6(\001)2167 5007 y Gc(s)2224 4993 y Ga(T)p 2224
5008 66 4 v 13 w F6(h)p Ga(U)p 2325 5008 72 4 v 10 w
F6(i)2432 5007 y Gc(t)2770 4993 y Gg(by)e(De\002nition)i(2.6.17)504
5117 y(\(2\))101 b Ga(n)25 b F6(\025)g Ga(s;)15 b(r)m(;)g(t)1622
b Gg(by)23 b(Lemma)g(2.6.19\(i,ii\))504 5241 y(\(3\))p
712 5241 28 4 v 730 5241 V 747 5241 V 166 w F6(h)p 812
5241 V 830 5241 V 847 5241 V 64 w(i)909 5255 y Gc(n)982
5241 y F6(\035)p 1100 5241 V 1118 5241 V 1135 5241 V
110 w(\001)1208 5255 y Gc(s)p 1267 5241 V 1285 5241 V
1302 5241 V 2487 5241 a Gg(by)h(\(2\))f(and)h(De\002nition)h(2.6.14)p
Black Black eop end
%%Page: 154 166
TeXDict begin 154 165 bop Black -144 51 a Gb(154)2658
b(Details)24 b(f)n(or)g(some)g(Pr)n(oofs)p -144 88 3691
4 v Black 549 384 a Gg(\(4\))100 b F4(\()p Ga(S)p 789
399 61 4 v 26 w F6(\001)896 398 y Gc(m)983 384 y Ga(T)p
983 399 66 4 v 13 w F4(\))p F6(h)p Ga(U)p 1119 399 72
4 v 10 w F6(i)1226 398 y Gc(n)1299 384 y Ga(>)1370 351
y Gc(r)r(po)1502 384 y Ga(S)p 1502 399 61 4 v 53 w Gg(and)50
b F4(\()p Ga(S)p 1826 399 V 25 w F6(\001)1932 398 y Gc(m)2019
384 y Ga(T)p 2019 399 66 4 v 13 w F4(\))p F6(h)p Ga(U)p
2155 399 72 4 v 11 w F6(i)2263 398 y Gc(n)2335 384 y
Ga(>)2406 351 y Gc(r)r(po)2539 384 y Ga(U)p 2539 399
V 625 w Gg(by)23 b(rpo\(i\))549 508 y(\(5\))100 b F6(f)-24
b(j)p F4(\()p Ga(S)p 835 523 61 4 v 27 w F6(\001)943
522 y Gc(m)1030 508 y Ga(T)p 1030 523 66 4 v 13 w F4(\))p
Ga(;)15 b(U)p 1171 523 72 4 v 10 w F6(j)-24 b(g)27 b
Ga(>)1387 464 y Gc(r)r(po)1387 537 y(mul)q(t)1566 508
y F6(f)-24 b(j)p Ga(S)p 1612 523 61 4 v 6 w(;)15 b(U)p
1714 523 72 4 v 11 w F6(j)-24 b(g)1393 b Gg(by)23 b(rpo\(i\))549
632 y(\(6\))100 b F4(\()p Ga(S)p 789 647 61 4 v 26 w
F6(\001)896 646 y Gc(m)983 632 y Ga(T)p 983 647 66 4
v 13 w F4(\))p F6(h)p Ga(U)p 1119 647 72 4 v 10 w F6(i)1226
646 y Gc(n)1299 632 y Ga(>)1370 599 y Gc(r)r(po)1502
632 y Ga(S)p 1502 647 61 4 v 5 w F6(h)p Ga(U)p 1598 647
72 4 v 11 w F6(i)1706 646 y Gc(r)2370 632 y Gg(if)23
b Ga(n)i F4(=)g Ga(r)s Gg(,)d(then)i(by)g(\(5\))g(and)g(rpo\(iii\))2395
756 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(\()p Ga(S)p 789 896 61 4 v 26
w F6(\001)896 895 y Gc(m)983 881 y Ga(T)p 983 896 66
4 v 13 w F4(\))p F6(h)p Ga(U)p 1119 896 72 4 v 10 w F6(i)1226
895 y Gc(n)1299 881 y Ga(>)1370 848 y Gc(r)r(po)1502
881 y Ga(T)p 1502 896 66 4 v 13 w F6(h)p Ga(U)p 1603
896 72 4 v 10 w F6(i)1710 895 y Gc(t)2819 881 y Gg(analogous)27
b(to)c(\(4,5,6\))549 1005 y(\(8\))100 b Ga(M)p 754 1020
99 4 v 36 w(>)949 972 y Gc(r)r(po)1081 1005 y Ga(N)p
1081 1020 83 4 v 1627 w Gg(by)24 b(\(3,6,7\))g(and)g(rpo\(ii\))549
1294 y Ga(M)35 b F6(\021)25 b FL(Cut)847 1247 y FC( )908
1294 y F4(\()943 1282 y FX(h)970 1294 y Ga(a)1018 1282
y FX(i)1046 1294 y FL(Cut)p F4(\()1219 1282 y FX(h)1247
1294 y Ga(b)1286 1282 y FX(i)1313 1294 y Ga(S)5 b(;)1414
1282 y F9(\()1442 1294 y Ga(x)1494 1282 y F9(\))1521
1294 y FL(Ax)p F4(\()p Ga(x;)15 b(a)p F4(\))q(\))p Ga(;)1910
1282 y F9(\()1938 1294 y Ga(y)1986 1282 y F9(\))2013
1294 y Ga(U)10 b F4(\))826 1381 y Gc(x)761 1418 y F6(\000)-31
b(\000)g(!)25 b FL(Cut)p F4(\()1130 1406 y FX(h)1157
1418 y Ga(b)1196 1406 y FX(i)1224 1418 y FL(Cut)1303
1371 y FC( )1364 1418 y F4(\()1399 1406 y FX(h)1426 1418
y Ga(a)1474 1406 y FX(i)1502 1418 y Ga(S)5 b(;)1603 1406
y F9(\()1631 1418 y Ga(y)1679 1406 y F9(\))1706 1418
y Ga(U)10 b F4(\))p Ga(;)1853 1406 y F9(\()1881 1418
y Ga(y)1929 1406 y F9(\))1956 1418 y Ga(U)g F4(\))26
b F6(\021)f Ga(N)549 1543 y Gg(\(1\))100 b Ga(M)p 754
1558 99 4 v 36 w F4(=)25 b(\()p Ga(S)p 1009 1558 61 4
v 25 w F6(\001)1115 1557 y Gc(m)1202 1543 y Ga(?)p F4(\))p
F6(h)p Ga(U)p 1317 1558 72 4 v 11 w F6(i)1425 1557 y
Gc(n)1521 1543 y Gg(and)49 b Ga(N)p 1700 1558 83 4 v
35 w F4(=)25 b Ga(S)p 1904 1558 61 4 v 5 w F6(h)p Ga(U)p
2000 1558 72 4 v 10 w F6(i)2107 1557 y Gc(r)2166 1543
y F6(\001)2191 1557 y Gc(s)2248 1543 y Ga(U)p 2248 1558
V 504 w Gg(by)f(De\002nition)g(2.6.17)549 1667 y(\(2\))100
b 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 774
1791 V 791 1791 V 165 w F6(h)p 856 1791 V 874 1791 V
891 1791 V 65 w(i)954 1805 y Gc(n)1026 1791 y F6(\035)p
1144 1791 V 1162 1791 V 1180 1791 V 110 w(\001)1252 1805
y Gc(s)p 1311 1791 V 1329 1791 V 1347 1791 V 2531 1791
a Gg(by)i(\(2\))g(and)g(De\002nition)g(2.6.14)549 1915
y(\(4\))100 b F4(\()p Ga(S)p 789 1930 61 4 v 26 w F6(\001)896
1929 y Gc(m)983 1915 y Ga(?)p F4(\))p F6(h)p Ga(U)p 1098
1930 72 4 v 11 w F6(i)1206 1929 y Gc(n)1278 1915 y Ga(>)1349
1882 y Gc(r)r(po)1482 1915 y Ga(S)p 1482 1930 61 4 v
53 w Gg(and)49 b F4(\()p Ga(S)p 1805 1930 V 26 w F6(\001)1912
1929 y Gc(m)1999 1915 y Ga(?)p F4(\))p F6(h)p Ga(U)p
2114 1930 72 4 v 11 w F6(i)2222 1929 y Gc(n)2295 1915
y Ga(>)2366 1882 y Gc(r)r(po)2498 1915 y Ga(U)p 2498
1930 V 666 w Gg(by)23 b(rpo\(i\))549 2040 y(\(5\))100
b F6(f)-24 b(j)p F4(\()p Ga(S)p 835 2055 61 4 v 27 w
F6(\001)943 2054 y Gc(m)1030 2040 y Ga(?)p F4(\))p Ga(;)15
b(U)p 1150 2055 72 4 v 11 w F6(j)-24 b(g)26 b Ga(>)1366
1995 y Gc(r)r(po)1366 2069 y(mul)q(t)1546 2040 y F6(f)-24
b(j)p Ga(S)p 1592 2055 61 4 v 6 w(;)15 b(U)p 1694 2055
72 4 v 11 w F6(j)-24 b(g)1413 b Gg(by)23 b(rpo\(i\))549
2164 y(\(6\))100 b F4(\()p Ga(S)p 789 2179 61 4 v 26
w F6(\001)896 2178 y Gc(m)983 2164 y Ga(?)p F4(\))p F6(h)p
Ga(U)p 1098 2179 72 4 v 11 w F6(i)1206 2178 y Gc(n)1278
2164 y Ga(>)1349 2131 y Gc(r)r(po)1482 2164 y Ga(S)p
1482 2179 61 4 v 5 w F6(h)p Ga(U)p 1578 2179 72 4 v 10
w F6(i)1685 2178 y Gc(r)2370 2164 y Gg(if)23 b Ga(n)i
F4(=)g Ga(r)s Gg(,)d(then)i(by)g(\(5\))g(and)g(rpo\(iii\))2395
2288 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(>)949
2379 y Gc(r)r(po)1081 2412 y Ga(N)p 1081 2427 83 4 v
1627 w Gg(by)24 b(\(3,4,6\))g(and)g(rpo\(ii\))549 2702
y Ga(M)35 b F6(\021)25 b FL(Cut)847 2654 y FC( )908 2702
y F4(\()943 2690 y FX(h)970 2702 y Ga(a)1018 2690 y FX(i)1046
2702 y FL(Ax)o F4(\()p Ga(x;)15 b(a)p F4(\))r Ga(;)1400
2690 y F9(\()1427 2702 y Ga(y)1475 2690 y F9(\))1503
2702 y Ga(S)5 b F4(\))1690 2664 y Gc(x)1624 2702 y F6(\000)-31
b(\000)g(!)25 b FL(Cut)p F4(\()1993 2690 y FX(h)2020
2702 y Ga(a)2068 2690 y FX(i)2096 2702 y FL(Ax)o F4(\()p
Ga(x;)15 b(a)p F4(\))r Ga(;)2450 2690 y F9(\()2477 2702
y Ga(y)2525 2690 y F9(\))2553 2702 y Ga(S)5 b F4(\))25
b F6(\021)g Ga(N)549 2826 y Gg(\(1\))100 b Ga(M)p 754
2841 99 4 v 36 w F4(=)25 b Ga(?)15 b F6(h)p Ga(S)p 1069
2841 61 4 v 5 w F6(i)1165 2840 y Gc(m)1280 2826 y Gg(and)50
b Ga(N)p 1460 2841 83 4 v 35 w F4(=)25 b Ga(?)20 b F6(\001)1754
2840 y Gc(n)1822 2826 y Ga(S)p 1822 2841 61 4 v 936 w
Gg(by)k(De\002nition)g(2.6.17)549 2950 y(\(2\))100 b
Ga(m)25 b F6(\025)g Ga(n)1809 b Gg(by)24 b(Lemma)e(2.6.19\(i\))549
3074 y(\(3\))p 756 3074 28 4 v 774 3074 V 791 3074 V
165 w F6(h)p 856 3074 V 874 3074 V 891 3074 V 65 w(i)954
3088 y Gc(m)1046 3074 y F6(\035)p 1164 3074 V 1182 3074
V 1199 3074 V 110 w(\001)1272 3088 y Gc(n)p 1341 3074
V 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(?)15
b F6(h)p Ga(S)p 849 3213 61 4 v 6 w F6(i)946 3212 y Gc(m)1038
3198 y Ga(>)1109 3165 y Gc(r)r(po)1242 3198 y Ga(?)48
b Gg(and)i Ga(?)15 b F6(h)p Ga(S)p 1610 3213 V 6 w F6(i)1707
3212 y Gc(m)1799 3198 y Ga(>)1870 3165 y Gc(r)r(po)2002
3198 y Ga(S)p 2002 3213 V 1168 w Gg(by)23 b(rpo\(i\))549
3323 y(\(5\))100 b Ga(M)p 754 3338 99 4 v 36 w(>)949
3290 y Gc(r)r(po)1081 3323 y Ga(N)p 1081 3338 83 4 v
1696 w Gg(by)23 b(\(3,4\))h(and)g(rpo\(ii\))p Black 321
3603 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)p
F4(\()941 3791 y FX(h)969 3803 y Ga(a)1017 3791 y FX(i)1044
3803 y Ga(S)5 b(;)1145 3791 y F9(\()1173 3803 y Ga(x)1225
3791 y F9(\))1252 3803 y Ga(T)13 b F4(\))1428 3766 y
Gc(c)1459 3742 y FC(00)1379 3803 y F6(\000)-32 b(\000)h(!)25
b FL(Cut)1653 3755 y FC( )1714 3803 y F4(\()1749 3791
y FX(h)1777 3803 y Ga(a)1825 3791 y FX(i)1852 3803 y
Ga(S)5 b(;)1953 3791 y F9(\()1981 3803 y Ga(x)2033 3791
y F9(\))2060 3803 y Ga(T)13 b F4(\))26 b F6(\021)f Ga(N)549
3927 y Gg(\(1\))100 b Ga(M)p 754 3942 99 4 v 36 w F4(=)25
b Ga(S)p 974 3942 61 4 v 25 w F6(\001)1080 3941 y Gc(m)1167
3927 y Ga(T)p 1167 3942 66 4 v 60 w Gg(and)50 b Ga(N)p
1460 3942 83 4 v 35 w F4(=)25 b Ga(S)p 1664 3942 61 4
v 5 w F6(h)p Ga(T)p 1760 3942 66 4 v 13 w F6(i)1861 3941
y Gc(n)2814 3927 y Gg(by)f(De\002nition)g(2.6.17)549
4051 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 774
4175 V 791 4175 V 185 w F6(\001)864 4189 y Gc(m)p 953
4175 V 971 4175 V 988 4175 V 1041 4175 a F6(\035)p 1159
4175 V 1177 4175 V 1194 4175 V 89 w(h)p 1258 4175 V 1277
4175 V 1294 4175 V 65 w(i)1356 4189 y Gc(n)2531 4175
y Gg(by)h(\(2\))g(and)g(De\002nition)g(2.6.14)549 4299
y(\(4\))100 b Ga(S)p 754 4314 61 4 v 25 w F6(\001)860
4313 y Gc(m)947 4299 y Ga(T)p 947 4314 66 4 v 38 w(>)1109
4266 y Gc(r)r(po)1242 4299 y Ga(S)p 1242 4314 61 4 v
53 w Gg(and)49 b Ga(S)p 1530 4314 V 25 w F6(\001)1636
4313 y Gc(m)1723 4299 y Ga(T)p 1723 4314 66 4 v 38 w(>)1885
4266 y Gc(r)r(po)2018 4299 y Ga(T)p 2018 4314 V 1155
w Gg(by)23 b(rpo\(i\))549 4424 y(\(5\))100 b Ga(M)p 754
4439 99 4 v 36 w(>)949 4391 y Gc(r)r(po)1081 4424 y Ga(N)p
1081 4439 83 4 v 1696 w Gg(by)23 b(\(3,4\))h(and)g(rpo\(ii\))p
Black 321 4704 a Gb(Logical)h(Reduction:)p Black 46 w
Gg(W)-7 b(e)22 b(tackle)j(three)g(representati)n(v)o(e)i(cases.)549
4905 y Ga(M)35 b F6(\021)25 b FL(Cut)p F4(\()941 4893
y FX(h)969 4905 y Ga(a)1017 4893 y FX(i)1044 4905 y FL(Ax)p
F4(\()p Ga(x;)15 b(a)p F4(\))q Ga(;)1398 4893 y F9(\()1426
4905 y Ga(y)1474 4893 y F9(\))1501 4905 y Ga(S)5 b F4(\))1697
4868 y Gc(l)1622 4905 y F6(\000)-31 b(\000)g(!)25 b Ga(S)5
b F4([)p Ga(y)13 b F6(7!)d Ga(x)p F4(])26 b F6(\021)f
Ga(N)549 5029 y Gg(\(1\))100 b Ga(M)p 754 5044 99 4 v
36 w F4(=)25 b Ga(?)20 b F6(\001)1064 5043 y Gc(n)1132
5029 y Ga(S)p 1132 5044 61 4 v 53 w Gg(and)49 b Ga(N)p
1420 5044 83 4 v 35 w F4(=)25 b Ga(S)p 1624 5044 61 4
v 1134 w Gg(by)f(De\002nition)g(2.6.17)549 5153 y(\(2\))100
b Ga(M)p 754 5168 99 4 v 36 w(>)949 5120 y Gc(r)r(po)1081
5153 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: 155 167
TeXDict 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 504 384
a Ga(M)36 b F6(\021)25 b FL(Cut)p F4(\()897 372 y FX(h)924
384 y Ga(c)963 372 y FX(i)991 384 y FL(And)1146 398 y
Gc(R)1203 384 y F4(\()1238 372 y FX(h)1266 384 y Ga(a)1314
372 y FX(i)1342 384 y Ga(S)5 b(;)1443 372 y FX(h)1471
384 y Ga(b)1510 372 y FX(i)1537 384 y Ga(T)13 b(;)i(c)p
F4(\))q Ga(;)1758 372 y F9(\()1786 384 y Ga(y)1834 372
y F9(\))1861 384 y FL(And)2016 347 y F9(1)2016 407 y
Gc(L)2068 384 y F4(\()2103 372 y F9(\()2130 384 y Ga(x)2182
372 y F9(\))2210 384 y Ga(U)10 b(;)15 b(y)s F4(\)\))2540
347 y Gc(l)2466 384 y F6(\000)-31 b(\000)f(!)26 b FL(Cut)o
F4(\()2834 372 y FX(h)2862 384 y Ga(a)2910 372 y FX(i)2938
384 y Ga(S)5 b(;)3039 372 y F9(\()3067 384 y Ga(x)3119
372 y F9(\))3146 384 y Ga(U)10 b F4(\))26 b F6(\021)f
Ga(N)504 508 y Gg(\(1\))101 b Ga(M)p 710 523 99 4 v 35
w F4(=)25 b FB(L)p Ga(S)p 964 523 61 4 v 6 w(;)15 b(T)p
1066 523 66 4 v 13 w FB(M)20 b F6(\001)1212 522 y Gc(m)1299
508 y FB(L)p Ga(U)p 1334 523 72 4 v 11 w FB(M)j Gg(and)h
Ga(N)p 1619 523 83 4 v 35 w F4(=)h Ga(S)p 1823 523 61
4 v 25 w F6(\001)1929 522 y Gc(n)1997 508 y Ga(U)p 1997
523 72 4 v 711 w Gg(by)e(De\002nition)i(2.6.17)504 632
y(\(2\))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 5
w(;)15 b(T)p 846 771 66 4 v 14 w FB(M)20 b F6(\001)993
770 y Gc(m)1080 756 y FB(L)p Ga(U)p 1115 771 72 4 v 10
w FB(M)26 b Ga(>)1319 723 y Gc(r)r(po)1452 756 y Ga(S)p
1452 771 61 4 v 53 w Gg(,)47 b FB(L)p Ga(S)p 1666 771
V 6 w(;)15 b(T)p 1768 771 66 4 v 13 w FB(M)20 b F6(\001)1914
770 y Gc(m)2001 756 y FB(L)p Ga(U)p 2036 771 72 4 v 11
w FB(M)25 b Ga(>)2240 723 y Gc(r)r(po)2373 756 y Ga(U)p
2373 771 V 747 w Gg(by)e(rpo\(i\))504 881 y(\(4\))101
b Ga(M)p 710 896 99 4 v 35 w(>)904 848 y Gc(r)r(po)1037
881 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)p
F4(\()897 1104 y FX(h)924 1116 y Ga(b)963 1104 y FX(i)991
1116 y FL(Imp)1135 1138 y Gc(R)1193 1116 y F4(\()1228
1104 y F9(\()1256 1116 y Ga(x)1308 1104 y F9(\))p FX(h)1363
1116 y Ga(a)1411 1104 y FX(i)1438 1116 y Ga(S)5 b(;)15
b(b)p F4(\))q Ga(;)1654 1104 y F9(\()1682 1116 y Ga(z)1728
1104 y F9(\))1755 1116 y FL(Imp)1900 1138 y Gc(L)1952
1116 y F4(\()1987 1104 y FX(h)2015 1116 y Ga(c)2054 1104
y FX(i)2082 1116 y Ga(T)d(;)2187 1104 y F9(\()2215 1116
y Ga(y)2263 1104 y F9(\))2291 1116 y Ga(U)e(;)15 b(z)t
F4(\))q(\))791 1203 y Gc(l)717 1240 y F6(\000)-31 b(\000)f(!)26
b FL(Cut)o F4(\()1085 1228 y FX(h)1113 1240 y Ga(a)1161
1228 y FX(i)1189 1240 y FL(Cut)p F4(\()1362 1228 y FX(h)1389
1240 y Ga(c)1428 1228 y FX(i)1456 1240 y Ga(T)13 b(;)1562
1228 y F9(\()1590 1240 y Ga(x)1642 1228 y F9(\))1669
1240 y Ga(S)5 b F4(\))p Ga(;)1805 1228 y F9(\()1833 1240
y Ga(y)1881 1228 y F9(\))1909 1240 y Ga(U)10 b F4(\))25
b F6(\021)g Ga(N)504 1364 y Gg(\(1\))101 b Ga(M)p 710
1379 99 4 v 35 w F4(=)25 b FB(L)p Ga(S)p 964 1379 61
4 v 6 w FB(M)20 b F6(\001)1106 1378 y Gc(m)1193 1364
y FB(L)p Ga(T)p 1228 1379 66 4 v 13 w(;)15 b(U)p 1334
1379 72 4 v 11 w FB(M)23 b Gg(and)h Ga(N)p 1619 1379
83 4 v 35 w F4(=)h(\()p Ga(T)p 1858 1379 66 4 v 33 w
F6(\001)1969 1378 y Gc(s)2027 1364 y Ga(S)p 2027 1379
61 4 v 5 w F4(\))20 b F6(\001)2168 1378 y Gc(t)2218 1364
y Ga(U)p 2218 1379 72 4 v 490 w Gg(by)j(De\002nition)i(2.6.17)504
1488 y(\(2\))101 b Ga(m)25 b(>)g(s;)15 b(t)1624 b Gg(by)24
b(Lemma)e(2.6.19\(iii,ii\))504 1613 y(\(3\))101 b FB(L)p
Ga(S)p 745 1628 61 4 v 5 w FB(M)21 b F6(\001)887 1627
y Gc(m)974 1613 y FB(L)p Ga(T)p 1009 1628 66 4 v 13 w(;)15
b(U)p 1115 1628 72 4 v 10 w FB(M)26 b Ga(>)1319 1580
y Gc(r)r(po)1452 1613 y Ga(S)p 1452 1628 61 4 v 53 w
Gg(,)47 b FB(L)p Ga(S)p 1666 1628 V 6 w FB(M)20 b F6(\001)1808
1627 y Gc(m)1895 1613 y FB(L)p Ga(T)p 1930 1628 66 4
v 13 w(;)15 b(U)p 2036 1628 72 4 v 11 w FB(M)25 b Ga(>)2240
1580 y Gc(r)r(po)2373 1613 y Ga(T)p 2373 1628 66 4 v
756 w Gg(by)e(rpo\(i\))504 1737 y(\(4\))101 b FB(L)p
Ga(S)p 745 1752 61 4 v 5 w FB(M)21 b F6(\001)887 1751
y Gc(m)974 1737 y FB(L)p Ga(T)p 1009 1752 66 4 v 13 w(;)15
b(U)p 1115 1752 72 4 v 10 w FB(M)26 b Ga(>)1319 1704
y Gc(r)r(po)1452 1737 y Ga(T)p 1452 1752 66 4 v 33 w
F6(\001)1563 1751 y Gc(s)1620 1737 y Ga(S)p 1620 1752
61 4 v 1129 w Gg(by)e(\(2,3\))g(and)g(rpo\(ii\))504 1861
y(\(5\))101 b FB(L)p Ga(S)p 745 1876 V 5 w FB(M)21 b
F6(\001)887 1875 y Gc(m)974 1861 y FB(L)p Ga(T)p 1009
1876 66 4 v 13 w(;)15 b(U)p 1115 1876 72 4 v 10 w FB(M)26
b Ga(>)1319 1828 y Gc(r)r(po)1452 1861 y Ga(U)p 1452
1876 V 1170 w Gg(by)e(De\002nition)g(2.6.12\(i\))504
1985 y(\(6\))101 b Ga(M)p 710 2000 99 4 v 35 w(>)904
1952 y Gc(r)r(po)1037 1985 y Ga(N)p 1037 2000 83 4 v
1627 w Gg(by)24 b(\(2,4,5\))g(and)g(rpo\(ii\))p Black
277 2157 a Gb(Garbage)g(Reduction:)p Black 46 w Gg(Finally)-6
b(,)23 b(we)e(gi)n(v)o(e)h(one)h(case)g(where)f(a)g(garbage)h
(reduction)i(is)d(performed.)504 2303 y Ga(M)36 b F6(\021)25
b FL(Cut)803 2256 y FC( )863 2303 y F4(\()898 2291 y
FX(h)926 2303 y Ga(a)974 2291 y FX(i)1002 2303 y Ga(S)5
b(;)1103 2291 y F9(\()1131 2303 y Ga(x)1183 2291 y F9(\))1210
2303 y Ga(T)13 b F4(\))1388 2266 y Gc(g)r(c)1336 2303
y F6(\000)-31 b(\000)g(!)25 b Ga(S)30 b F6(\021)25 b
Ga(N)504 2427 y Gg(\(1\))101 b Ga(M)p 710 2442 99 4 v
35 w F4(=)25 b Ga(S)p 929 2442 61 4 v 5 w F6(h)p Ga(T)p
1025 2442 66 4 v 13 w F6(i)1126 2441 y Gc(m)1241 2427
y Gg(and)50 b Ga(N)p 1421 2442 83 4 v 35 w F4(=)25 b
Ga(S)p 1625 2442 61 4 v 1089 w Gg(by)e(De\002nition)i(2.6.17)504
2552 y(\(2\))101 b Ga(M)p 710 2567 99 4 v 35 w(>)904
2519 y Gc(r)r(po)1037 2552 y Ga(N)p 1037 2567 83 4 v
1789 w Gg(by)23 b(\(1\))h(and)g(rpo\(i\))p 3436 2659
4 62 v 3440 2600 55 4 v 3440 2659 V 3494 2659 4 62 v
Black 277 2871 a Gb(Pr)n(oof)k(of)g(Lemma)f(2.6.22.)p
Black 34 w Gg(W)-7 b(e)27 b(gi)n(v)o(e)g(the)h(details)h(of)f(ho)n(w)f
(to)g(replace)j FL(Cut)2707 2824 y FC( )2767 2871 y Gg(-instances.)44
b(Suppose)277 2984 y FL(Cut)356 2937 y FC( )417 2984
y F4(\()452 2972 y FX(h)480 2984 y Ga(a)528 2972 y FX(i)555
2984 y Ga(S)5 b(;)656 2972 y F9(\()684 2984 y Ga(x)736
2972 y F9(\))763 2984 y Ga(T)13 b F4(\))23 b Gg(is)h(a)f(subterm)h(of)g
Ga(M)33 b Gg(with)23 b(the)h(typing)h(judgement)1271
3151 y F4(\000)1328 3165 y F9(1)1393 3139 y Gc(.)1448
3151 y Ga(S)1534 3139 y Gc(.)1589 3151 y F4(\001)1665
3165 y F9(1)1845 3151 y F4(\000)1902 3165 y F9(2)1967
3139 y Gc(.)2022 3151 y Ga(T)2113 3139 y Gc(.)2168 3151
y F4(\001)2244 3165 y F9(2)p 1151 3184 1252 4 v 1151
3269 a F4(\000)1208 3283 y F9(1)1248 3269 y Ga(;)15 b
F4(\000)1345 3283 y F9(2)1410 3257 y Gc(.)1464 3269 y
FL(Cut)1543 3222 y FC( )1604 3269 y F4(\()1639 3257 y
FX(h)1667 3269 y Ga(a)1715 3257 y FX(i)1742 3269 y Ga(S)5
b(;)1843 3257 y F9(\()1871 3269 y Ga(x)1923 3257 y F9(\))1951
3269 y Ga(T)12 b F4(\))2077 3257 y Gc(.)2132 3269 y F4(\001)2208
3283 y F9(1)2247 3269 y Ga(;)j F4(\001)2363 3283 y F9(2)2444
3217 y Gg(Cut)2516 3170 y FC( )2603 3217 y Ga(:)277 3456
y Gg(Our)23 b(ar)n(gument)j(splits)e(into)h(tw)o(o)e(cases:)p
Black 414 3650 a F6(\017)p Black 45 w Gg(If)35 b(the)g(subterm)h
Ga(S)j Gg(does)c(not)h(freshly)g(introduce)h Ga(a)p Gg(,)g(then)e(we)f
(replace)j FL(Cut)2994 3603 y FC( )3055 3650 y F4(\()3090
3638 y FX(h)3117 3650 y Ga(a)3165 3638 y FX(i)3193 3650
y Ga(S)5 b(;)3294 3638 y F9(\()3322 3650 y Ga(x)3374
3638 y F9(\))3401 3650 y Ga(T)13 b F4(\))504 3763 y Gg(simply)31
b(by)f FL(Cut)p F4(\()1074 3751 y FX(h)1102 3763 y Ga(a)1150
3751 y FX(i)1177 3763 y Ga(S)5 b(;)1278 3751 y F9(\()1306
3763 y Ga(x)1358 3751 y F9(\))1385 3763 y Ga(T)13 b F4(\))29
b Gg(\(both)i(terms)f(ha)n(v)o(e)h(the)f(same)g(typing)h(judgement\).)
50 b(In)30 b(this)504 3876 y(case)25 b(we)d(ha)n(v)o(e)i
FL(Cut)p F4(\()1176 3864 y FX(h)1204 3876 y Ga(a)1252
3864 y FX(i)1280 3876 y Ga(S)5 b(;)1381 3864 y F9(\()1409
3876 y Ga(x)1461 3864 y F9(\))1488 3876 y Ga(T)13 b F4(\))1664
3839 y Gc(c)1695 3816 y FC(00)1614 3876 y F6(\000)-31
b(\000)g(!)25 b FL(Cut)1889 3829 y FC( )1949 3876 y F4(\()1984
3864 y FX(h)2012 3876 y Ga(a)2060 3864 y FX(i)2088 3876
y Ga(S)5 b(;)2189 3864 y F9(\()2217 3876 y Ga(x)2269
3864 y F9(\))2296 3876 y Ga(T)13 b F4(\))p Gg(.)p Black
414 4052 a F6(\017)p Black 45 w Gg(The)24 b(more)g(interesting)k(case)c
(is)h(where)f Ga(S)k Gg(freshly)e(introduces)h Ga(a)p
Gg(.)j(Here)24 b(we)g(cannot)i(simply)504 4165 y(replace)e
FL(Cut)867 4118 y FC( )948 4165 y Gg(with)e FL(Cut)p
Gg(,)f(because)j(there)e(is)g(no)g(reduction)i(that)e(gi)n(v)o(es)h
Ga(N)2899 4128 y Gc(l)q(oc)2857 4165 y F6(\000)-31 b(\000)f(!)3027
4132 y F9(+)3111 4165 y Ga(M)10 b Gg(.)28 b(There-)504
4278 y(fore)k(we)e(replace)j FL(Cut)1189 4231 y FC( )1250
4278 y F4(\()1285 4266 y FX(h)1312 4278 y Ga(a)1360 4266
y FX(i)1388 4278 y Ga(S)5 b(;)1489 4266 y F9(\()1517
4278 y Ga(x)1569 4266 y F9(\))1596 4278 y Ga(T)13 b F4(\))30
b Gg(by)i FL(Cut)p F4(\()2022 4266 y FX(h)2049 4278 y
Ga(a)2097 4266 y FX(i)2125 4278 y FL(Cut)p F4(\()2298
4266 y FX(h)2325 4278 y Ga(b)2364 4266 y FX(i)2392 4278
y Ga(S)5 b(;)2493 4266 y F9(\()2521 4278 y Ga(y)2569
4266 y F9(\))2596 4278 y FL(Ax)p F4(\()p Ga(y)s(;)15
b(c)p F4(\))q(\))p Ga(;)2972 4266 y F9(\()3000 4278 y
Ga(x)3052 4266 y F9(\))3079 4278 y Ga(T)e F4(\))31 b
Gg(where)g Ga(b)504 4391 y Gg(and)i Ga(c)f Gg(are)h(fresh)g(co-names)h
(that)f(do)g(not)f(occur)i(an)o(ywhere)f(else.)56 b(On)32
b(the)h(le)n(v)o(el)f(of)h(type)504 4504 y(deri)n(v)n(ations)27
b(this)d(means)g(that)g(an)f(instance)j(of)d(the)h(form)1410
4652 y F4(\000)1467 4666 y F9(1)1532 4640 y Gc(.)1587
4652 y Ga(S)1673 4640 y Gc(.)1728 4652 y F4(\001)1804
4666 y F9(1)1984 4652 y F4(\000)2041 4666 y F9(2)2106
4640 y Gc(.)2161 4652 y Ga(T)2252 4640 y Gc(.)2307 4652
y F4(\001)2383 4666 y F9(2)p 1290 4686 V 1290 4770 a
F4(\000)1347 4784 y F9(1)1387 4770 y Ga(;)15 b F4(\000)1484
4784 y F9(2)1548 4758 y Gc(.)1603 4770 y FL(Cut)1682
4723 y FC( )1743 4770 y F4(\()1778 4758 y FX(h)1806 4770
y Ga(a)1854 4758 y FX(i)1881 4770 y Ga(S)5 b(;)1982 4758
y F9(\()2010 4770 y Ga(x)2062 4758 y F9(\))2090 4770
y Ga(T)12 b F4(\))2216 4758 y Gc(.)2271 4770 y F4(\001)2347
4784 y F9(1)2386 4770 y Ga(;)j F4(\001)2502 4784 y F9(2)2583
4718 y Gg(Cut)2655 4671 y FC( )504 4940 y Gg(is)24 b(replaced)h(by)782
5130 y F4(\000)839 5144 y F9(1)903 5118 y Gc(.)958 5130
y Ga(S)1044 5118 y Gc(.)1099 5130 y F4(\001)1175 5144
y F9(1)1215 5130 y Ga(;)15 b(b)i F4(:)h Ga(B)p 1518 5045
815 4 v 95 w(y)i F4(:)d Ga(B)1724 5118 y Gc(.)1779 5130
y FL(Ax)p F4(\()p Ga(y)s(;)e(c)p F4(\))2105 5118 y Gc(.)2160
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%%Page: 159 171
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F6(j)1720 2531 y Fu(n)686 2688 y F4(=)51 b Ga(x)p F4([)p
Ga(x)26 b F4(:=)f F6(j)p Ga(M)10 b F6(j)1232 2655 y Fu(n)1273
2688 y F4(])1684 b Gg(by)23 b(\(1,2\))h(of)g F6(j)p 3418
2688 28 4 v 3436 2688 V 3453 2688 V 64 w(j)3505 2655
y Fu(n)686 2813 y F4(=)51 b F6(j)p Ga(M)10 b F6(j)956
2780 y Fu(n)686 2937 y F6(\021)51 b(j)p Ga(M)10 b F4([)p
Ga(a)g F6(7!)g Ga(b)p F4(])p F6(j)1204 2904 y Fu(n)p
Black 321 3109 a Gb(Logical)25 b(Cut)d Fb(^)871 3123
y Fy(R)936 3109 y FO(=)p Fb(^)1058 3123 y Fy(L)1111 3131
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Ga(M)10 b(;)1305 3226 y FX(h)1333 3238 y Ga(b)1372 3226
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3226 y F9(\()1665 3238 y Ga(y)1713 3226 y F9(\))1740
3238 y FL(And)1895 3201 y F9(1)1895 3261 y Gc(L)1947
3238 y F4(\()1982 3226 y F9(\()2010 3238 y Ga(x)2062
3226 y F9(\))2089 3238 y Ga(P)e(;)i(y)s F4(\))q(\))2383
3201 y Gc(int)2344 3238 y F6(\000)-31 b(\000)g(!)25 b
FL(Cut)p F4(\()2713 3226 y FX(h)2740 3238 y Ga(a)2788
3226 y FX(i)2816 3238 y Ga(M)10 b(;)2954 3226 y F9(\()2982
3238 y Ga(x)3034 3226 y F9(\))3061 3238 y Ga(P)j F4(\))810
3385 y F6(j)p FL(Cut)p F4(\()1008 3373 y FX(h)1036 3385
y Ga(c)1075 3373 y FX(i)1103 3385 y FL(And)1257 3399
y Gc(R)1315 3385 y F4(\()1350 3373 y FX(h)1378 3385 y
Ga(a)1426 3373 y FX(i)1454 3385 y Ga(M)d(;)1592 3373
y FX(h)1619 3385 y Ga(b)1658 3373 y FX(i)1686 3385 y
Ga(N)g(;)15 b(c)p F4(\))q Ga(;)1924 3373 y F9(\()1952
3385 y Ga(y)2000 3373 y F9(\))2027 3385 y FL(And)2182
3349 y F9(1)2182 3409 y Gc(L)2234 3385 y F4(\()2269 3373
y F9(\()2297 3385 y Ga(x)2349 3373 y F9(\))2376 3385
y Ga(P)e(;)i(y)s F4(\))q(\))p F6(j)2631 3352 y Fu(n)648
3510 y F4(=)91 b F6(j)p Ga(P)13 b F6(j)931 3477 y Fu(n)972
3510 y F4([)p Ga(x)26 b F4(:=)f Fp(fst)o F4(\()p Ga(y)s
F4(\)][)p Ga(y)k F4(:=)d F6(hj)p Ga(M)10 b F6(j)1886
3477 y Fu(n)1927 3510 y Ga(;)15 b F6(j)p Ga(N)10 b F6(j)2100
3477 y Fu(n)2142 3510 y F6(i)p F4(])712 b Gg(by)23 b(\(2,3,7\))h(of)g
F6(j)p 3418 3510 V 3436 3510 V 3453 3510 V 64 w(j)3505
3477 y Fu(n)648 3634 y F6(\021)91 b(j)p Ga(P)13 b F6(j)931
3601 y Fu(n)972 3634 y F4([)p Ga(x)26 b F4(:=)f Fp(fst)o
F4(\()p F6(hj)p Ga(M)10 b F6(j)1557 3601 y Fu(n)1599
3634 y Ga(;)15 b F6(j)p Ga(N)10 b F6(j)1772 3601 y Fu(n)1814
3634 y F6(i)p F4(\)])250 b Ga(y)28 b F6(62)d Ga(F)13
b(V)20 b F4(\()p F6(j)p Ga(P)13 b F6(j)2618 3601 y Fu(n)2659
3634 y F4(\))24 b Gg(by)f(logical)i(cut)f F6(^)3296 3648
y Gc(R)3354 3634 y Ga(=)p F6(^)3460 3648 y Gc(L)3508
3657 y FV(1)621 3721 y Gc(\023)549 3758 y F6(\000)-32
b(\000)h(!)728 3725 y FX(\003)810 3758 y F6(j)p Ga(P)13
b F6(j)931 3725 y Fu(n)972 3758 y F4([)p Ga(x)26 b F4(:=)f
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3882 y(=)91 b F6(j)p FL(Cut)p F4(\()1008 3870 y FX(h)1036
3882 y Ga(a)1084 3870 y FX(i)1112 3882 y Ga(M)10 b(;)1250
3870 y F9(\()1278 3882 y Ga(x)1330 3870 y F9(\))1357
3882 y Ga(P)j F4(\))p F6(j)1488 3849 y Fu(n)3050 3882
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V 3453 3882 V 64 w(j)3505 3849 y Fu(n)p Black 321 4054
a Gb(Logical)h(Cut)d Fb(\033)882 4068 y Fy(R)948 4054
y FO(=)p Fb(\033)1081 4068 y Fy(L)1139 4054 y Gb(:)p
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y Ga(b)838 4169 y FX(i)866 4181 y FL(Imp)1010 4203 y
Gc(R)1068 4181 y F4(\()1103 4169 y F9(\()1130 4181 y
Ga(x)1182 4169 y F9(\))q FX(h)1237 4181 y Ga(a)1285 4169
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4169 y F9(\()1594 4181 y Ga(z)1640 4169 y F9(\))1667
4181 y FL(Imp)1812 4203 y Gc(L)1864 4181 y F4(\()1899
4169 y FX(h)1927 4181 y Ga(c)1966 4169 y FX(i)1993 4181
y Ga(P)e(;)2104 4169 y F9(\()2132 4181 y Ga(y)2180 4169
y F9(\))2208 4181 y Ga(Q)o(;)i(z)t F4(\))q(\))728 4257
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4282 y FX(i)1428 4294 y Ga(P)13 b(;)1539 4282 y F9(\()1567
4294 y Ga(x)1619 4282 y F9(\))1647 4294 y Ga(M)d F4(\))p
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4294 y Ga(Q)p F4(\))74 b Gg(or)728 4370 y Gc(int)689
4407 y F6(\000)-31 b(\000)g(!)25 b FL(Cut)p F4(\()1058
4395 y FX(h)1085 4407 y Ga(c)1124 4395 y FX(i)1152 4407
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4395 y F9(\))1371 4407 y FL(Cut)o F4(\()1543 4395 y FX(h)1571
4407 y Ga(a)1619 4395 y FX(i)1647 4407 y Ga(M)d(;)1785
4395 y F9(\()1813 4407 y Ga(y)1861 4395 y F9(\))1888
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i(we)e(ha)n(v)o(e:)810 4679 y F6(j)p FL(Cut)p F4(\()1008
4667 y FX(h)1036 4679 y Ga(b)1075 4667 y FX(i)1103 4679
y FL(Imp)1247 4701 y Gc(R)1305 4679 y F4(\()1340 4667
y F9(\()1368 4679 y Ga(x)1420 4667 y F9(\))p FX(h)1474
4679 y Ga(a)1522 4667 y FX(i)1550 4679 y Ga(M)10 b(;)15
b(b)p F4(\))q Ga(;)1803 4667 y F9(\()1831 4679 y Ga(z)1877
4667 y F9(\))1904 4679 y FL(Imp)2049 4701 y Gc(L)2101
4679 y F4(\()2136 4667 y FX(h)2164 4679 y Ga(c)2203 4667
y FX(i)2231 4679 y Ga(P)e(;)2342 4667 y F9(\()2369 4679
y Ga(y)2417 4667 y F9(\))2445 4679 y Ga(Q;)i(z)t F4(\))q(\))p
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4798 y F4(\)][)p Ga(z)30 b F4(:=)25 b Ga(\025x:)p F6(j)p
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b Gg(by)24 b(\(2,6,10\))g(of)g F6(j)p 3418 4798 V 3436
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b F6(j)1506 4884 y Fu(n)1548 4917 y F4(\))40 b F6(j)p
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b(V)20 b F4(\()p F6(j)p Ga(Q)p F6(j)3267 4884 y Fu(n)3308
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4917 y F4(\))621 4998 y Gc(\023)549 5035 y F6(\000)-32
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5154 y Ga(x)1570 5142 y F9(\))1597 5154 y Ga(M)d F4(\))q
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y Gg(by)24 b(\(2\))f(of)h F6(j)p 3418 5154 V 3436 5154
V 3453 5154 V 64 w(j)3505 5121 y Fu(n)598 5319 y Gg(F)o(or)f(the)h
(other)g(reduct)h(we)e(ha)n(v)o(e:)810 5438 y F6(j)p
FL(Cut)p F4(\()1008 5426 y FX(h)1036 5438 y Ga(c)1075
5426 y FX(i)1103 5438 y Ga(P)13 b(;)1214 5426 y F9(\()1242
5438 y Ga(x)1294 5426 y F9(\))1321 5438 y FL(Cut)p F4(\()1494
5426 y FX(h)1522 5438 y Ga(a)1570 5426 y FX(i)1597 5438
y Ga(M)d(;)1735 5426 y F9(\()1763 5438 y Ga(y)1811 5426
y F9(\))1839 5438 y Ga(Q)o F4(\))q(\))p F6(j)2006 5405
y Fu(n)648 5557 y F4(=)91 b F6(j)p Ga(Q)p F6(j)932 5524
y Fu(n)973 5557 y F4([)p Ga(y)29 b F4(:=)c F6(j)p Ga(M)10
b F6(j)1341 5524 y Fu(n)1382 5557 y F4(][)p Ga(x)26 b
F4(:=)f F6(j)p Ga(P)13 b F6(j)1752 5524 y Fu(n)1793 5557
y F4(])1232 b Gg(by)24 b(\(2\))f(of)h F6(j)p 3418 5557
V 3436 5557 V 3453 5557 V 64 w(j)3505 5524 y Fu(n)648
5675 y F6(\021)91 b(j)p Ga(Q)p F6(j)932 5642 y Fu(n)973
5675 y F4([)p Ga(y)29 b F4(:=)c F6(j)p Ga(M)10 b F6(j)1341
5642 y Fu(n)1382 5675 y F4([)p Ga(x)25 b F4(:=)h F6(j)p
Ga(P)13 b F6(j)1727 5642 y Fu(n)1768 5675 y F4(]])559
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Black Black eop end
%%Page: 161 173
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y Ga(d)1273 4528 y FX(i)1301 4540 y Ga(T)12 b(;)j(a)p
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y Ga(;)1206 4675 y FX(h)1234 4687 y Ga(d)1281 4675 y
FX(i)1309 4687 y F6(j)p Ga(T)13 b F6(j)1425 4654 y Fu(S)1468
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4687 y F4([)p Ga(\033)s F4(])1766 4654 y Fu(S)549 4806
y F4(=)42 b FL(And)816 4820 y Gc(R)874 4806 y F4(\()909
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4806 y Gg(by)24 b(\(3\))f(of)h F6(j)p 3415 4806 V 3433
4806 V 3450 4806 V 65 w(j)3503 4773 y Fu(S)549 4924 y
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4912 y FX(i)938 4924 y FL(And)1093 4938 y Gc(R)1150 4924
y F4(\()1185 4912 y FX(h)1213 4924 y Ga(c)1252 4912 y
FX(i)1280 4924 y F6(j)p Ga(S)5 b F6(j)1391 4891 y Fu(S)1435
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FX(i)1726 4924 y F6(j)p Ga(T)13 b F6(j)1842 4891 y Fu(S)1886
4924 y F4([)p Ga(\033)s F4(])1991 4891 y Fu(S)2035 4924
y Ga(;)i(a)p F4(\))q Ga(;)2199 4912 y F9(\()2227 4924
y Ga(z)2273 4912 y F9(\))2300 4924 y FL(And)2455 4887
y Gc(i)2455 4947 y(L)2507 4924 y F4(\()2542 4912 y F9(\()2570
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5043 y Ga(a)910 5031 y FX(i)938 5043 y FL(And)1093 5057
y Gc(R)1150 5043 y F4(\()1185 5031 y FX(h)1213 5043 y
Ga(c)1252 5031 y FX(i)1280 5043 y F6(j)p Ga(S)5 b Fs(^)q
Ga(\033)s Fs(_)p F6(j)1511 5010 y Fu(S)1555 5043 y Ga(;)1595
5031 y FX(h)1623 5043 y Ga(d)1670 5031 y FX(i)1697 5043
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5010 y Fu(S)1977 5043 y Ga(;)i(a)p F4(\))q Ga(;)2141
5031 y F9(\()2169 5043 y Ga(z)2215 5031 y F9(\))2243
5043 y FL(And)2397 5006 y Gc(i)2397 5066 y(L)2449 5043
y F4(\()2484 5031 y F9(\()2512 5043 y Ga(x)2564 5031
y F9(\))2591 5043 y F6(j)p Ga(N)10 b F6(j)2724 5010 y
Fu(S)2768 5043 y Ga(;)15 b(z)t F4(\))q(\))412 b Gg(by)23
b(IH)549 5161 y F4(=)42 b F6(j)p FL(And)842 5124 y Gc(i)842
5184 y(E)901 5161 y F4(\()936 5149 y FX(h)964 5161 y
Ga(a)1012 5149 y FX(i)1039 5161 y FL(And)1194 5175 y
Gc(I)1234 5161 y F4(\()1269 5149 y FX(h)1297 5161 y Ga(c)1336
5149 y FX(i)1364 5161 y Ga(S)5 b Fs(^)p Ga(\033)s Fs(_)q
Ga(;)1585 5149 y FX(h)1613 5161 y Ga(d)1660 5149 y FX(i)1687
5161 y Ga(T)13 b Fs(^)p Ga(\033)s Fs(_)q Ga(;)i(a)p F4(\))q
Ga(;)2037 5149 y F9(\()2065 5161 y Ga(x)2117 5149 y F9(\))2144
5161 y Ga(N)10 b F4(\))p F6(j)2287 5128 y Fu(S)2933 5161
y Gg(by)24 b(\(2,11\))g(of)g F6(j)p 3415 5161 V 3433
5161 V 3450 5161 V 65 w(j)3503 5128 y Fu(S)549 5280 y
F4(=)42 b F6(j)p FL(And)842 5294 y Gc(I)882 5280 y F4(\()917
5268 y FX(h)944 5280 y Ga(c)983 5268 y FX(i)1011 5280
y Ga(S)5 b(;)1112 5268 y FX(h)1140 5280 y Ga(d)1187 5268
y FX(i)1215 5280 y Ga(T)12 b(;)j(a)p F4(\))p Fs(^)r Ga(\033)s
Fs(_)p F6(j)1549 5247 y Fu(S)3076 5280 y Gg(by)24 b(\(2\))f(of)h
Fs(^)p 3451 5280 V 3469 5280 V 3487 5280 V 65 w(_)p 3480
5385 4 62 v 3484 5327 55 4 v 3484 5385 V 3538 5385 4
62 v Black Black eop end
%%Page: 163 175
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(Chapter)f(3)2639 b(163)p 277 88 3691 4 v Black Black
277 388 a(Pr)n(oof)24 b(of)g(Theor)n(em)f(3.4.4.)p Black
34 w Gg(W)-7 b(e)23 b(gi)n(v)o(e)g(some)h(illustrati)n(v)o(e)i(e)o
(xamples.)p Black 277 612 a Gb(Beta-Reduction:)p Black
410 748 a FL(Imp)554 770 y Gc(E)614 748 y F4(\()649 736
y FX(h)677 748 y Ga(b)716 736 y FX(i)743 748 y FL(Imp)888
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736 y FX(h)1453 748 y Ga(c)1492 736 y FX(i)1520 748 y
Ga(N)10 b(;)1643 736 y F9(\()1671 748 y Ga(y)1719 736
y F9(\))1746 748 y Ga(P)j F4(\))1940 711 y Gc(\014)1876
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736 y FX(h)2345 748 y Ga(c)2384 736 y FX(i)2412 748 y
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y F9(\))2642 748 y FL(Subst)o F4(\()2889 736 y FX(h)2917
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y F9(\()3158 748 y Ga(y)3206 736 y F9(\))3234 748 y Ga(P)i
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920 y FL(Imp)1201 942 y Gc(I)1241 920 y F4(\()1276 908
y F9(\()1304 920 y Ga(x)1356 908 y F9(\))p FX(h)1411
920 y Ga(a)1459 908 y FX(i)1486 920 y Ga(M)d(;)15 b(b)p
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y FX(i)1834 920 y Ga(N)10 b(;)1957 908 y F9(\()1985 920
y Ga(y)2033 908 y F9(\))2060 920 y Ga(P)j F4(\))p F6(j)2191
887 y Fu(S)604 1039 y F4(=)23 b FL(Cut)p F4(\()871 1027
y FX(h)899 1039 y Ga(b)938 1027 y FX(i)965 1039 y FL(Imp)1110
1061 y Gc(R)1168 1039 y F4(\()1203 1027 y F9(\()1230
1039 y Ga(x)1282 1027 y F9(\))q FX(h)1337 1039 y Ga(a)1385
1027 y FX(i)1413 1039 y F6(j)p Ga(M)10 b F6(j)1561 1006
y Fu(S)1605 1039 y Ga(;)15 b(b)p F4(\))p Ga(;)1759 1027
y F9(\()1787 1039 y Ga(z)1833 1027 y F9(\))1861 1039
y FL(Imp)2005 1061 y Gc(L)2058 1039 y F4(\()2093 1027
y FX(h)2120 1039 y Ga(c)2159 1027 y FX(i)2187 1039 y
F6(j)p Ga(N)10 b F6(j)2320 1006 y Fu(S)2364 1039 y Ga(;)2404
1027 y F9(\()2432 1039 y Ga(y)2480 1027 y F9(\))2507
1039 y F6(j)p Ga(P)j F6(j)2628 1006 y Fu(S)2672 1039
y Ga(;)i(z)t F4(\))q(\))60 b Gg(by)24 b(\(5,13\))g(of)g
F6(j)p 3371 1039 28 4 v 3389 1039 V 3406 1039 V 65 w(j)3459
1006 y Fu(S)535 1120 y Gc(cut)504 1157 y F6(\000)-31
b(\000)g(!)23 b FL(Cut)p F4(\()871 1145 y FX(h)899 1157
y Ga(c)938 1145 y FX(i)966 1157 y F6(j)p Ga(N)10 b F6(j)1099
1124 y Fu(S)1143 1157 y Ga(;)1183 1145 y F9(\()1210 1157
y Ga(x)1262 1145 y F9(\))1290 1157 y FL(Cut)p F4(\()1463
1145 y FX(h)1490 1157 y Ga(a)1538 1145 y FX(i)1566 1157
y F6(j)p Ga(M)g F6(j)1714 1124 y Fu(S)1758 1157 y Ga(;)1798
1145 y F9(\()1826 1157 y Ga(y)1874 1145 y F9(\))1901
1157 y F6(j)p Ga(P)j F6(j)2022 1124 y Fu(S)2066 1157
y 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 V
3389 1276 V 3406 1276 V 65 w(j)3459 1243 y Fu(S)2232
1394 y Gg(and)g Ga(b)f Gg(is)h(freshly)h(introduced)h(by)3396
1357 y Gc(\014)3332 1394 y F6(\000)-31 b(\000)f(!)604
1513 y F4(=)23 b F6(j)p FL(Subst)p F4(\()971 1501 y FX(h)998
1513 y Ga(c)1037 1501 y FX(i)1065 1513 y Ga(N)10 b(;)1188
1501 y F9(\()1216 1513 y Ga(x)1268 1501 y F9(\))1295
1513 y FL(Subst)p F4(\()1543 1501 y FX(h)1570 1513 y
Ga(a)1618 1501 y FX(i)1646 1513 y Ga(M)g(;)1784 1501
y F9(\()1812 1513 y Ga(y)1860 1501 y F9(\))1887 1513
y Ga(P)j F4(\)\))p F6(j)2053 1480 y Fu(S)3003 1513 y
Gg(by)24 b(\(2\))f(of)h F6(j)p 3371 1513 V 3389 1513
V 3406 1513 V 65 w(j)3459 1480 y Fu(S)p Black 277 1713
a Gb(Commuting)e(Reduction:)p Black 504 1850 a FL(And)659
1813 y Gc(i)659 1873 y(E)719 1850 y F4(\()754 1838 y
FX(h)781 1850 y Ga(a)829 1838 y FX(i)857 1850 y Ga(M)10
b(;)995 1838 y F9(\()1023 1850 y Ga(x)1075 1838 y F9(\))1102
1850 y Ga(N)g F4(\))1311 1813 y Gc(\015)1246 1850 y F6(\000)-31
b(\000)f(!)25 b Ga(M)10 b Fs(^)q FL(And)1726 1813 y Gc(i)1726
1873 y(E)1786 1850 y F4(\()1821 1838 y FX(h)1849 1850
y Ga(a)1897 1838 y FX(i)p 1926 1850 V 1944 1850 V 1962
1850 V 1989 1850 a Ga(;)2029 1838 y F9(\()2057 1850 y
Ga(x)2109 1838 y F9(\))2136 1850 y Ga(N)g F4(\))p Fs(_)717
2011 y F6(j)p FL(And)897 1974 y Gc(i)897 2034 y(E)957
2011 y F4(\()992 1999 y FX(h)1019 2011 y Ga(a)1067 1999
y FX(i)1095 2011 y Ga(M)g(;)1233 1999 y F9(\()1261 2011
y Ga(x)1313 1999 y F9(\))1340 2011 y Ga(N)g F4(\))p F6(j)1483
1978 y Fu(S)604 2130 y F4(=)42 b FL(Cut)p F4(\()890 2118
y FX(h)918 2130 y Ga(a)966 2118 y FX(i)993 2130 y F6(j)p
Ga(M)10 b F6(j)1141 2097 y Fu(S)1185 2130 y Ga(;)1225
2118 y F9(\()1253 2130 y Ga(z)1299 2118 y F9(\))1327
2130 y FL(And)1481 2093 y Gc(i)1481 2153 y(L)1534 2130
y F4(\()1569 2118 y F9(\()1596 2130 y Ga(x)1648 2118
y F9(\))1676 2130 y F6(j)p Ga(N)g F6(j)1809 2097 y Fu(S)1853
2130 y Ga(;)15 b(z)t F4(\))q(\))947 b Gg(by)24 b(\(11\))g(of)g
F6(j)p 3371 2130 V 3389 2130 V 3406 2130 V 65 w(j)3459
2097 y Fu(S)535 2211 y Gc(cut)504 2248 y F6(\000)-31
b(\000)g(!)42 b(j)p Ga(M)10 b F6(j)865 2215 y Fu(S)909
2248 y F4([)p Ga(a)26 b F4(:=)1129 2236 y F9(\()1156
2248 y Ga(z)1202 2236 y F9(\))1230 2248 y FL(And)1385
2211 y Gc(i)1385 2271 y(L)1437 2248 y F4(\()1472 2236
y F9(\()1500 2248 y Ga(x)1552 2236 y F9(\))1579 2248
y F6(j)p Ga(N)10 b F6(j)1712 2215 y Fu(S)1756 2248 y
Ga(;)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)-31
b(\000)f(!)604 2367 y(\021)42 b(j)p Ga(M)10 b Fs(^)q
FL(And)1028 2330 y Gc(i)1028 2390 y(E)1087 2367 y F4(\()1122
2355 y FX(h)1150 2367 y Ga(a)1198 2355 y FX(i)p 1228
2367 V 1245 2367 V 1263 2367 V 1290 2367 a Ga(;)1330
2355 y F9(\()1358 2367 y Ga(x)1410 2355 y F9(\))1437
2367 y Ga(N)g F4(\))p Fs(_)q F6(j)1613 2334 y Fu(S)2906
2367 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(\()752
2692 y FX(h)779 2704 y Ga(a)827 2692 y FX(i)855 2704
y Ga(M)10 b(;)993 2692 y F9(\()1021 2704 y Ga(x)1073
2692 y F9(\))1100 2704 y Ga(N)g F4(\))1382 2667 y Gc(\033)1318
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b Ga(a)26 b F4(:=)1906 2692 y F9(\()1933 2704 y Ga(x)1985
2692 y F9(\))2013 2704 y Ga(N)s Fs(\))717 2880 y F6(j)p
FL(Subst)p F4(\()990 2868 y FX(h)1017 2880 y Ga(a)1065
2868 y FX(i)1093 2880 y Ga(M)10 b(;)1231 2868 y F9(\()1259
2880 y Ga(x)1311 2868 y F9(\))1338 2880 y Ga(N)g F4(\))p
F6(j)1481 2847 y Fu(S)604 3004 y F4(=)42 b FL(Cut)p F4(\()890
2992 y FX(h)918 3004 y Ga(a)966 2992 y FX(i)993 3004
y F6(j)p Ga(M)10 b F6(j)1141 2971 y Fu(S)1185 3004 y
Ga(;)1225 2992 y F9(\()1253 3004 y Ga(x)1305 2992 y F9(\))1333
3004 y F6(j)p Ga(N)g F6(j)1466 2971 y Fu(S)1509 3004
y F4(\))1459 b Gg(by)24 b(\(2\))f(of)h F6(j)p 3371 3004
V 3389 3004 V 3406 3004 V 65 w(j)3459 2971 y Fu(S)535
3091 y Gc(cut)504 3128 y F6(\000)-31 b(\000)g(!)42 b(j)p
Ga(M)10 b F6(j)865 3095 y Fu(S)909 3128 y F4([)p Ga(a)26
b F4(:=)1129 3116 y F9(\()1156 3128 y Ga(x)1208 3116
y F9(\))1236 3128 y F6(j)p Ga(N)10 b F6(j)1369 3095 y
Fu(S)1413 3128 y F4(])800 b Ga(a)23 b Gg(is)h(not)g(freshly)h
(introduced)h(by)3396 3091 y Gc(\033)3332 3128 y F6(\000)-31
b(\000)f(!)604 3252 y(\021)42 b(j)p Ga(M)10 b Fs(\()-6
b Ga(a)25 b F4(:=)1060 3240 y F9(\()1088 3252 y Ga(x)1140
3240 y F9(\))1167 3252 y Ga(N)s Fs(\))q F6(j)1301 3219
y Fu(S)2906 3252 y Gg(by)f(Lemma)e(3.4.1)504 3424 y FL(Subst)p
F4(\()752 3412 y FX(h)779 3424 y Ga(a)827 3412 y FX(i)855
3424 y Ga(M)10 b(;)993 3412 y F9(\()1021 3424 y Ga(x)1073
3412 y F9(\))1100 3424 y Ga(N)g F4(\))1382 3387 y Gc(\033)1318
3424 y F6(\000)-31 b(\000)f(!)100 b Ga(N)10 b Fs(\()-7
b Ga(x)26 b F4(:=)1895 3412 y FX(h)1922 3424 y Ga(a)1970
3412 y FX(i)1998 3424 y Ga(M)s Fs(\))741 3600 y F6(j)p
FL(Subst)p F4(\()1014 3588 y FX(h)1042 3600 y Ga(a)1090
3588 y FX(i)1117 3600 y Ga(M)10 b(;)1255 3588 y F9(\()1283
3600 y Ga(x)1335 3588 y F9(\))1362 3600 y Ga(N)g F4(\))p
F6(j)1505 3567 y Fu(S)628 3724 y F4(=)42 b FL(Cut)p F4(\()914
3712 y FX(h)942 3724 y Ga(a)990 3712 y FX(i)1018 3724
y F6(j)p Ga(M)10 b F6(j)1166 3691 y Fu(S)1210 3724 y
Ga(;)1250 3712 y F9(\()1277 3724 y Ga(x)1329 3712 y F9(\))1357
3724 y F6(j)p Ga(N)g F6(j)1490 3691 y Fu(S)1534 3724
y F4(\))1434 b Gg(by)24 b(\(2\))f(of)h F6(j)p 3371 3724
V 3389 3724 V 3406 3724 V 65 w(j)3459 3691 y Fu(S)559
3811 y Gc(cut)529 3848 y F6(\000)-32 b(\000)h(!)42 b(j)p
Ga(N)10 b F6(j)874 3815 y Fu(S)918 3848 y F4([)p Ga(x)26
b F4(:=)1142 3836 y FX(h)1169 3848 y Ga(a)1217 3836 y
FX(i)1245 3848 y F6(j)p Ga(M)10 b F6(j)1393 3815 y Fu(S)1437
3848 y F4(])773 b Ga(x)22 b Gg(is)i(not)g(freshly)h(introduced)h(by)
3396 3811 y Gc(\033)3332 3848 y F6(\000)-31 b(\000)f(!)550
3936 y Gc(cut)520 3973 y F6(\000)g(\000)h(!)690 3940
y FX(\003)741 3973 y F6(j)p Ga(N)10 b Fs(\()-6 b Ga(x)25
b F4(:=)1073 3961 y FX(h)1101 3973 y Ga(a)1149 3961 y
FX(i)1176 3973 y Ga(M)s Fs(\))q F6(j)1325 3940 y Fu(S)2906
3973 y Gg(by)f(Lemma)e(3.4.2)p Black 277 4175 a Gb(Inner)h(Reduction:)p
Black 46 w Gg(The)38 b(non-tri)n(vial)k(cases)d(are)g(where)g
Ga(M)49 b Gg(is)38 b(translated)k(using)e(the)f(clauses)504
4288 y(\(11\)\226\(14\))26 b(of)e F6(j)p 1001 4288 V
1019 4288 V 1036 4288 V 65 w(j)1089 4255 y Fu(S)1132
4288 y Gg(,)f(while)h Ga(N)32 b Gg(using)25 b(\(7\)\226\(10\).)31
b(W)-7 b(e)22 b(gi)n(v)o(e)i(one)g(case.)504 4447 y FL(And)659
4411 y Gc(i)659 4471 y(E)719 4447 y F4(\()754 4435 y
FX(h)781 4447 y Ga(a)829 4435 y FX(i)857 4447 y Ga(S)5
b(;)958 4435 y F9(\()986 4447 y Ga(x)1038 4435 y F9(\))1065
4447 y Ga(T)13 b F4(\))1256 4410 y Gc(\024)1191 4447
y F6(\000)-31 b(\000)g(!)25 b FL(And)1541 4411 y Gc(i)1541
4471 y(E)1601 4447 y F4(\()1636 4435 y FX(h)1664 4447
y Ga(a)1712 4435 y FX(i)1739 4447 y Ga(S)1800 4414 y
FX(0)1824 4447 y Ga(;)1864 4435 y F9(\()1891 4447 y Ga(x)1943
4435 y F9(\))1971 4447 y Ga(T)13 b F4(\))23 b Gg(with)g
Ga(S)2340 4414 y FX(0)2389 4447 y F6(\021)i FL(Id)p F4(\()p
Ga(y)s(;)15 b(a)p F4(\))741 4609 y F6(j)p FL(And)921
4572 y Gc(i)921 4632 y(E)981 4609 y F4(\()1016 4597 y
FX(h)1044 4609 y Ga(a)1092 4597 y FX(i)1119 4609 y Ga(S)5
b(;)1220 4597 y F9(\()1248 4609 y Ga(x)1300 4597 y F9(\))1327
4609 y Ga(T)13 b F4(\))p F6(j)1453 4576 y Fu(S)628 4727
y F4(=)42 b FL(Cut)p F4(\()914 4715 y FX(h)942 4727 y
Ga(a)990 4715 y FX(i)1018 4727 y F6(j)p Ga(S)5 b F6(j)1129
4694 y Fu(S)1172 4727 y Ga(;)1212 4715 y F9(\()1240 4727
y Ga(z)1286 4715 y F9(\))1314 4727 y FL(And)1469 4691
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end
%%Page: 166 178
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Ga(x)2152 1534 y F9(\))2180 1546 y F6(j)p Ga(P)e F6(j)2301
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3147 y F9(\()1909 3159 y Ga(y)1957 3147 y F9(\))1984
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3324 y F4(\()1300 3312 y F9(\()1328 3324 y Ga(x)1380
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3324 y Ga(z)1800 3312 y F9(\))1828 3324 y FL(Imp)1972
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3404 3448 V 3422 3448 V 3440 3448 V 65 w(j)3492 3415
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3560 y FX(h)1722 3572 y Ga(a)1770 3560 y FX(i)1798 3572
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5033 y F9(\))1320 5045 y FL(And)1474 5008 y Gc(i)1474
5068 y(L)1527 5045 y F4(\()1562 5033 y F9(\()1589 5045
y Ga(y)1637 5033 y F9(\))1665 5045 y Ga(P)13 b(;)i(x)p
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5157 y FX(h)1087 5169 y Ga(a)1135 5157 y FX(i)1163 5169
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5157 y F9(\()1396 5169 y Ga(y)1444 5157 y F9(\))1471
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V 3422 5169 V 3440 5169 V 65 w(j)3492 5136 y Fu(N)613
5256 y Gc(\024)549 5293 y F6(\000)-32 b(\000)h(!)91 b(j)p
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V 1380 5293 V 1398 5293 V 1425 5293 a Ga(;)1465 5281
y F9(\()1493 5293 y Ga(y)1541 5281 y F9(\))1568 5293
y F6(j)p Ga(P)13 b F6(j)1689 5260 y Fu(N)1744 5293 y
F4(\))p Fs(_)613 5380 y Gc(\024)549 5417 y F6(\000)-32
b(\000)h(!)728 5384 y FX(\003)810 5417 y F6(j)p Ga(S)5
b F4([)p Ga(a)26 b F4(:=)1116 5405 y F9(\()1144 5417
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F6(j)1339 5384 y Fu(N)1419 5417 y F6(\021)25 b(j)p Ga(N)10
b F6(j)1648 5384 y Fu(N)2950 5417 y Gg(by)24 b(Lemma)f(3.4.7)p
Black Black eop end
%%Page: 167 179
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1068 y F9(\))1208 1080 y Ga(T)13 b F4(\))1365 1042 y
Gc(cut)1334 1079 y F6(\000)-31 b(\000)g(!)1530 1080 y
Ga(T)13 b F4([)p Ga(x)25 b F4(:=)1819 1068 y FX(h)1847
1080 y Ga(a)1895 1068 y FX(i)1922 1080 y Ga(S)5 b F4(])26
b F6(\021)f Ga(N)727 1246 y F6(j)p FL(Cut)p F4(\()925
1234 y FX(h)953 1246 y Ga(a)1001 1234 y FX(i)1028 1246
y Ga(S)5 b(;)1129 1234 y F9(\()1157 1246 y Ga(x)1209
1234 y F9(\))1236 1246 y Ga(T)13 b F4(\))p F6(j)1362
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1358 y FX(h)1002 1370 y Ga(a)1050 1358 y FX(i)1077 1370
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1358 y F9(\()1310 1370 y Ga(x)1362 1358 y F9(\))1390
1370 y F6(j)p Ga(T)13 b F6(j)1506 1337 y Fu(N)1560 1370
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V 3378 1370 V 3396 1370 V 65 w(j)3448 1337 y Fu(N)569
1457 y Gc(\024)504 1494 y F6(\000)-31 b(\000)g(!)52 b(j)p
Ga(T)13 b F6(j)843 1461 y Fu(N)897 1494 y Fs(\()-7 b
Ga(x)25 b F4(:=)1121 1482 y FX(h)1148 1494 y Ga(a)1196
1482 y FX(i)1224 1494 y F6(j)p Ga(S)5 b F6(j)1335 1461
y Fu(N)1382 1494 y Fs(\))604 1618 y F6(\021)52 b(j)p
Ga(T)13 b F4([)p Ga(x)25 b F4(:=)1041 1606 y FX(h)1069
1618 y Ga(a)1117 1606 y FX(i)1144 1618 y Ga(S)5 b F4(])p
F6(j)1255 1585 y Fu(N)1335 1618 y F6(\021)25 b(j)p Ga(N)10
b F6(j)1564 1585 y Fu(N)2906 1618 y Gg(by)24 b(Lemma)e(3.4.6)p
Black 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 1913
V 65 w(j)1870 1880 y Fu(N)1951 1913 y Gg(and)g Ga(N)38
b Gg(by)28 b(one)h(of)f(the)h(clauses)h(\(10\22613\).)45
b(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)2496
2014 y F9(\()2523 2026 y Ga(x)2575 2014 y F9(\))2602
2026 y Ga(T)13 b Gg(,)23 b(b)n(ut)h(not)g(in)3083 2014
y F9(\()3111 2026 y Ga(x)3163 2014 y F9(\))3190 2026
y Ga(T)3256 1993 y FX(0)3279 2026 y Gg(.)504 2176 y Ga(M)36
b F6(\021)25 b FL(Cut)p F4(\()897 2164 y FX(h)924 2176
y Ga(c)963 2164 y FX(i)991 2176 y Ga(S)5 b(;)1092 2164
y F9(\()1120 2176 y Ga(y)1168 2164 y F9(\))1195 2176
y FL(And)1350 2139 y Gc(i)1350 2199 y(L)1402 2176 y F4(\()1437
2164 y F9(\()1465 2176 y Ga(x)1517 2164 y F9(\))1544
2176 y Ga(T)13 b(;)i(y)s F4(\))q(\))1825 2139 y Gc(cut)1794
2176 y F6(\000)-31 b(\000)f(!)26 b FL(Cut)p F4(\()2163
2164 y FX(h)2190 2176 y Ga(c)2229 2164 y FX(i)2257 2176
y Ga(S)5 b(;)2358 2164 y F9(\()2386 2176 y Ga(y)2434
2164 y F9(\))2461 2176 y FL(And)2616 2139 y Gc(i)2616
2199 y(L)2668 2176 y F4(\()2703 2164 y F9(\()2731 2176
y Ga(x)2783 2164 y F9(\))2810 2176 y Ga(T)2876 2143 y
FX(0)2899 2176 y Ga(;)15 b(y)s F4(\))q(\))25 b F6(\021)g
Ga(N)766 2331 y F6(j)p FL(Cut)p F4(\()964 2319 y FX(h)992
2331 y Ga(c)1031 2319 y FX(i)1059 2331 y Ga(S)5 b(;)1160
2319 y F9(\()1188 2331 y Ga(y)1236 2319 y F9(\))1263
2331 y FL(And)1417 2294 y Gc(i)1417 2354 y(L)1470 2331
y F4(\()1505 2319 y F9(\()1532 2331 y Ga(x)1584 2319
y F9(\))1612 2331 y Ga(T)13 b(;)i(y)s F4(\)\))p F6(j)1861
2298 y Fu(N)604 2455 y F4(=)91 b FL(Subst)o F4(\()1013
2443 y FX(h)1041 2455 y Ga(c)1080 2443 y FX(i)1108 2455
y F6(j)p Ga(S)5 b F6(j)1219 2422 y Fu(N)1273 2455 y Ga(;)1313
2443 y F9(\()1341 2455 y Ga(y)1389 2443 y F9(\))1416
2455 y FL(And)1571 2418 y Gc(i)1571 2478 y(E)1630 2455
y F4(\()1665 2443 y FX(h)1693 2455 y Ga(a)1741 2443 y
FX(i)1769 2455 y FL(Id)p F4(\()p Ga(a;)15 b(y)s F4(\))q
Ga(;)2088 2443 y F9(\()2116 2455 y Ga(x)2168 2443 y F9(\))2195
2455 y F6(j)p Ga(T)e F6(j)2311 2422 y Fu(N)2365 2455
y F4(\))q(\))443 b Gg(by)23 b(\(6,14\))i(of)e F6(j)p
3360 2455 V 3378 2455 V 3396 2455 V 65 w(j)3448 2422
y Fu(N)569 2542 y Gc(\024)504 2580 y F6(\000)-31 b(\000)g(!)684
2547 y FX(\003)766 2580 y FL(Subst)o F4(\()1013 2568
y FX(h)1041 2580 y Ga(c)1080 2568 y FX(i)1108 2580 y
F6(j)p Ga(S)5 b F6(j)1219 2547 y Fu(N)1273 2580 y Ga(;)1313
2568 y F9(\()1341 2580 y Ga(y)1389 2568 y F9(\))1416
2580 y FL(And)1571 2543 y Gc(i)1571 2603 y(E)1630 2580
y F4(\()1665 2568 y FX(h)1693 2580 y Ga(a)1741 2568 y
FX(i)1769 2580 y FL(Id)p F4(\()p Ga(a;)15 b(y)s F4(\))q
Ga(;)2088 2568 y F9(\()2116 2580 y Ga(x)2168 2568 y F9(\))2195
2580 y F6(j)p Ga(T)2286 2547 y FX(0)2310 2580 y F6(j)2335
2547 y Fu(N)2389 2580 y F4(\)\))834 b Gg(by)23 b(IH)569
2667 y Gc(\024)504 2704 y F6(\000)-31 b(\000)g(!)91 b
FL(And)921 2667 y Gc(i)921 2727 y(E)980 2704 y F4(\()1015
2692 y FX(h)1043 2704 y Ga(a)1091 2692 y FX(i)1118 2704
y FL(Id)q F4(\()p Ga(a;)15 b(y)s F4(\))q Ga(;)1438 2692
y F9(\()1466 2704 y Ga(x)1518 2692 y F9(\))1545 2704
y F6(j)p Ga(T)1636 2671 y FX(0)1659 2704 y F6(j)1684
2671 y Fu(N)1738 2704 y F4(\))p Fs(\()-6 b Ga(y)28 b
F4(:=)1993 2692 y FX(h)2021 2704 y Ga(c)2060 2692 y FX(i)2088
2704 y F6(j)p Ga(S)5 b F6(j)2199 2671 y Fu(N)2246 2704
y Fs(\))604 2828 y F4(=)91 b FL(And)921 2791 y Gc(i)921
2851 y(E)980 2828 y F4(\()1015 2816 y FX(h)1043 2828
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2795 y Fu(N)1275 2828 y Ga(;)1315 2816 y F9(\()1343 2828
y Ga(x)1395 2816 y F9(\))1422 2828 y F6(j)p Ga(T)1513
2795 y FX(0)1537 2828 y F6(j)1562 2795 y Fu(N)1616 2828
y F4(\))721 b Gg(by)24 b(assumption)i Ga(y)i F6(62)d
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2816 y F9(\))3378 2828 y Ga(T)3444 2795 y FX(0)3467 2828
y F4(\))604 2952 y(=)91 b F6(j)p FL(Cut)p F4(\()964 2940
y FX(h)992 2952 y Ga(c)1031 2940 y FX(i)1059 2952 y Ga(S)5
b(;)1160 2940 y F9(\()1188 2952 y Ga(y)1236 2940 y F9(\))1263
2952 y FL(And)1417 2915 y Gc(i)1417 2975 y(L)1470 2952
y F4(\()1505 2940 y F9(\()1532 2952 y Ga(x)1584 2940
y F9(\))1612 2952 y Ga(T)1678 2919 y FX(0)1701 2952 y
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y F6(\021)25 b(j)p Ga(N)10 b F6(j)2193 2919 y Fu(N)2947
2952 y Gg(by)24 b(\(10\))g(of)f F6(j)p 3360 2952 V 3378
2952 V 3396 2952 V 65 w(j)3448 2919 y Fu(N)p 3436 3059
4 62 v 3440 3001 55 4 v 3440 3059 V 3494 3059 4 62 v
277 3368 a Ge(B.3)119 b(Pr)n(oofs)29 b(of)g(Chapter)i(4)277
3591 y Gg(In)i(this)h(section)h(we)e(pro)o(v)o(e)h(that)g(a)e
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3554 y Gc(aux)2984 3591 y F6(\000)-31 b(\000)f(!)33 b
Gg(does)h(not)277 3704 y(restrict)25 b(the)f(collection)i(of)e
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Black 277 3842 a Gb(Pr)n(oof)i(of)e(Lemma)g(4.1.2.)p
Black 34 w Gg(By)g(induction)k(on)d(the)g(structure)i(of)e
Ga(M)2454 3856 y F9(1)2494 3842 y Gg(.)32 b(W)-7 b(e)24
b(analyse)i(four)g(represen-)277 3955 y(tati)n(v)o(e)e(cases.)p
Black 414 4157 a F6(\017)p Black 45 w Gg(Suppose)h(we)e(ha)n(v)o(e)h
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y FL(And)804 4429 y Gc(R)861 4415 y F4(\()896 4403 y
FX(h)924 4415 y Ga(a)972 4403 y FX(i)1000 4415 y Ga(M)10
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4415 y Ga(N)g(;)15 b(c)p F4(\))1483 4378 y Gc(bad)1455
4415 y F6(\000)-31 b(\000)g(!)25 b FL(And)1805 4429 y
Gc(R)1863 4415 y F4(\()1898 4403 y FX(h)1926 4415 y Ga(a)1974
4403 y FX(i)2001 4415 y Ga(M)11 b(;)2140 4403 y FX(h)2167
4415 y Ga(b)2206 4403 y FX(i)2234 4415 y Ga(S)5 b(;)15
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Gc(R)2843 4415 y F4(\()2878 4403 y FX(h)2906 4415 y Ga(a)2954
4403 y FX(i)2981 4415 y Ga(T)13 b(;)3087 4403 y FX(h)3115
4415 y Ga(b)3154 4403 y FX(i)3181 4415 y Ga(S)5 b(;)15
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FX(h)904 5025 y Ga(a)952 5013 y FX(i)980 5025 y Ga(M)10
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5025 y Ga(N)g(;)15 b(c)p F4(\))p 1456 4950 V 1456 4988
a Gc(aux)1435 5025 y F6(\000)-31 b(\000)g(!)25 b FL(And)1785
5039 y Gc(R)1843 5025 y F4(\()1878 5013 y FX(h)1906 5025
y Ga(a)1954 5013 y FX(i)1981 5025 y Ga(T)13 b(;)2087
5013 y FX(h)2115 5025 y Ga(b)2154 5013 y FX(i)2181 5025
y Ga(N)d(;)15 b(c)p F4(\))2425 4988 y Gc(aux)2405 5025
y F6(\000)-31 b(\000)f(!)25 b FL(And)2755 5039 y Gc(R)2813
5025 y F4(\()2848 5013 y FX(h)2875 5025 y Ga(a)2923 5013
y FX(i)2951 5025 y Ga(T)13 b(;)3057 5013 y FX(h)3084
5025 y Ga(b)3123 5013 y FX(i)3151 5025 y Ga(S)5 b(;)15
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y F4(\()893 5510 y FX(h)921 5522 y Ga(a)969 5510 y FX(i)996
5522 y Ga(M)10 b(;)1134 5510 y FX(h)1162 5522 y Ga(b)1201
5510 y FX(i)1229 5522 y Ga(N)g(;)15 b(c)p F4(\))1479
5485 y Gc(bad)1452 5522 y F6(\000)-31 b(\000)f(!)26 b
FL(And)1802 5536 y Gc(R)1860 5522 y F4(\()1895 5510 y
FX(h)1923 5522 y Ga(a)1971 5510 y FX(i)1998 5522 y Ga(S)5
b(;)2099 5510 y FX(h)2127 5522 y Ga(b)2166 5510 y FX(i)2193
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b(;)3068 5510 y FX(h)3096 5522 y Ga(b)3135 5510 y FX(i)3163
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%%Page: 168 180
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b(;)3111 942 y FX(h)3139 954 y Ga(b)3178 942 y FX(i)3206
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b(104)363 3257 y Gc(l)q(oc)321 3294 y F6(\000)-31 b(\000)g(!)p
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4 v 366 3954 V 384 3954 V 65 w(j)436 3921 y Gc(\024)481
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4068 V 384 4068 V 65 w(j)436 4035 y Gc(\026)483 4068
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V 384 4522 V 65 w(j)436 4489 y Fu(s)p FV(+)514 4522 y
Gg(,)h(120)321 4635 y F6(j)p 348 4635 V 366 4635 V 384
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4716 y Fu(Sym)568 4749 y Gg(,)h(63)321 4862 y F6(j)p
348 4862 V 366 4862 V 384 4862 V 65 w(j)436 4876 y Gc(x)480
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F4(R)p Gg(,)g(84)2079 1703 y FY(T)t Gg(,)d(22)2079 1816
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y Gb(A)2079 2878 y Gg(Abramsk)o(y)-6 b(,)24 b(5,)f(21)2079
2991 y(antecedent,)j(10)2079 3184 y Gb(B)2079 3297 y
Gg(Barbanera,)i(6,)e(8,)g(9,)h(19,)f(31,)h(61,)f(114,)h(123,)2411
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Black Black eop end
%%Page: 177 189
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%%Page: 178 190
TeXDict begin 178 189 bop Black -144 51 a Gb(178)3333
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751 y(well-typed,)i(22)321 864 y(typing)f(judgement,)h(22,)d(48,)g(69,)
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1677 y Gb(W)321 1790 y Gg(weak)g(normalisation,)i(14)321
1986 y Gb(Z)321 2099 y Gg(Zuck)o(er)l(,)f(3,)e(60,)g(73,)g(74,)h(95,)f
(126)p Black Black Black Black eop end
%%Trailer
userdict /end-hook known{end-hook}if
%%EOF