Slides/cam01.ps
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Thu, 15 Mar 2012 10:13:14 +0000
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%!PS-Adobe-2.0
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%%Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software
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%%Title: slides-01.dvi
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%%Pages: 22
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%%PageOrder: Ascend
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%%BoundingBox: 0 0 595 842
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%%DocumentFonts: Times-Bold ComicSansMS ComicSansMS-Bold
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%%DocumentPaperSizes: a4
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%%EndComments
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%DVIPSWebPage: (www.radicaleye.com)
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%DVIPSCommandLine: dvips slides-01.dvi -o slides-01.ps
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%DVIPSParameters: dpi=600
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%DVIPSSource:  TeX output 2005.12.05:1425
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%%BeginProcSet: tex.pro 0 0
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%!
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/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S
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N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72
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mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0
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0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{
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landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize
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mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[
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matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round
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exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{
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statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0]
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N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin
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/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array
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/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2
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array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N
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df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A
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definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get
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}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub}
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B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr
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1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S
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/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy
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setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask
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restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn
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/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put
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}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{
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bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A
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mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{
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SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{
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userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X
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1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4
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index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N
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/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{
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/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)
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(LaserWriter 16/600)]{A length product length le{A length product exch 0
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exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse
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end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask
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grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot}
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imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round
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exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto
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fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p
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delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}
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B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{
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p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S
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rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end
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%%EndProcSet
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%%BeginProcSet: pstricks.pro 0 0
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%!
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% PostScript prologue for pstricks.tex.
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% Version 97 patch 4, 04/05/10
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% For distribution, see pstricks.tex.
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%
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/tx@Dict 200 dict def tx@Dict begin
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/ADict 25 dict def
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/CM { matrix currentmatrix } bind def
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/SLW /setlinewidth load def
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/CLW /currentlinewidth load def
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/CP /currentpoint load def
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/ED { exch def } bind def
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/L /lineto load def
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/T /translate load def
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/TMatrix { } def
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/RAngle { 0 } def
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/Atan { /atan load stopped { pop pop 0 } if } def
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/Div { dup 0 eq { pop } { div } ifelse } def
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/NET { neg exch neg exch T } def
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/Pyth { dup mul exch dup mul add sqrt } def
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/PtoC { 2 copy cos mul 3 1 roll sin mul } def
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/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def }
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def
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/PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
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} { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ }
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/pathforall load stopped { pop pop pop pop } if z } def
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/STP { .996264 dup scale } def
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/STV { SDict begin normalscale end STP  } def
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%
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%%-------------- DG begin patch 15 ---------------%%
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%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def
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%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y
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%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul
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%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ]
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%0 } ifelse setdash stroke } def
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/DashLine {
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  dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse
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  /b ED /x1 ED /y1 ED /x ED /y ED 
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  /z y x add y1 add x1 add def
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  /Coef b a .5 sub 2 mul y mul sub z Div round 
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  z mul a .5 sub 2 mul y mul add b exch Div def 
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  /y y Coef mul def /x x Coef mul def /y1 y1 Coef mul def /x1 x1 Coef mul def
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  x1 0 gt y1 0 gt x 0 gt y 0 gt and { [ y x y1 x1 ] 1 a sub y mul}
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  { [ 1 0] 0 } ifelse setdash stroke
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} def
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%%-------------- DG end patch 15 ---------------%%
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/DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt
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{ /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y add
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def } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if
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] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1
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setlinecap stroke } def
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/LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch
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2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25
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% DG/SR modification begin - Dec. 12, 1997 - Patch 2
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%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
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itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
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% DG/SR modification end
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Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict
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/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1
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% DG/SR modification begin - Jun.  1, 1998 - Patch 3 (from Michael Vulis)
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% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }
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% def
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a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore
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pop pop } def
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% DG/SR modification end
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/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg
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exch 3 index sub exch Atan rotate newpath } def
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/EndArrow { @mtrx setmatrix CP grestore end } def
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/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1
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scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill
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grestore } def
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/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0
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CLW moveto } def
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/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2
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div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0
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CLW moveto } def
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/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW
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2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0
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curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto }
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def
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/SD { 0 360 arc fill } def
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/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS
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CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def
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/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
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/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
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load } if ] cvx newpath 3 1 roll T exec } def
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/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch
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cvi def } def
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/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if
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f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
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/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub
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def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def
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/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }
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ifelse { pop } repeat a } 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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and { pop pop /n n 1 sub def } if } def
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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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repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1
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ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1
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moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto
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Lineto pop pop closepath } ifelse } def
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/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul
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neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add
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def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2
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div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
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setmatrix } def
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% DG modification begin - Jan. 15, 1997
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%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {
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%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
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%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0
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%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
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%setmatrix } def
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/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup
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CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
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div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0
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d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
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% DG/SR modification begin - Jun.  1, 1998 - Patch 3 (from Michael Vulis)
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% setmatrix } def
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setmatrix pop } def
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% DG/SR modification end
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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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def } def
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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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def } def
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/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
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def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
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mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos
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abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def
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/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul
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m mul neg def } def
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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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ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }
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def
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/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
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/NC { CC x1 y1 x2 y2 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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/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
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/NAC { x2 y2 x y curveto CC x1 y1 } def
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/EAC { x2 y2 x y ArrowB curveto pop pop } def
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/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def
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    n { NC } repeat EOC } ifelse } def
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/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload
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/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop
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pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def
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/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {
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CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }
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repeat closepath pop pop } ifelse } def
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/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
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/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
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/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }
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def
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/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix
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rotate matrix concatmatrix exch findfont exch makefont setfont } def
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/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
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x1 y1 lineto closepath } def
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/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
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y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
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exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse
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/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto
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x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }
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ifelse } def
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/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add
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/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {
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pop pop Rect } { OvalFrame } ifelse } def
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/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop
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} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]
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aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
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/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6
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2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }
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ifelse } def
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/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {
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6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def
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/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1
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sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }
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def
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/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
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sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
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x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
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y0 x0 2 mul x1 sub y1 ] def } def
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/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 }
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if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if
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/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div
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round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div
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round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub
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0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def
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/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def }
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if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def }
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{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
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exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n
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div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1
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dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt {
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dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {
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pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup
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stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}
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{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i
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w add def } repeat grestore gsave n 0 gt
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% DG/SR modification begin - Nov. 7, 1997 - Patch 1
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%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
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{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
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% DG/SR modification end
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{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul
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n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n
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div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop
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1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs
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dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt
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{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g
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exch t L stroke /i i h add def } repeat grestore } def
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/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0
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1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add
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exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
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mul neg d } def
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/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
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/Rot { CP CP translate 3 -1 roll neg rotate NET  } def
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/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }
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def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle
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dup a add ] cvx def } def
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/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]
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cvx def } def
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/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
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/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
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/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
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/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
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abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
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div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
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h1 abs h sub dup s mul abs } ifelse } def
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/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
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mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
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{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
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exch } def
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/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
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/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
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} if } ifelse } def
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/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
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/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
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neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
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/IfVisible true def } def
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end
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% END pstricks.pro
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%%EndProcSet
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%%BeginProcSet: pst-dots.pro 0 0
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%!PS-Adobe-2.0
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%%Title: Dot Font for PSTricks
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%%Creator: Timothy Van Zandt <tvz@Princeton.EDU>
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%%Creation Date: May 7, 1993
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%% Version 97 patch 1, 99/12/16
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%% Modified by Etienne Riga <etienne.riga@skynet.be> - Dec. 16, 1999
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%% to add /Diamond, /SolidDiamond and /BoldDiamond
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10 dict dup begin
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  /FontType 3 def
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  /FontMatrix [ .001 0 0 .001 0 0 ] def
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  /FontBBox [ 0 0 0 0 ] def
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  /Encoding 256 array def
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  0 1 255 { Encoding exch /.notdef put } for
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  Encoding
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    dup (b) 0 get /Bullet put
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    dup (c) 0 get /Circle put
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    dup (C) 0 get /BoldCircle put
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    dup (u) 0 get /SolidTriangle put
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    dup (t) 0 get /Triangle put
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    dup (T) 0 get /BoldTriangle put
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    dup (r) 0 get /SolidSquare put
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    dup (s) 0 get /Square put
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    dup (S) 0 get /BoldSquare put
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    dup (q) 0 get /SolidPentagon put
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    dup (p) 0 get /Pentagon put
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    dup (P) 0 get /BoldPentagon put
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% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga
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    dup (l) 0 get /SolidDiamond put
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    dup (d) 0 get /Diamond put
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        (D) 0 get /BoldDiamond put
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% DG/SR modification end
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  /Metrics 13 dict def
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  Metrics begin
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    /Bullet        1000   def
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    /Circle        1000   def
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    /BoldCircle    1000   def
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    /SolidTriangle 1344   def
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    /Triangle      1344   def
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    /BoldTriangle  1344   def
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    /SolidSquare    886   def
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    /Square         886   def
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    /BoldSquare     886   def
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    /SolidPentagon 1093.2 def
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    /Pentagon      1093.2 def
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    /BoldPentagon  1093.2 def
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% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga
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    /SolidDiamond  1008   def
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    /Diamond       1008   def
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    /BoldDiamond   1008   def
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% DG/SR modification end
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    /.notdef 0 def
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  end
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  /BBoxes 13 dict def
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  BBoxes begin
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    /Circle        { -550 -550 550 550 } def
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    /BoldCircle    /Circle load def
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    /Bullet        /Circle load def
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    /Triangle      { -571.5 -330 571.5 660 } def
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    /BoldTriangle  /Triangle load def
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    /SolidTriangle /Triangle load def
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    /Square        { -450 -450 450 450 } def
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    /BoldSquare    /Square load def
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    /SolidSquare   /Square load def
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    /Pentagon      { -546.6 -465 546.6 574.7 } def
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    /BoldPentagon  /Pentagon load def
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    /SolidPentagon /Pentagon load def
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% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga
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    /Diamond       { -428.5 -742.5 428.5 742.5 } def
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    /BoldDiamond   /Diamond load def
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    /SolidDiamond  /Diamond load def
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% DG/SR modification end
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    /.notdef { 0 0 0 0 } def
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  end
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  /CharProcs 20 dict def
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  CharProcs begin
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    /Adjust {
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      2 copy dtransform floor .5 add exch floor .5 add exch idtransform
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      3 -1 roll div 3 1 roll exch div exch scale
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    } def
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    /CirclePath    { 0 0 500 0 360 arc closepath } def
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    /Bullet        { 500 500 Adjust CirclePath fill } def
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    /Circle        { 500 500 Adjust CirclePath .9 .9 scale CirclePath
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                     eofill } def
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    /BoldCircle    { 500 500 Adjust CirclePath .8 .8 scale CirclePath
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                     eofill } def
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    /BoldCircle    { CirclePath .8 .8 scale CirclePath eofill } def
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    /TrianglePath  { 0  660 moveto -571.5 -330 lineto 571.5 -330 lineto
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                     closepath } def
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    /SolidTriangle { TrianglePath fill } def
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    /Triangle      { TrianglePath .85 .85 scale TrianglePath eofill } def
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    /BoldTriangle  { TrianglePath .7 .7 scale TrianglePath eofill } def
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    /SquarePath    { -450 450 moveto 450 450 lineto 450 -450 lineto
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                     -450 -450 lineto closepath } def
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    /SolidSquare   { SquarePath fill } def
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    /Square        { SquarePath .89 .89 scale SquarePath eofill } def
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    /BoldSquare    { SquarePath .78 .78 scale SquarePath eofill } def
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    /PentagonPath  {
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      -337.8 -465   moveto
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       337.8 -465   lineto
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       546.6  177.6 lineto
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         0    574.7 lineto
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      -546.6  177.6 lineto
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      closepath
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    } def
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    /SolidPentagon { PentagonPath fill } def
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    /Pentagon      { PentagonPath .89 .89 scale PentagonPath eofill } def
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    /BoldPentagon  { PentagonPath .78 .78 scale PentagonPath eofill } def
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% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga
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    /DiamondPath   { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto
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                     428.5 0 lineto closepath } def
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    /SolidDiamond  { DiamondPath fill } def
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    /Diamond       { DiamondPath .85 .85 scale DiamondPath eofill } def
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    /BoldDiamond   { DiamondPath .7 .7 scale DiamondPath eofill } def
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% DG/SR modification end
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    /.notdef { } def
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  end
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  /BuildGlyph {
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    exch
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    begin
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      Metrics 1 index get exec 0
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      BBoxes 3 index get exec
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      setcachedevice
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      CharProcs begin load exec end
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    end
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  } def
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  /BuildChar {
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    1 index /Encoding get exch get
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    1 index /BuildGlyph get exec
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  } bind def
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end
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/PSTricksDotFont exch definefont pop
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   433
%END pst-dots.pro
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   434
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   435
%%EndProcSet
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   436
%%BeginProcSet: pst-node.pro 0 0
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   437
%!
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diff changeset
   438
% PostScript prologue for pst-node.tex.
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diff changeset
   439
% Version 97 patch 1, 97/05/09.
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diff changeset
   440
% For distribution, see pstricks.tex.
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diff changeset
   441
%
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parents:
diff changeset
   442
/tx@NodeDict 400 dict def tx@NodeDict begin
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parents:
diff changeset
   443
tx@Dict begin /T /translate load def end
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parents:
diff changeset
   444
/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }
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parents:
diff changeset
   445
if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   446
grestore } def
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parents:
diff changeset
   447
/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def
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parents:
diff changeset
   448
} def
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parents:
diff changeset
   449
/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch
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parents:
diff changeset
   450
Sin mul } def } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   451
/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def
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parents:
diff changeset
   452
} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def }
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parents:
diff changeset
   453
ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   454
dup Sin mul Cos Div } ifelse } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   455
/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub
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parents:
diff changeset
   456
/u ED /NodePos { GetRnodePos } def } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   457
/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   458
Cos mul exch Sin mul } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   459
/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h
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parents:
diff changeset
   460
mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   461
} ifelse } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   462
/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   463
ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   464
sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan
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parents:
diff changeset
   465
sin def /NodePos { TriNodePos } def } def
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parents:
diff changeset
   466
/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   467
hh mul Atan dup cos ww mul exch sin hh mul } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   468
/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   469
/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   470
Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg }
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   471
{ 0 Dist Sin mul } ifelse } ifelse Do } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   472
/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   473
exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   474
dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   475
XYPos } ifelse } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   476
/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   477
roll sin mul sub exch } ifelse } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   478
/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   479
AddOffset yA add /yA1 ED xA add /xA1 ED } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   480
/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   481
AddOffset yB add /yB1 ED xB add /xB1 ED } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   482
/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   483
AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED
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parents:
diff changeset
   484
ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   485
} ifelse } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   486
/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   487
AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   488
ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   489
} ifelse } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   490
/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   491
/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   492
known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   493
ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   494
/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   495
mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   496
/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   497
{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   498
} repeat LPutLine cleartomark } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   499
/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   500
/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   501
mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   502
sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   503
add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   504
y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   505
mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   506
/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   507
} def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   508
/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   509
/NAngle yyB yyA sub xxB xxA sub Atan def } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   510
/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd  } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   511
/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   512
} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   513
} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   514
} def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   515
/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   516
} def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   517
/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   518
/NAngle yyB yyA sub xxB xxA sub Atan def } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   519
/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd  } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   520
/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   521
} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   522
exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   523
VPosEnd  } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   524
/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   525
roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   526
def grestore exec /LPutVar /SaveLPutVar load def } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   527
/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   528
GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   529
LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   530
LPutVar VPutLine } def LPutVar } def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   531
/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   532
end } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   533
/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   534
Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   535
/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   536
yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos {
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   537
LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   538
ifelse } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   539
/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   540
roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   541
GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   542
begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   543
cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   544
} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   545
/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   546
def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   547
itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   548
yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   549
yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   550
/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   551
/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   552
yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   553
/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   554
tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ]
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   555
cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   556
VPutLines } def } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   557
/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   558
xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   559
transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def }
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   560
{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   561
0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   562
begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   563
def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   564
VPutLines } def } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   565
/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   566
xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   567
/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   568
LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   569
def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   570
/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   571
GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   572
false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   573
LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   574
def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   575
/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   576
def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   577
mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   578
mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   579
xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   580
Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   581
cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   582
VPutLines } def } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   583
% DG/SR modification begin - May 9, 1997 - Patch 1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   584
%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   585
%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   586
%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   587
%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   588
/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   589
r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   590
exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   591
mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   592
% DG/SR modification end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   593
} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   594
AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   595
Div def /y ED /x ED } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   596
/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   597
180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   598
mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   599
/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   600
add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   601
{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   602
tx@Dict begin false Polygon end } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   603
/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   604
def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   605
mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   606
/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   607
def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   608
GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   609
sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   610
eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn }
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   611
{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   612
0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   613
roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   614
0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   615
roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat }
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   616
ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   617
{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le {
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   618
r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC }
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   619
{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   620
add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   621
mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   622
sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   623
y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos {
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   624
LPutPos } def } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   625
/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   626
sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   627
ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   628
w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   629
{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   630
{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   631
def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   632
/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   633
/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   634
exch X sub neg exch moveto setmatrix CP grestore } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   635
/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   636
def } ifelse LPutCoor  } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   637
/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg }
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   638
if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop }
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   639
ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED }
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   640
def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   641
/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   642
r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop }
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   643
ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED }
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   644
def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   645
end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   646
% END pst-node.pro
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   647
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   648
%%EndProcSet
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   649
%%BeginProcSet: pst-text.pro 0 0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   650
%!
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   651
% PostScript header file pst-text.pro
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   652
% Version 97, 94/04/20; patched MV 10-09-99 00:36
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   653
% For distribution, see pstricks.tex.
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   654
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   655
/tx@TextPathDict 40 dict def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   656
tx@TextPathDict begin
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   657
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   658
% Syntax:  <dist> PathPosition -
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   659
% Function: Searches for position of currentpath distance <dist> from
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   660
%           beginning. Sets (X,Y)=position, and Angle=tangent.
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   661
/PathPosition
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   662
{ /targetdist exch def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   663
  /pathdist 0 def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   664
  /continue true def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   665
  /X { newx } def /Y { newy } def /Angle 0 def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   666
  gsave
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   667
    flattenpath
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   668
    { movetoproc }  { linetoproc } { } { firstx firsty linetoproc }
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   669
    /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   670
  grestore
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   671
} def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   672
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   673
/movetoproc { continue { @movetoproc } { pop pop } ifelse } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   674
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   675
/@movetoproc
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   676
{ /newy exch def /newx exch def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   677
  /firstx newx def /firsty newy def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   678
} def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   679
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   680
/linetoproc { continue { @linetoproc } { pop pop } ifelse } def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   681
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   682
/@linetoproc
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   683
{
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   684
  /oldx newx def /oldy newy def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   685
  /newy exch def /newx exch def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   686
  /dx newx oldx sub def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   687
  /dy newy oldy sub def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   688
  /dist dx dup mul dy dup mul add sqrt def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   689
  /pathdist pathdist dist add def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   690
  pathdist targetdist ge
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   691
  { pathdist targetdist sub dist div dup
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   692
    dy mul neg newy add /Y exch def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   693
    dx mul neg newx add /X exch def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   694
    /Angle dy dx atan def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   695
    /continue false def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   696
  } if
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   697
} def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   698
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   699
/TextPathShow
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   700
{ /String exch def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   701
  /CharCount 0 def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   702
  String length
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   703
  { String CharCount 1 getinterval ShowChar
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   704
    /CharCount CharCount 1 add def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   705
  } repeat
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   706
} def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   707
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   708
% Syntax: <pathlength> <position> InitTextPath -
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   709
/InitTextPath
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   710
{ gsave
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   711
    currentpoint /Y exch def /X exch def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   712
    exch X Hoffset sub sub mul
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   713
    Voffset Hoffset sub add
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   714
    neg X add /Hoffset exch def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   715
    /Voffset Y def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   716
  grestore
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   717
} def
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parents:
diff changeset
   718
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parents:
diff changeset
   719
/Transform
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parents:
diff changeset
   720
{ PathPosition
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   721
  dup
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   722
  Angle cos mul Y add exch
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   723
  Angle sin mul neg X add exch
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   724
  translate
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   725
  Angle rotate
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   726
} def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   727
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   728
/ShowChar
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   729
{ /Char exch def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   730
  gsave
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   731
    Char end stringwidth
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   732
    tx@TextPathDict begin
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   733
    2 div /Sy exch def 2 div /Sx exch def
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parents:
diff changeset
   734
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Christian Urban <urbanc@in.tum.de>
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diff changeset
   735
%%%  MV 10-09-99 00:36
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parents:
diff changeset
   736
    /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   737
%   currentpoint
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parents:
diff changeset
   738
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   739
    Voffset sub Sy add exch
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Christian Urban <urbanc@in.tum.de>
parents:
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   740
    Hoffset sub Sx add
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Christian Urban <urbanc@in.tum.de>
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diff changeset
   741
    Transform
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   742
    Sx neg Sy neg moveto
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   743
    Char end tx@TextPathSavedShow
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Christian Urban <urbanc@in.tum.de>
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   744
    tx@TextPathDict begin
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   745
  grestore
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   746
  Sx 2 mul Sy 2 mul rmoveto
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   747
} def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   748
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   749
end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   750
% END pst-text.pro
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   751
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Christian Urban <urbanc@in.tum.de>
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diff changeset
   752
%%EndProcSet
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Christian Urban <urbanc@in.tum.de>
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diff changeset
   753
%%BeginProcSet: 8r.enc 0 0
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diff changeset
   754
% File 8r.enc  TeX Base 1 Encoding  Revision 2.0  2002-10-30
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diff changeset
   755
%
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   756
% @@psencodingfile@{
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parents:
diff changeset
   757
%   author    = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry,
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parents:
diff changeset
   758
%                W. Schmidt, P. Lehman",
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Christian Urban <urbanc@in.tum.de>
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diff changeset
   759
%   version   = "2.0",
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   760
%   date      = "30 October 2002",
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   761
%   filename  = "8r.enc",
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   762
%   email     = "tex-fonts@@tug.org",
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   763
%   docstring = "This is the encoding vector for Type1 and TrueType
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   764
%                fonts to be used with TeX.  This file is part of the
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Christian Urban <urbanc@in.tum.de>
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diff changeset
   765
%                PSNFSS bundle, version 9"
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   766
% @}
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   767
% 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   768
% The idea is to have all the characters normally included in Type 1 fonts
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   769
% available for typesetting. This is effectively the characters in Adobe
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   770
% Standard encoding, ISO Latin 1, Windows ANSI including the euro symbol,
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   771
% MacRoman, and some extra characters from Lucida.
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   772
% 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   773
% Character code assignments were made as follows:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   774
% 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   775
% (1) the Windows ANSI characters are almost all in their Windows ANSI
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   776
% positions, because some Windows users cannot easily reencode the
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   777
% fonts, and it makes no difference on other systems. The only Windows
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   778
% ANSI characters not available are those that make no sense for
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   779
% typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   780
% (173). quotesingle and grave are moved just because it's such an
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   781
% irritation not having them in TeX positions.
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   782
% 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   783
% (2) Remaining characters are assigned arbitrarily to the lower part
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   784
% of the range, avoiding 0, 10 and 13 in case we meet dumb software.
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   785
% 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   786
% (3) Y&Y Lucida Bright includes some extra text characters; in the
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   787
% hopes that other PostScript fonts, perhaps created for public
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   788
% consumption, will include them, they are included starting at 0x12.
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   789
% These are /dotlessj /ff /ffi /ffl.
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   790
% 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   791
% (4) hyphen appears twice for compatibility with both ASCII and Windows.
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   792
%
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   793
% (5) /Euro was assigned to 128, as in Windows ANSI
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   794
%
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   795
% (6) Missing characters from MacRoman encoding incorporated as follows:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   796
%
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   797
%     PostScript      MacRoman        TeXBase1
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   798
%     --------------  --------------  --------------
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   799
%     /notequal       173             0x16
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   800
%     /infinity       176             0x17
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   801
%     /lessequal      178             0x18
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   802
%     /greaterequal   179             0x19
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   803
%     /partialdiff    182             0x1A
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   804
%     /summation      183             0x1B
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   805
%     /product        184             0x1C
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   806
%     /pi             185             0x1D
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   807
%     /integral       186             0x81
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   808
%     /Omega          189             0x8D
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   809
%     /radical        195             0x8E
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   810
%     /approxequal    197             0x8F
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   811
%     /Delta          198             0x9D
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   812
%     /lozenge        215             0x9E
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   813
%
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   814
/TeXBase1Encoding [
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   815
% 0x00
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   816
 /.notdef /dotaccent /fi /fl
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   817
 /fraction /hungarumlaut /Lslash /lslash
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   818
 /ogonek /ring /.notdef /breve
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   819
 /minus /.notdef /Zcaron /zcaron
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   820
% 0x10
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   821
 /caron /dotlessi /dotlessj /ff
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   822
 /ffi /ffl /notequal /infinity
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   823
 /lessequal /greaterequal /partialdiff /summation
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   824
 /product /pi /grave /quotesingle
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   825
% 0x20
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   826
 /space /exclam /quotedbl /numbersign
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   827
 /dollar /percent /ampersand /quoteright
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   828
 /parenleft /parenright /asterisk /plus
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   829
 /comma /hyphen /period /slash
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   830
% 0x30
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   831
 /zero /one /two /three
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   832
 /four /five /six /seven
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   833
 /eight /nine /colon /semicolon
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   834
 /less /equal /greater /question
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   835
% 0x40
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   836
 /at /A /B /C
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   837
 /D /E /F /G
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   838
 /H /I /J /K
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   839
 /L /M /N /O
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   840
% 0x50
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   841
 /P /Q /R /S
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   842
 /T /U /V /W
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   843
 /X /Y /Z /bracketleft
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   844
 /backslash /bracketright /asciicircum /underscore
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   845
% 0x60
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   846
 /quoteleft /a /b /c
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   847
 /d /e /f /g
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   848
 /h /i /j /k
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   849
 /l /m /n /o
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   850
% 0x70
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   851
 /p /q /r /s
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   852
 /t /u /v /w
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   853
 /x /y /z /braceleft
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   854
 /bar /braceright /asciitilde /.notdef
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   855
% 0x80
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   856
 /Euro /integral /quotesinglbase /florin
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   857
 /quotedblbase /ellipsis /dagger /daggerdbl
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   858
 /circumflex /perthousand /Scaron /guilsinglleft
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   859
 /OE /Omega /radical /approxequal
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   860
% 0x90
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   861
 /.notdef /.notdef /.notdef /quotedblleft
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   862
 /quotedblright /bullet /endash /emdash
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   863
 /tilde /trademark /scaron /guilsinglright
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   864
 /oe /Delta /lozenge /Ydieresis
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   865
% 0xA0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   866
 /.notdef /exclamdown /cent /sterling
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   867
 /currency /yen /brokenbar /section
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   868
 /dieresis /copyright /ordfeminine /guillemotleft
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   869
 /logicalnot /hyphen /registered /macron
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   870
% 0xD0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   871
 /degree /plusminus /twosuperior /threesuperior
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   872
 /acute /mu /paragraph /periodcentered
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   873
 /cedilla /onesuperior /ordmasculine /guillemotright
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   874
 /onequarter /onehalf /threequarters /questiondown
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   875
% 0xC0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   876
 /Agrave /Aacute /Acircumflex /Atilde
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   877
 /Adieresis /Aring /AE /Ccedilla
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   878
 /Egrave /Eacute /Ecircumflex /Edieresis
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   879
 /Igrave /Iacute /Icircumflex /Idieresis
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   880
% 0xD0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   881
 /Eth /Ntilde /Ograve /Oacute
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   882
 /Ocircumflex /Otilde /Odieresis /multiply
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   883
 /Oslash /Ugrave /Uacute /Ucircumflex
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   884
 /Udieresis /Yacute /Thorn /germandbls
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   885
% 0xE0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   886
 /agrave /aacute /acircumflex /atilde
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   887
 /adieresis /aring /ae /ccedilla
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   888
 /egrave /eacute /ecircumflex /edieresis
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   889
 /igrave /iacute /icircumflex /idieresis
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   890
% 0xF0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   891
 /eth /ntilde /ograve /oacute
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   892
 /ocircumflex /otilde /odieresis /divide
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   893
 /oslash /ugrave /uacute /ucircumflex
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   894
 /udieresis /yacute /thorn /ydieresis
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   895
] def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   896
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   897
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   898
%%EndProcSet
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   899
%%BeginProcSet: texmital.enc 0 0
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   900
% TeX math italic encoding.
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   901
% No ligatures or kerns.
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   902
% 
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   903
/TeXMathItalicEncoding [          % now 256 chars follow
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   904
% 0x0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   905
/Gamma
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   906
/Delta
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   907
/Theta
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   908
/Lambda
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   909
/Xi
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   910
/Pi
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   911
/Sigma
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   912
/Upsilon
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   913
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   914
% 0x8
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   915
/Phi
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   916
/Psi
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   917
/Omega
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   918
/alpha
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   919
/beta
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   920
/gamma
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   921
/delta
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   922
/epsilon1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   923
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   924
% 0x10
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   925
/zeta
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   926
/eta
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   927
/theta
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   928
/iota
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   929
/kappa
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   930
/lambda
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   931
/mu
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   932
/nu
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   933
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   934
% 0x18
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   935
/xi
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   936
/pi
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   937
/rho
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   938
/sigma
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   939
/tau
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   940
/upsilon
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   941
/phi
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   942
/chi
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   943
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   944
% 0x20
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   945
/psi
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   946
/omega
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   947
/epsilon
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   948
/theta1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   949
/pi1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   950
/rho1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   951
/sigma1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   952
/phi1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   953
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   954
% 0x28
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   955
/arrowlefttophalf
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   956
/arrowleftbothalf
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   957
/arrowrighttophalf
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   958
/arrowrightbothalf
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   959
/arrowhookleft
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   960
/arrowhookright
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   961
/triangleright
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   962
/triangleleft
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   963
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   964
% 0x30
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   965
/zerooldstyle
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   966
/oneoldstyle
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   967
/twooldstyle
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   968
/threeoldstyle
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   969
/fouroldstyle
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   970
/fiveoldstyle
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   971
/sixoldstyle
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   972
/sevenoldstyle
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   973
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   974
% 0x38
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   975
/eightoldstyle
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   976
/nineoldstyle
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   977
/period
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   978
/comma
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   979
/less
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   980
/slash
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   981
/greater
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   982
/star
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   983
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   984
% 0x40
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   985
/partialdiff
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   986
/A
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   987
/B
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   988
/C
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   989
/D
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   990
/E
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   991
/F
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   992
/G
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   993
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   994
% 0x48
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   995
/H
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   996
/I
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   997
/J
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   998
/K
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
   999
/L
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1000
/M
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1001
/N
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1002
/O
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1003
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1004
% 0x50
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1005
/P
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1006
/Q
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1007
/R
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1008
/S
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1009
/T
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1010
/U
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1011
/V
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1012
/W
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1013
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1014
% 0x58
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1015
/X
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1016
/Y
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1017
/Z
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1018
/flat
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1019
/natural
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1020
/sharp
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1021
/slurbelow
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1022
/slurabove
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1023
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1024
% 0x60
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1025
/lscript
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1026
/a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1027
/b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1028
/c
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1029
/d
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1030
/e
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1031
/f
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1032
/g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1033
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1034
% 0x68
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1035
/h
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1036
/i
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1037
/j
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1038
/k
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1039
/l
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1040
/m
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1041
/n
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1042
/o
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1043
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1044
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parents:
diff changeset
  1045
/p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1046
/q
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1047
/r
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1048
/s
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1049
/t
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1050
/u
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1051
/v
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1052
/w
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1053
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1054
% 0x78
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1055
/x
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1056
/y
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1057
/z
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1058
/dotlessi
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1059
/dotlessj
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1060
/weierstrass
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1061
/vector
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1062
/tie
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1063
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1064
% Have to have 128 .notdef's now to fill things out.
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1065
% 
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1066
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1067
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1068
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1069
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1070
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1071
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1072
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1073
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1074
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1075
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1076
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1077
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1078
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1079
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1080
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1081
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1082
] def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1083
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Christian Urban <urbanc@in.tum.de>
parents:
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  1084
%%EndProcSet
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1085
%%BeginProcSet: texps.pro 0 0
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1086
%!
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1087
TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1088
index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1089
exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]FontType 0
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1090
ne{/Metrics exch def dict begin Encoding{exch dup type/integertype ne{
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1091
pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1092
div def}ifelse}forall Metrics/Metrics currentdict end def}{{1 index type
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1093
/nametype eq{exit}if exch pop}loop}ifelse[2 index currentdict end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1094
definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{dup
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1095
sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1096
mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1097
exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}if}
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1098
forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}def
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1099
end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1100
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1101
%%EndProcSet
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1102
%%BeginProcSet: special.pro 0 0
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1103
%!
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1104
TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1105
/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1106
/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1107
/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1108
/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1109
X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1110
/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1111
/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1112
{userdict/md get type/dicttype eq{userdict begin md length 10 add md
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1113
maxlength ge{/md md dup length 20 add dict copy def}if end md begin
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1114
/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1115
atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1116
itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1117
transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1118
curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1119
pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1120
if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1121
-1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1122
get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1123
yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1124
neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1125
noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1126
90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1127
neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1128
1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1129
2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1130
-1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1131
TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1132
Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1133
}if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1134
save N userdict maxlength dict begin/magscale true def normalscale
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1135
currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1136
/psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1137
psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1138
psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1139
TR/showpage{}N/erasepage{}N/setpagedevice{pop}N/copypage{}N/p 3 def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1140
@MacSetUp}N/doclip{psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1141
newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1142
closepath clip newpath moveto}N/endTexFig{end psf$SavedState restore}N
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1143
/@beginspecial{SDict begin/SpecialSave save N gsave normalscale
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1144
currentpoint TR @SpecialDefaults count/ocount X/dcount countdictstack N}
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1145
N/@setspecial{CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1146
neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1147
rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1148
scale llx neg lly neg TR}{rhiSeen{rhi ury lly sub div dup scale llx neg
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1149
lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1150
ury lineto llx ury lineto closepath clip}if/showpage{}N/erasepage{}N
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1151
/setpagedevice{pop}N/copypage{}N newpath}N/@endspecial{count ocount sub{
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1152
pop}repeat countdictstack dcount sub{end}repeat grestore SpecialSave
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1153
restore end}N/@defspecial{SDict begin}N/@fedspecial{end}B/li{lineto}B
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1154
/rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1155
setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1156
moveto}N/ellipse{/endangle X/startangle X/yrad X/xrad X/savematrix
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1157
matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1158
savematrix setmatrix}N end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1159
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1160
%%EndProcSet
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1161
%%BeginProcSet: color.pro 0 0
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1162
%!
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1163
TeXDict begin/setcmykcolor where{pop}{/setcmykcolor{dup 10 eq{pop
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1164
setrgbcolor}{1 sub 4 1 roll 3{3 index add neg dup 0 lt{pop 0}if 3 1 roll
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1165
}repeat setrgbcolor pop}ifelse}B}ifelse/TeXcolorcmyk{setcmykcolor}def
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1166
/TeXcolorrgb{setrgbcolor}def/TeXcolorgrey{setgray}def/TeXcolorgray{
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1167
setgray}def/TeXcolorhsb{sethsbcolor}def/currentcmykcolor where{pop}{
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1168
/currentcmykcolor{currentrgbcolor 10}B}ifelse/DC{exch dup userdict exch
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1169
known{pop pop}{X}ifelse}B/GreenYellow{0.15 0 0.69 0 setcmykcolor}DC
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1170
/Yellow{0 0 1 0 setcmykcolor}DC/Goldenrod{0 0.10 0.84 0 setcmykcolor}DC
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1171
/Dandelion{0 0.29 0.84 0 setcmykcolor}DC/Apricot{0 0.32 0.52 0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1172
setcmykcolor}DC/Peach{0 0.50 0.70 0 setcmykcolor}DC/Melon{0 0.46 0.50 0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1173
setcmykcolor}DC/YellowOrange{0 0.42 1 0 setcmykcolor}DC/Orange{0 0.61
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1174
0.87 0 setcmykcolor}DC/BurntOrange{0 0.51 1 0 setcmykcolor}DC
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1175
/Bittersweet{0 0.75 1 0.24 setcmykcolor}DC/RedOrange{0 0.77 0.87 0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1176
setcmykcolor}DC/Mahogany{0 0.85 0.87 0.35 setcmykcolor}DC/Maroon{0 0.87
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1177
0.68 0.32 setcmykcolor}DC/BrickRed{0 0.89 0.94 0.28 setcmykcolor}DC/Red{
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1178
0 1 1 0 setcmykcolor}DC/OrangeRed{0 1 0.50 0 setcmykcolor}DC/RubineRed{
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1179
0 1 0.13 0 setcmykcolor}DC/WildStrawberry{0 0.96 0.39 0 setcmykcolor}DC
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1180
/Salmon{0 0.53 0.38 0 setcmykcolor}DC/CarnationPink{0 0.63 0 0
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1181
setcmykcolor}DC/Magenta{0 1 0 0 setcmykcolor}DC/VioletRed{0 0.81 0 0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1182
setcmykcolor}DC/Rhodamine{0 0.82 0 0 setcmykcolor}DC/Mulberry{0.34 0.90
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1183
0 0.02 setcmykcolor}DC/RedViolet{0.07 0.90 0 0.34 setcmykcolor}DC
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1184
/Fuchsia{0.47 0.91 0 0.08 setcmykcolor}DC/Lavender{0 0.48 0 0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1185
setcmykcolor}DC/Thistle{0.12 0.59 0 0 setcmykcolor}DC/Orchid{0.32 0.64 0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1186
0 setcmykcolor}DC/DarkOrchid{0.40 0.80 0.20 0 setcmykcolor}DC/Purple{
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1187
0.45 0.86 0 0 setcmykcolor}DC/Plum{0.50 1 0 0 setcmykcolor}DC/Violet{
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1188
0.79 0.88 0 0 setcmykcolor}DC/RoyalPurple{0.75 0.90 0 0 setcmykcolor}DC
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1189
/BlueViolet{0.86 0.91 0 0.04 setcmykcolor}DC/Periwinkle{0.57 0.55 0 0
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1190
setcmykcolor}DC/CadetBlue{0.62 0.57 0.23 0 setcmykcolor}DC
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1191
/CornflowerBlue{0.65 0.13 0 0 setcmykcolor}DC/MidnightBlue{0.98 0.13 0
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1192
0.43 setcmykcolor}DC/NavyBlue{0.94 0.54 0 0 setcmykcolor}DC/RoyalBlue{1
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1193
0.50 0 0 setcmykcolor}DC/Blue{1 1 0 0 setcmykcolor}DC/Cerulean{0.94 0.11
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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861E6A4520A9D0BA362E18F28432FC1B5AEB41F6598B3C018762A9D351438D8D
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Christian Urban <urbanc@in.tum.de>
parents:
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  1839
973B5A82E38C8DB913BDEB321FE99537EF6F68BF8D3AC972C91E47BBE4895720
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Christian Urban <urbanc@in.tum.de>
parents:
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  1840
42F0062C243E11C1B6D9A37D58A2801C8A8574D3CAC43324D6A3420874C7BD81
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Christian Urban <urbanc@in.tum.de>
parents:
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  1841
78D867C31527077D02D4F0492CFD97EEBAA7E57D455A6042840869B9745A3F46
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1842
5647BB39558364DD65D08F12EC94429886039D97B3BF555B9367B79DDD7ACF0A
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1843
8D8148007254DDF754A2B276754BCFABAE482C88C16E0E06767EC56616B6B87E
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Christian Urban <urbanc@in.tum.de>
parents:
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  1844
A5C0629C37ABA31B2056EDADF919A218FEC6267882BE4B7D94E399100EDC4702
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1845
8E711D53685D7999C70365FE5A36CF32A5C386BB2E6987F80885E34E4037E170
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1846
B62916C28B1E4F16CD3990C8C0A80A75F39D2442912CCDA6662C24BD6E19553D
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1847
C42A815FD0404130566785045F287E415AECEFF08E60189289F59ED43AA1F069
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1848
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1849
E0AD3096776C0CADE617EA95F69292F43A7F1FBB6EA44F8AE0E8EFBC166076CC
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Christian Urban <urbanc@in.tum.de>
parents:
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  1850
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1851
D909F70FBBE5A14A93BA90150E14346B2ADF61108469CABA51A5D6A159D7D922
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1852
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1853
4718D58F965B810CA23A9919FBBC946CA5D27008E31B6171C58314A64A072C26
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1854
4317D3DDF4EC782E19E3F722FD2353DA9C06B91610E5EB64DB8EBF0EAB026B8C
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1855
98F2F9EA2B983CF4ED20D916AEB46ED56936EB84D0DC1E2356331B9A6EA4F544
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1856
AB081D9E202A0B24D572EBE57C327B180F09E09F95621FF4F402AC0254023256
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1857
8198429A2ACA8D090AB8A44C66DDAB8A40559E9418A264F013400B01A1573942
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1858
576704DD90ABC902843EA28DC2934C2A8907004013722F0CEDDE391E7507035C
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1859
65F84CF79365042C064FF3F3F4029C4A8FD472401B7F5C5286A97E33194C8F2C
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1860
8DCC9D35440EC4B436D1BB82FED68D2335D797E4E6CEA5DEF1D95F746336F678
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1861
D34F85F3DF8BBBA0AF71686334EC9C3292101A126A4927F9727D8BB4C0B5B6E0
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1862
53331B83C3E67E84199B34469CA8E2D6D0E19B512A824055176959A39E5A47E8
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1863
750743F582C1048D1E77B1C4D4A9AE1A358BF2ED38D16E9F1CF7B821FE3852EE
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1864
DB33FCE3545ED77AB19922243DE3912B03BD9453D897D4CBAD7F8FE89BCAECA7
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1865
19042777F198B034D707475CA8B32A31B62CA1061535E707C4B0C2E80EB7B9F1
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1866
EA4A6B7318C5DE6CE88480672002EAD7F150C47EDB3EF3DF6E07814BB878592C
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1867
FBE230414A12BD9283D172C395C80F6EB87E51C0E26593C83511A0B53F0B7CC7
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1868
35BB7DDD628E7FDCD8F082A7FDA593128442B5A8713D78F437DAE501E0DAB00A
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1869
652FB0610C15AF62BE4B1AF0F72CFEF1E97CD1E3848C5E8FB4F1AEB77A3409AC
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1870
0F8A206508DD63F31B0D24D7E42904938194B217D48ED43D0C40E40F36ABC409
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1871
D3C55B358D87276A2DC109F3D5E3ADC20668DA41E10BF6DBA79F10D86002B263
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1872
558DF5529F6002D8DF300AC3D1EEF224FDF44947568F27718EAAD1535147B4A2
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1873
9ADEF4752DA8E2D4FEC6FAC065DA86D5C8FE30D80B7689894039FEB06E07F0F5
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1874
A04C8445B08800D5FA721FB3847B54CF717DA7FC966DE8EE390F566887742086
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1875
3BD95020BFD1ADDE18910A1BC4CCD59F625B600E507735D99DEB8C9453636DCE
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1876
E6791F4778E1905B202CADA9A18BEC37B23FEA36A6D2E4082F286DF51C04E958
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1877
96AD00509DE31ACF86C3E6680967BEFC19A7F14DB63E3085001A19CB52DD5BAD
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1878
7EAED09EA68714A188FA27C32FE31B92C7AF1AEC8350BE093B28D8D3982AC7EC
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1879
1A2E485FDB6A572D1954C06B5B6E8BD5D40BF0C88DE923E0952DC265C3D73710
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1880
B98B870EF4BC374D7CA7C041075893DE2C672F223844303ACAC64B2C9BB41B5B
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1881
E695B4B2DC916E737E380020FA346BF944CBBB0EFB0B79912761392A5A16A934
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1882
FC0001905162C79FF46C64C2573C670C39EE5F2539953630140EF489480F7F9F
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1883
DFD2061D1BCFA0CA0100CFECB35740B06D5A3C9000A52A2358BA9D4523C4E571
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1884
5085322BE54A6F628D19450676D1F15589343A95666B1742CB2CE5C8DC73458B
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1885
DA9F31F18855AE99240AB64C04B3D2948B29D5583F9737A602E20B6AB94B0AEF
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1886
C636FD1F01D5B949A2AAE2F68D56ED9082064773008EA9263EA4CC4A5415F960
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1887
F568A9B6B4969C4AFA16FFB02900785C1CD0029916588EE8372E36DBEE6440AA
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1888
DD439A69BCD38D043BAB037FA91EAE9234733F1542DFE6023750D7A382EB4527
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1889
EBF34F6281D9F1BBC551F445D4986E06BE40C32439DE2BAE6A748BE3328D1FC1
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1890
1C3A962E00EECF73E62E6B4677DFEEFB763CD38B31141CD882FCA67E71D2BF6B
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1891
DD14F448C62DB1FF0593AD223F907227AD8B8A622F1D70DA62DB649228D0CC22
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1892
B60DE73B07454C48469821B47902A87DFA8EB3A012F0A550F5F998B8095538CE
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1893
DE528C08D3F7C4137266B6EED5005255E4BAE46297AF1EC08BE90503FCD0EBCF
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1894
64E160DC2923D70DA7909D655B510810957D9C954A9A08A6BD3E3E216D9B40EA
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1895
0D25F4120BEC143B787E51F109AD1841ED1B6F2AE894C9EF161812025FE586A6
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1896
B3AE666A8EC6706F748AA9E2269D0AF9519BB56825C9E16BB7FE8FBA185DE3CF
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1897
42C7BB61DD234EA97302FE1D08141925CAE5ABD47F9E9506496D85500956B060
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1898
23496A437F4C0267ECB82809F7C3AECFCCEAAB42EC6429399B96D0D81018021E
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1899
B83F68206542BA63AEBDCD99CDA2EBAD81EB74ABA3FB44390AF79411383F4872
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1900
2969EF6D58016F5E1CB5DD6F5012EB533A27A13616C7C1DAAD39CF7EA5E9D5F1
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1901
76F1EE9F81371ACB1A50DE60C3EC4AB85687CA6E23E8C654B54165434C40AF8A
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1902
9AD741A0293144B4E2556CC55007FC2E3FE1BE1232B0011784682D603DF1FE2A
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1903
A9889F36B7DAF399292EBBB2AC6D2A16460E1CCF8230B9481D65D05E8A8B853B
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1904
0707776E4D2FEDA62845FE86B05A6C0ADB240CCC5CA1548E87908C97CC7073F9
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1905
E1DA8D2C1F5874A747B4264A52580B9AD1F13915702E7B70044D909249715A3C
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1906
76D577DF44CFC6D5C8D9F2DE8E188E68EA7D6BEB2766F720A7CE1161EA85C984
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1907
9DDA8DB90815278CD8D8FEB390743E65113EEDA291EBB7C5EF87213FEB253759
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1908
CB058A3BA22F7A6096BA798024968D6D08801D5BE037808ECFC55EB9C0B904FF
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1909
BA59C4C961DC2B4F08E7B6C2814B4A8F23C1276D8F56B038903300C094B0DAA7
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1910
9BE8E12967564B5646679273F08A68F978A29B6696B1DAC160F6AC788C12F0B9
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1911
FEDBE572C516F22C8BE553D6A9A54805C12C5DD709FA0C3DAB82C4C0FF0727D4
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1912
E139CD181B1187C384B0E4DFF4292D8BC5526443B7D7FDE9E984F9E05C4A423C
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1913
5307C1EA3EA969DFE6E2B1749F3E452D7883B6F0902886B26997EBD6AD3639C4
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1914
6F75DD366B8EFD4679C2776CFB702D2A95344A9BC70FC0A82E330F976170E268
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1915
DBA2E9DC931FD10EEC123712BF8D64BC09C5A78331768D903F5355F9E8BECF1C
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1916
10042299AD67E2BB7E26A7B14EA7A9F393941973C45370300CE2204398D87107
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1917
63E1DF9D11EF132FAD820CC2E6EEF9B03DD2A0E02BA76861C00B16BF8E3A1DDE
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1918
C57B60ACC0EF251D5FF4A41E8376EE0D3D23EE87BEBB07CC24B93784584D5BDB
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1919
000ABB16E1DB1AFCDB590B762B8332FAF201669D88810F9E86F2D3FB45B5CC63
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1920
4B20C81136E82E17ABCABC74510CAAA1F15516BACD282BFA25F266DABC558583
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1921
E31F99DC199394AC604C8B698703D54487BB6751F5C237BDD4E0DFEA74F5CFB1
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1922
AFAE06A7761ECB1404099622952814EADE8BDA68C6A4B16800929D3695A86C50
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1923
9B7E78A19AC2CC0D7F6A28E98D7298DFF5701CCD150690629870F72A9CFFC6F1
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1924
7657326D1F57430FB509DD1B7C4614E654B2DC0060F27F1607EEAEEE72C83644
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1925
649F9FDFE3740F6BAE7A003591C0629711C80D902E624F84ADE874213BA64DFF
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1926
AEAC80EB65F8D9F6BFF432FF4F8C455E57CB765AA71A35EB78A257266C8735BD
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1927
7A478FE3FCD6E0AA2A4A570416D132E5AAB635E58AE9E2893724363FCF724080
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1928
E3E622FFEFE1D39AA8281BD686570B1D68E6D014F62E60D610A006458A52B68E
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1929
70AEE5B03776701582D6AAB2554553382AE077015496ED84A0BF220FD58CBB89
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1930
E106AD20502C15D1BC3BAC0EC1C88E1B8E17BB8A1F2BF8DE3D10B76A78D293EA
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1931
4C2A251E7F1CEAEFAD514F72C97D2253FE85013FC2002F3E4566DC6CF0FECA96
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1932
3313A6116BCCFA2DBBA1AECB7EE71B39A2AB8569DF8773E244EADC53C225715D
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1933
D3DDDD73D1F52A054F58F44AFB3CFFB707907DE04FAEB773FF97EC8687D9562E
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1934
1FB2D410C3641A9DD3F93DC50AAF0543911F5A2111998DADBD19F0FCD0DBE37F
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1935
FA29C26F5FABDC97DEE6C2221B41B08D749B3DD924E2833DE9640D00FDA81FA3
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1936
CD4C2CA217344E5E08B50BB114FC43FA19D95739B18EB123A21F809CC45C3A51
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1937
13D261399370B11C563614331E84AE575DFD87FF839A647776122A26396D18FF
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1938
04272348BD356D093A434EC3F585569372B6FFD4B9ED293B2B3075C52F79913A
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1939
E016CE84FEE1C6B0D3A017DA8DBA26839E92768D1B63A7BFB1A7C9711B2FD906
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1940
44D4E80D56DDEAE470B65D0B50EDC2111F56A29A05C0E33CC49AD1AB495B6BF1
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1941
6C19BEC346A0D849107B5F6378A12301EE8AF0235D45A0DC38FFCE9C0F018E7B
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1942
D0C754397B77C095C5EA7F5C6840FF86F555D9E37214F8A0C0AC392A2F772A1E
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1943
2EC1384B05B1A07F9FA3E5C5FB62128B2212BC6C9E13542E664BEE61261E2F26
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1944
91CAC7836D810D1E7E168A0CFF460F10697B7EC03590483084E6387ADBB3272A
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1945
2A3788239CA75B277B4F0B316B93C7C395BC6BC67B508008DDACB32FD5EC5EE4
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1946
9F1BDA5B266E5ED44110DD484DC5E7EDA7ECB838544E237A4A152C594F51CCA0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1947
C74232159C628C8FE4D053D7EE4FB491A8414A1F39963569F4059D70593B2C61
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1948
9C759F9B6EE43E7C6DA3486849BF991781E42FB932BE8E00DC5AE496CA8E5304
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1949
CD3ED99ABBB426D737F5A69DDA1F32983EE51FD50E1B7F6C8FB02183D346708D
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1950
7FCCC28567EAA68E25D89F0D913DF2C4F3DCD907E852536B2D2165EE00C9EB7C
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1951
8226061AA07B3AACC0C5D3656A70F3B7E7CFBB6704953902395B2F366B0F7A1D
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1952
F0F27A5290B7B58EA6764CC04EB63AC30B332C89099707BCDF24BA4B41EE53A6
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1953
9034BA6014B7390065AB935539EDAC4EAFFDAD01849C619CF8F8BB584FB48643
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1954
3F301A647E4BAEC63F381286FD04D790603A0C8A11BACC9CFC5D1CECFE594149
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1955
0D70656F61783CAA260024C5E5C85ED933581E693BF2CFB2BC09A63A0906A5E0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1956
5ECC01B06FCAD645279312DCE4B679812D97C24884CA6BA46811FA55F4C01029
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1957
7DFB2F4AD5C11ABA4A0953262C97138BCC81AFA856539B303EFD6806D5147507
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1958
0B49AEC1C0CB000CC1551770EAC39ED55DAD3319A79D4DDC20778FAD4301C2C9
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1959
B7FBDBB8C263B6E170603083848F47788EC1A69C54CF7B695DB55EB1215E4557
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1960
ACDB9EFB83E3E9B9E80D73F19D4F0EFA78F4985FA23AA6A464074C52CA719DFC
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1961
15839B01F38A330E0A2D22D25C9927AD838EB107D27B74AED87B218362408E90
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1962
D07BC014FF59DCB53D1A7B5519ABB2647015D2599D6DBF584AB229826E011129
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1963
1266DD3089FEAC11748F9B23F3B4F527587259202B4D79774CFE37DEC43555E3
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1964
9D71B0753B7124ACF9725E11F0ADFAE1499264D82B213047846FE40513E662B1
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1965
31F766CB64B59C5D015F7AD02EFD2F9AE11F5D1ADE8C039614606B1BDCAB40DF
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1966
471EE99B329027144B2C5198D4DDA95C33BA1DE3C511E593890ADACC9CC939E1
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1967
3DB379A57178A0FA8DDDDE974C25997DABD8D524B722752DF7935A96ACEB676E
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1968
4C4732D6AEE7E5F79B4BB5A2343C677BD81632EA39BC8396874506377322C413
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1969
83BB9B6CB12ED357D00188DFAD0B7950EFF4B44475955EF27F9AE352A46F392F
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1970
A2CB193B310304D8BD86AE1F2F519AFA5F63F44ADCB0F994C8B085F6FF67908F
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1971
8267A75812E8520F9FB0767B04C3327967BCC7AD0F8F1FA33F4B50227C1A6CAA
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1972
BE18C7231CF357A0DBC94F91C5D31233490B5D8161238824E867B78021060BA1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1973
D822F7CA36BC76C0D553CC885FBCA729D8B0475C3DC67AD9AAF367BA94311747
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1974
15C79E3F83FF7451C37032B1AA7C717403265E85BC528D1A33F830691E4B0860
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1975
EC6F879B6CDC166F22A53BD94F222B5900C4A0926D36DE1D5F9FB4DC36DC2879
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1976
7C14D8115374D9F219F055D70C815AE767CDCFE834745201E327601C6658BB5D
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1977
20FC2F8F283C444BB8F563D50899525C130DBCF0C73B277E2C0878D35054ACD7
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1978
FB3C7BAFEB01A55B48AFE5B714026F5E4956CF46A4C71E9A8D7711463EA2FCF1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1979
C2669B11FB3392B731D6DE3A96E33A039F2B3907952B87E64D2550DD61BBFE09
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1980
71A15448A26CCFA46F44A1782877DBBD57648E398FDA9C150263AD3DE203D294
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1981
2E9D5E79D2E7C1D85B61357FB2A8C2F4C99CCF61FCED301806B42F3064C31EC5
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1982
7A4F92370D675571D06FF3D6695EC555FED9E95D1796FE441A85E879D6B5A80D
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1983
D5E71E26FD4E3054B0E3152B7BA7DA526A666189F14DA6E0584BFBDD0964AD0B
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1984
502A08B45AB319251B9EB5A26DEF9E7AE61842537261B13AE0EE4F7C00B85FD1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1985
1A1CC8D09657508E595F66239733588DD9414661B04BBC8193A9AA2A4B2107B6
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1986
D6A7B77B23830B27FE839C109A3EB38ED9D7F355B76F59B5C096614DEFA727E7
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1987
8F6439C8A2ACB5020A864EEF5DDE08BD037894F0BC69A16891E48189FB073B43
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1988
66113E02CC75848E8EA6BF0E22FC399655610E8CF26F3D578C218DF989C07A6B
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1989
51710AEE88575D0024138856650552A595D86EC930261B10F1CDDDBFBE414A5E
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1990
6AAA5789053BE0E8B05E098304438D2AA5188D7B217A6A705AD00FB64DB3F319
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1991
312F472F7B45842127FAE36B658ACFA38FDC3AAD4CAB146B46832834192B74A2
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1992
E1699D4D32972C843384C818DE4B651701405930887E3D959A62A8FEB6628571
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1993
C378D127C6AC231EF748C9D42FE3532FDA12C474F887FA29441CCFD25F6FDC60
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1994
FB346D377D9983D6C8E1CFD54F07DCB2FA1FE892DFA11EA2A8FB6484CE703A5C
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1995
A0597BEAFE42535A8C08654CE959CCCE619C803B0E44A6059BBEB7C5BA0830F8
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1996
31F8ECCCDBDDCA65F16F2F299853718989157ADE84A83BE0B6A6F15B930EDE89
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1997
3EBC774A8A962C16E60EF1BF1246214F96A4F33EBCC767FD1FC5E4C227EF1A83
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1998
BA009418C3E8423E9AA8007917ADC79389E8CE12D6303D5177C1781DFB2EB121
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1999
81E11EBC5647DBE0AC195F7182A52EE254ADC1E7A4EC9757286149F62F50A4B3
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2000
AEE477B0D8EADFCD21955C51D74D05D1C13A3FC8FFA6EB79C963DBF7C92DA190
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2001
40FD4B7F86D397CB713269EAA4B1DE7F50BEE1690810AD89647D05A95D3C1E26
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2002
A894991C8D35BE5AE0FE36217FCFF0FBDF1A408543C47208B565B78595E4C885
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2003
4EEDDCD0F5ABEA1171E3C54FFD18CA47757FA5C78A025BF0A54B91DD447D241C
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2004
B4405FC6DC5422484FEF7D719F3BBFB7BE2783FB359E86013533A8235C68208B
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2005
021C53CEB1B0667874369BE48BBF6B71B70C6CEA2AD1065428C432AFDCDD4523
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2006
418D06D3B6F7BC3EE11603C6EA0B899F671E3D143E8245F2237340C9312D8964
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2007
BAC725BFE36241C528B0BB93DE81A0C4A8244DEFE88F027709788E921E5C92F8
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2008
CEF7DDD64F0F476FA6D8944BBD89F51AAC6430A156DA8229E6D730EF48347121
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2009
319FCE159480F6E711E6624F0E0BAAC7B26A490E4F6A976F763ADCCEDBBAE280
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2010
F766E406AB4A724F20442077647A1FEF4FDC7F20F6706DA9FF953629160E405B
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2011
739281572888396B8703241988F5C677DFAD81094612A1C3EF35BA4B73C681E1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2012
09F3449AB46EEAC4FA335B86BF9571E00F2AC2BEDDBACA739F49B850F7A0380A
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2013
283B8031E8FD07C4271CBAB45D90EC4FA5FBA21D234B2133407F8AFE73D8434E
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2014
2B9073ABC49C14804820F28E049BF88013855044245E4E4A4CFD7A29C7FF24D8
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2015
B01BACD5E70C8F7B2DB6D9C61007E20ADAA3D36F1A690BA989078910F3D70211
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2016
E53B9E98A7C8E7FC5099FF2421F4DF57D4B14F4B982903F898A6467515AA8C16
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2017
C1D9C4B0BF886820F94832BB40A6FC8AC36005697D434FEA5CBBEAC55A47F446
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2018
E606C13FC4CE957AB532D2DEAC740C6CC8CB624E79CEBB6D116B605BA5FAD006
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2019
046FD0C6B324EA38580321A4331753E7AEB2DB0691F50111E1E944C4E0B9B570
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2020
754369559CAEF41FF6B97CBFEFB834D714FBA0C0B799C288E7D3E9CCD38620F1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2021
FDC3FD197D5CA6090C997E997BD113BB926D0CC5511595315D38FC1A3D5CF78D
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2022
D958ADBABBFD799D06674B6E33EB47E1488F5A6001A5687D1B46A2FADDF95DEE
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2023
D9BFBDE976A4413DB537E8DFF6A6B6E124DAF580F1C70ECF83287C5C5CD6A031
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2024
1FE5A0D2EB40D1F2DF1077276966AFDD06B78706C71283CC8BAD94CAFEE455F7
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2025
51F4754B55A13A1C09BB1FA350FA96872D4FA37630BF894DFA8A44D9FC94A27E
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2026
1E25582E75487B94E3F49B150475BF6FB729A2B7EA14BD2C72ED770BFC337400
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2027
D74C66DAA60817E5CC6070FB835BD06557D80EEA68DEAD0613A6AC8E9C239D74
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2028
6C75931183A6A436CB340CABEFCE195215CA0686EB379D37D037BA7FCD9B9378
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2029
414298F2FE522093126B0C1285ED045AA1387D7E2FFAF4FD971159AFC1FB6639
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2030
089FB3904BBD39A549A761602695B60196D8CDC11385DE86F825B932E38BB6CD
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2031
815CD07127BAAB97D7ED3BB2E27B0A0CFBCD9FAC5BD8E87F760D7200C55914E6
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2032
B443647FAC6C840D899ED7CBC3F418B972427BABA1E52ED009C6DC43A1B0CDC0
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2033
12CA10C88E2DE37DB405208C316CB75D5458D66F4356EC17B7E36EC74CA0F3C4
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2034
D67635ADFE1A4519B8B173C2992BBA05084C8266487F0558F2577E434632198F
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2035
D9722E1A3CF091F763E3A87C9F1C7C0BC482E6E830E04FC498E5B7477631E22B
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2036
1C9F5489BD81B01B91955EB48CD62F1163BEF734DA79B5DE75D3C1A22697AFDE
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2037
8DE14EF0F2172A761DC91B2470E1B015E72962745E40630E8B9287B932011373
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2038
DC6B4D1E647B4F430301E7013D9C73A3473782EB60D712CBACAC7ABF18FE7667
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2039
D993C98DABAF735A41C025B9019D1313587060DD84CC26978B3C8C9E4E761212
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2040
CD335A0D51D98ED1617C44BFB2B07D52098C344651B05EF1940D00602B803B98
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2041
E125200C6CDAC3B7BE09E5004B45A5A80679285456D8F58E0BADDEBEA9D1A4C3
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2042
0F5169943CCBD244C95D3A86DF4B82A1E68B01E295B4748B4661AAD92F32C2D1
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2043
09D095EB0DB3897D04F8F9C61A6FA94C98B55A69D51619A47A30F60F429D111D
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2044
7BADB00D2F83B1F390EB58FED983CC6132F84363CBF219640A2A98B19F806443
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2045
CD70803FF4A5B4BD2606A3985CF4A33D03EA042E3C82BF6F9FE9ACDA39E5AACE
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2046
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Fu(:=)f Fw(N)24 b Fu([)p Fw(y)74 b Fu(:=)66 b Fw(L)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8055
Fu(]])p Black Fx(.)4553 6029 y Fv(\017)100 b Fz(Case)81
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8056
b(3:)p Blue 71 w Fw(M)91 b Fv(\021)68 b Fw(M)6345 6060
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8057
y Ft(1)6448 6029 y Fw(M)6684 6060 y Ft(2)p Black 6788
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8058
6029 a Fx(.)j(The)57 b(statement)e(follows)g(again)h(from)h(the)e
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8059
(induc-)4772 6249 y(tion)f(hypothesis.)4243 b(\223)40
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8060
b Fs(\003)f Fx(\224)p 0 TeXcolorgray 10797 5925 a
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8061
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8062
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8063
5925 a 0.5 TeXcolorgray 8969 6307 a FB(Cambridge,)27
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8064
b(5.)g(December)g(2005)g(\226)g(p.3)h(\(1/6\))p 0 TeXcolorgray
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8065
4360 6416 a
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8068
%%Page: 3 4
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8069
TeXDict begin 3 3 bop 0 TeXcolorgray 4360 6416 a
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8070
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8071
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8072
6416 a 4585 1909 a
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8073
SDict begin /product where{pop product(Distiller)search{pop pop pop
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8074
version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8075
closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8076
grestore}if}{pop}ifelse}{pop}ifelse}if end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8077
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8078
SDict begin H.S end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8080
a 0 TeXcolorgray 0 TeXcolorgray 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8081
SDict begin H.R end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8082
 4585 1909
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8083
a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8084
SDict begin [ /View [/XYZ H.V] /Dest (page.1) cvn H.B /DEST pdfmark
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8085
end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8086
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8087
SDict begin [ {ThisPage}<</Trans << /S /R >> >> /PUT pdfmark end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8088
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8089
0 TeXcolorgray Black 1 1 0.8 TeXcolorrgb 1 1 0.8 TeXcolorrgb
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8090
4561 2414 6035 718 v 1 1 0.8 TeXcolorrgb Black 4623 1915
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8091
a Fz(Substitution)79 b(Lemma:)69 b Fx(If)p Blue 56 w
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8092
Fw(x)d Fv(6\021)g Fw(y)p Black 63 w Fx(and)p Blue 55
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8093
w Fw(x)g Fv(62)h Fw(F)33 b(V)53 b Fu(\()p Fw(L)p Fu(\))p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8094
Black Fx(,)j(then)p Blue 5081 2226 a Fw(M)24 b Fu([)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8095
Fw(x)66 b Fu(:=)f Fw(N)24 b Fu(][)p Fw(y)74 b Fu(:=)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8096
b Fw(L)p Fu(])g Fv(\021)f Fw(M)24 b Fu([)p Fw(y)73 b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8097
Fu(:=)66 b Fw(L)p Fu(][)p Fw(x)g Fu(:=)g Fw(N)24 b Fu([)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8098
Fw(y)73 b Fu(:=)66 b Fw(L)p Fu(]])p Black Fx(.)p 1 1 0.8
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8099
TeXcolorrgb Black 4582 2638 a Fz(Proof:)j Fx(By)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8100
55 w(induction)56 b(on)f(the)g(structure)f(of)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8101
Blue 56 w Fw(M)p Black 24 w Fx(.)4553 2919 y Fv(\017)100
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8102
b Fz(Case)80 b(1:)p Blue 70 w Fw(M)p Black 79 w Fx(is)56
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8103
b(a)f(variable.)4830 3201 y(Case)h(1.1.)p Blue 88 w Fw(M)90
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8104
b Fv(\021)65 b Fw(x)p Black Fx(.)k(Then)56 b(both)f(sides)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8105
Black 56 w(equal)p Black Blue 54 w Fw(N)24 b Fu([)p Fw(y)74
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8106
b Fu(:=)65 b Fw(L)p Fu(])p Black 56 w Fx(since)p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8107
56 w Fw(x)h Fv(6\021)g Fw(y)p Black 8 w Fx(.)4830 3483
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8108
y(Case)56 b(1.2.)p Blue 59 w Fw(M)90 b Fv(\021)65 b Fw(y)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8109
Black 8 w Fx(.)k(Then)56 b(both)f(sides)p Black 56 w(equal)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8110
Black Blue 54 w Fw(L)p Black Fx(,)g(for)p Blue 56 w Fw(x)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8111
b Fv(62)h Fw(F)33 b(V)53 b Fu(\()p Fw(L)p Fu(\))p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8112
5633 3765 a Fx(implies)p Blue 56 w Fw(L)p Fu([)p Fw(x)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8113
b Fu(:=)g Fw(:)39 b(:)h(:)p Fu(])66 b Fv(\021)g Fw(L)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8114
Black Fx(.)4830 4047 y(Case)56 b(1.3.)p Blue 59 w Fw(M)90
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8115
b Fv(\021)65 b Fw(z)75 b Fv(6\021)65 b Fw(x;)40 b(y)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8116
Black 8 w Fx(.)69 b(Then)55 b(both)g(sides)p Black 56
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8117
w(equal)p Black Blue 55 w Fw(z)p Black 9 w Fx(.)4553
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8118
4329 y Fv(\017)100 b Fz(Case)108 b(2:)p Blue 106 w Fw(M)127
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8119
b Fv(\021)103 b Fw(\025z)9 b(:M)6807 4360 y Ft(1)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8120
6910 4329 a Fx(.)p Red 74 w(By)74 b(the)g(variable)g(convention)g(we)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8121
(may)g(assume)4772 4549 y(that)p Blue 43 w Fw(z)g Fv(6\021)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8122
b Fw(x;)40 b(y)p Red 52 w Fx(and)p Blue 44 w Fw(z)p Red
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8123
53 w Fx(is)45 b(not)e(free)h(in)p Blue 45 w Fw(N)10 b(;)40
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8124
b(L)p Red Black Fx(.)65 b(Then)45 b(by)f(induction)g(hypothesis)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8125
Blue 5198 4831 a Fu(\()p Fw(\025z)9 b(:M)5855 4862 y
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8126
Ft(1)5958 4831 y Fu(\)[)p Fw(x)66 b Fu(:=)g Fw(N)24 b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8127
Fu(][)p Fw(y)74 b Fu(:=)65 b Fw(L)p Fu(])p Black Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8128
4895 5130 a Fv(\021)p Black Blue 118 w Fw(\025z)9 b(:)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8129
Fu(\()p Fw(M)5855 5161 y Ft(1)5958 5130 y Fu([)p Fw(x)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8130
b Fu(:=)g Fw(N)24 b Fu(][)p Fw(y)73 b Fu(:=)66 b Fw(L)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8131
Fu(]\))p Black Blue 4895 5430 a Fv(\021)p Black Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8132
118 w Fw(\025z)9 b(:)p Fu(\()p Fw(M)5855 5461 y Ft(1)5958
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8133
5430 y Fu([)p Fw(y)73 b Fu(:=)66 b Fw(L)p Fu(][)p Fw(x)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8134
Fu(:=)g Fw(N)24 b Fu([)p Fw(y)73 b Fu(:=)66 b Fw(L)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8135
Fu(]]\))p Black Blue 4895 5729 a Fv(\021)p Black Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8136
118 w Fu(\()p Fw(\025z)9 b(:M)5855 5760 y Ft(1)5958 5729
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8137
y Fu(\)[)p Fw(y)74 b Fu(:=)66 b Fw(L)p Fu(][)p Fw(x)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8138
Fu(:=)f Fw(N)24 b Fu([)p Fw(y)74 b Fu(:=)66 b Fw(L)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8139
Fu(]])p Black Fx(.)4553 6029 y Fv(\017)100 b Fz(Case)81
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8140
b(3:)p Blue 71 w Fw(M)91 b Fv(\021)68 b Fw(M)6345 6060
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8141
y Ft(1)6448 6029 y Fw(M)6684 6060 y Ft(2)p Black 6788
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8142
6029 a Fx(.)j(The)57 b(statement)e(follows)g(again)h(from)h(the)e
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8143
(induc-)4772 6249 y(tion)f(hypothesis.)4243 b(\223)40
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8144
b Fs(\003)f Fx(\224)p 0 TeXcolorgray 10797 5925 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8145
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8146
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8147
5925 a 0.5 TeXcolorgray 8954 6307 a FB(Cambridge,)27
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8148
b(5.)h(December)e(2005)h(\226)h(p.3)f(\(2/6\))p 0 TeXcolorgray
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8149
4360 6416 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8150
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8151
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8152
%%Page: 3 5
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8153
TeXDict begin 3 4 bop 0 TeXcolorgray 4360 6416 a
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8154
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8155
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8156
6416 a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8157
SDict begin /product where{pop product(Distiller)search{pop pop pop
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8158
version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8159
closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8160
grestore}if}{pop}ifelse}{pop}ifelse}if end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8161
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8162
SDict begin H.S end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8164
a 0 TeXcolorgray 0 TeXcolorgray 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8165
SDict begin H.R end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8166
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8167
a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8168
SDict begin [ /View [/XYZ H.V] /Dest (page.1) cvn H.B /DEST pdfmark
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8169
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8170
 4585 1909 a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8171
SDict begin [ {ThisPage}<</Trans << /S /R >> >> /PUT pdfmark end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8172
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8173
0 TeXcolorgray Black 1 1 0.8 TeXcolorrgb 1 1 0.8 TeXcolorrgb
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8174
4561 2414 6035 718 v 1 1 0.8 TeXcolorrgb Black 4623 1915
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8175
a Fz(Substitution)79 b(Lemma:)69 b Fx(If)p Blue 56 w
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8176
Fw(x)d Fv(6\021)g Fw(y)p Black 63 w Fx(and)p Blue 55
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8177
w Fw(x)g Fv(62)h Fw(F)33 b(V)53 b Fu(\()p Fw(L)p Fu(\))p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8178
Black Fx(,)j(then)p Blue 5081 2226 a Fw(M)24 b Fu([)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8179
Fw(x)66 b Fu(:=)f Fw(N)24 b Fu(][)p Fw(y)74 b Fu(:=)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8180
b Fw(L)p Fu(])g Fv(\021)f Fw(M)24 b Fu([)p Fw(y)73 b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8181
Fu(:=)66 b Fw(L)p Fu(][)p Fw(x)g Fu(:=)g Fw(N)24 b Fu([)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8182
Fw(y)73 b Fu(:=)66 b Fw(L)p Fu(]])p Black Fx(.)p 1 1 0.8
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8183
TeXcolorrgb Black 4582 2638 a Fz(Proof:)j Fx(By)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8184
55 w(induction)56 b(on)f(the)g(structure)f(of)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8185
Blue 56 w Fw(M)p Black 24 w Fx(.)4553 2919 y Fv(\017)100
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8186
b Fz(Case)80 b(1:)p Blue 70 w Fw(M)p Black 79 w Fx(is)56
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8187
b(a)f(variable.)4830 3201 y(Case)h(1.1.)p Blue 88 w Fw(M)90
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8188
b Fv(\021)65 b Fw(x)p Black Fx(.)k(Then)56 b(both)f(sides)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8189
Red 56 w(equal)p Black Blue 54 w Fw(N)24 b Fu([)p Fw(y)74
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8190
b Fu(:=)65 b Fw(L)p Fu(])p Black 56 w Fx(since)p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8191
56 w Fw(x)h Fv(6\021)g Fw(y)p Black 8 w Fx(.)4830 3483
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8192
y(Case)56 b(1.2.)p Blue 59 w Fw(M)90 b Fv(\021)65 b Fw(y)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8193
Black 8 w Fx(.)k(Then)56 b(both)f(sides)p Red 56 w(equal)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8194
Black Blue 54 w Fw(L)p Black Fx(,)g(for)p Blue 56 w Fw(x)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8195
b Fv(62)h Fw(F)33 b(V)53 b Fu(\()p Fw(L)p Fu(\))p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8196
5633 3765 a Fx(implies)p Blue 56 w Fw(L)p Fu([)p Fw(x)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8197
b Fu(:=)g Fw(:)39 b(:)h(:)p Fu(])66 b Fv(\021)g Fw(L)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8198
Black Fx(.)4830 4047 y(Case)56 b(1.3.)p Blue 59 w Fw(M)90
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8199
b Fv(\021)65 b Fw(z)75 b Fv(6\021)65 b Fw(x;)40 b(y)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8200
Black 8 w Fx(.)69 b(Then)55 b(both)g(sides)p Red 56 w(equal)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8201
Black Blue 55 w Fw(z)p Black 9 w Fx(.)4553 4329 y Fv(\017)100
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8202
b Fz(Case)108 b(2:)p Blue 106 w Fw(M)127 b Fv(\021)103
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8203
b Fw(\025z)9 b(:M)6807 4360 y Ft(1)p Black 6910 4329
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8204
a Fx(.)p Black 74 w(By)74 b(the)g(variable)g(convention)g(we)g(may)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8205
(assume)4772 4549 y(that)p Blue 43 w Fw(z)g Fv(6\021)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8206
b Fw(x;)40 b(y)p Black 52 w Fx(and)p Blue 44 w Fw(z)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8207
Black 53 w Fx(is)45 b(not)e(free)h(in)p Blue 45 w Fw(N)10
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8208
b(;)40 b(L)p Black Black Fx(.)65 b(Then)45 b(by)f(induction)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8209
(hypothesis)p Blue 5198 4831 a Fu(\()p Fw(\025z)9 b(:M)5855
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8210
4862 y Ft(1)5958 4831 y Fu(\)[)p Fw(x)66 b Fu(:=)g Fw(N)24
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8211
b Fu(][)p Fw(y)74 b Fu(:=)65 b Fw(L)p Fu(])p Black Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8212
4895 5130 a Fv(\021)p Black Blue 118 w Fw(\025z)9 b(:)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8213
Fu(\()p Fw(M)5855 5161 y Ft(1)5958 5130 y Fu([)p Fw(x)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8214
b Fu(:=)g Fw(N)24 b Fu(][)p Fw(y)73 b Fu(:=)66 b Fw(L)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8215
Fu(]\))p Black Blue 4895 5430 a Fv(\021)p Black Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8216
118 w Fw(\025z)9 b(:)p Fu(\()p Fw(M)5855 5461 y Ft(1)5958
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8217
5430 y Fu([)p Fw(y)73 b Fu(:=)66 b Fw(L)p Fu(][)p Fw(x)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8218
Fu(:=)g Fw(N)24 b Fu([)p Fw(y)73 b Fu(:=)66 b Fw(L)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8219
Fu(]]\))p Black Blue 4895 5729 a Fv(\021)p Black Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8220
118 w Fu(\()p Fw(\025z)9 b(:M)5855 5760 y Ft(1)5958 5729
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8221
y Fu(\)[)p Fw(y)74 b Fu(:=)66 b Fw(L)p Fu(][)p Fw(x)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8222
Fu(:=)f Fw(N)24 b Fu([)p Fw(y)74 b Fu(:=)66 b Fw(L)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8223
Fu(]])p Black Fx(.)4553 6029 y Fv(\017)100 b Fz(Case)81
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8224
b(3:)p Blue 71 w Fw(M)91 b Fv(\021)68 b Fw(M)6345 6060
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8225
y Ft(1)6448 6029 y Fw(M)6684 6060 y Ft(2)p Black 6788
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8226
6029 a Fx(.)j(The)57 b(statement)e(follows)g(again)h(from)h(the)e
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8227
(induc-)4772 6249 y(tion)f(hypothesis.)4243 b(\223)40
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8228
b Fs(\003)f Fx(\224)p 0 TeXcolorgray 10797 5925 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8229
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8230
 10797
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8231
5925 a 0.5 TeXcolorgray 8954 6307 a FB(Cambridge,)27
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8232
b(5.)h(December)e(2005)h(\226)h(p.3)f(\(3/6\))p 0 TeXcolorgray
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8233
4360 6416 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8234
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8235
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8236
%%Page: 3 6
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8237
TeXDict begin 3 5 bop 0 TeXcolorgray 4360 6416 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8238
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8239
 4360
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8240
6416 a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8241
SDict begin /product where{pop product(Distiller)search{pop pop pop
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8242
version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8243
closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8244
grestore}if}{pop}ifelse}{pop}ifelse}if end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8245
 4585 1909 a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8246
SDict begin H.S end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8247
 4585 1909
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8248
a 0 TeXcolorgray 0 TeXcolorgray 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8249
SDict begin H.R end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8250
 4585 1909
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8251
a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8252
SDict begin [ /View [/XYZ H.V] /Dest (page.1) cvn H.B /DEST pdfmark
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8253
end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8254
 4585 1909 a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8255
SDict begin [ {ThisPage}<</Trans << /S /R >> >> /PUT pdfmark end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8256
 4585 1909 a Gray
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8257
0 TeXcolorgray Black 1 1 0.8 TeXcolorrgb 1 1 0.8 TeXcolorrgb
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8258
4561 2414 6035 718 v 1 1 0.8 TeXcolorrgb Black 4623 1915
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8259
a Fz(Substitution)79 b(Lemma:)69 b Fx(If)p Blue 56 w
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8260
Fw(x)d Fv(6\021)g Fw(y)p Black 63 w Fx(and)p Blue 55
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8261
w Fw(x)g Fv(62)h Fw(F)33 b(V)53 b Fu(\()p Fw(L)p Fu(\))p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8262
Black Fx(,)j(then)p Blue 5081 2226 a Fw(M)24 b Fu([)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8263
Fw(x)66 b Fu(:=)f Fw(N)24 b Fu(][)p Fw(y)74 b Fu(:=)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8264
b Fw(L)p Fu(])g Fv(\021)f Fw(M)24 b Fu([)p Fw(y)73 b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8265
Fu(:=)66 b Fw(L)p Fu(][)p Fw(x)g Fu(:=)g Fw(N)24 b Fu([)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8266
Fw(y)73 b Fu(:=)66 b Fw(L)p Fu(]])p Black Fx(.)p 1 1 0.8
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8267
TeXcolorrgb Black 4582 2638 a Fz(Proof:)j Fx(By)p Red
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8268
55 w(induction)56 b(on)f(the)g(structure)f(of)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8269
Blue 56 w Fw(M)p Black 24 w Fx(.)4553 2919 y Fv(\017)100
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8270
b Fz(Case)80 b(1:)p Blue 70 w Fw(M)p Black 79 w Fx(is)56
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8271
b(a)f(variable.)4830 3201 y(Case)h(1.1.)p Blue 88 w Fw(M)90
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8272
b Fv(\021)65 b Fw(x)p Black Fx(.)k(Then)56 b(both)f(sides)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8273
Red 56 w(equal)p Black Blue 54 w Fw(N)24 b Fu([)p Fw(y)74
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8274
b Fu(:=)65 b Fw(L)p Fu(])p Black 56 w Fx(since)p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8275
56 w Fw(x)h Fv(6\021)g Fw(y)p Black 8 w Fx(.)4830 3483
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8276
y(Case)56 b(1.2.)p Blue 59 w Fw(M)90 b Fv(\021)65 b Fw(y)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8277
Black 8 w Fx(.)k(Then)56 b(both)f(sides)p Red 56 w(equal)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8278
Black Blue 54 w Fw(L)p Black Fx(,)g(for)p Blue 56 w Fw(x)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8279
b Fv(62)h Fw(F)33 b(V)53 b Fu(\()p Fw(L)p Fu(\))p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8280
5633 3765 a Fx(implies)p Blue 56 w Fw(L)p Fu([)p Fw(x)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8281
b Fu(:=)g Fw(:)39 b(:)h(:)p Fu(])66 b Fv(\021)g Fw(L)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8282
Black Fx(.)4830 4047 y(Case)56 b(1.3.)p Blue 59 w Fw(M)90
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8283
b Fv(\021)65 b Fw(z)75 b Fv(6\021)65 b Fw(x;)40 b(y)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8284
Black 8 w Fx(.)69 b(Then)55 b(both)g(sides)p Red 56 w(equal)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8285
Black Blue 55 w Fw(z)p Black 9 w Fx(.)4553 4329 y Fv(\017)100
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8286
b Fz(Case)108 b(2:)p Blue 106 w Fw(M)127 b Fv(\021)103
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8287
b Fw(\025z)9 b(:M)6807 4360 y Ft(1)p Black 6910 4329
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8288
a Fx(.)p Black 74 w(By)74 b(the)g(variable)g(convention)g(we)g(may)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8289
(assume)4772 4549 y(that)p Blue 43 w Fw(z)g Fv(6\021)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8290
b Fw(x;)40 b(y)p Black 52 w Fx(and)p Blue 44 w Fw(z)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8291
Black 53 w Fx(is)45 b(not)e(free)h(in)p Blue 45 w Fw(N)10
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8292
b(;)40 b(L)p Black Black Fx(.)65 b(Then)45 b(by)f(induction)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8293
(hypothesis)p Blue 5198 4831 a Fu(\()p Fw(\025z)9 b(:M)5855
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8294
4862 y Ft(1)5958 4831 y Fu(\)[)p Fw(x)66 b Fu(:=)g Fw(N)24
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8295
b Fu(][)p Fw(y)74 b Fu(:=)65 b Fw(L)p Fu(])p Black Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8296
4895 5130 a Fv(\021)p Black Blue 118 w Fw(\025z)9 b(:)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8297
Fu(\()p Fw(M)5855 5161 y Ft(1)5958 5130 y Fu([)p Fw(x)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8298
b Fu(:=)g Fw(N)24 b Fu(][)p Fw(y)73 b Fu(:=)66 b Fw(L)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8299
Fu(]\))p Black Blue 4895 5430 a Fv(\021)p Black Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8300
118 w Fw(\025z)9 b(:)p Fu(\()p Fw(M)5855 5461 y Ft(1)5958
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8301
5430 y Fu([)p Fw(y)73 b Fu(:=)66 b Fw(L)p Fu(][)p Fw(x)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8302
Fu(:=)g Fw(N)24 b Fu([)p Fw(y)73 b Fu(:=)66 b Fw(L)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8303
Fu(]]\))p Black Blue 4895 5729 a Fv(\021)p Black Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8304
118 w Fu(\()p Fw(\025z)9 b(:M)5855 5760 y Ft(1)5958 5729
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8305
y Fu(\)[)p Fw(y)74 b Fu(:=)66 b Fw(L)p Fu(][)p Fw(x)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8306
Fu(:=)f Fw(N)24 b Fu([)p Fw(y)74 b Fu(:=)66 b Fw(L)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8307
Fu(]])p Black Fx(.)4553 6029 y Fv(\017)100 b Fz(Case)81
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8308
b(3:)p Blue 71 w Fw(M)91 b Fv(\021)68 b Fw(M)6345 6060
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8309
y Ft(1)6448 6029 y Fw(M)6684 6060 y Ft(2)p Black 6788
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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6029 a Fx(.)j(The)57 b(statement)e(follows)g(again)h(from)h(the)e
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8320
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8321
b(Terms)56 b(that)f(are)g Fw(\013)p Fx(-congruent)g(are)g
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8322
(identi\002ed.)69 b(So)4643 4786 y(now)55 b(we)g(write)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8323
Blue 55 w Fw(\025x:x)66 b Fv(\021)g Fw(\025y)8 b(:y)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8324
Black 62 w Fx(etcetera.)4643 5110 y Fz(2.1.13.)83 b(Variable)f
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8325
(Convention)p 4643 5153 2530 9 v -1 w Fx(:)69 b(If)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8326
Blue 56 w Fw(M)7784 5141 y Ft(1)7887 5110 y Fw(;)40 b(:)g(:)f(:)h(;)f
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8327
(M)8651 5141 y Fr(n)p Black 8836 5110 a Fx(occur)55 b(in)h(a)g(certain)
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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4643 5329 y(mathematical)f(context)f(\(e.g.)h(de\002nition,)h(proof\),)
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8329
g(then)f(in)g(these)g(terms)h(all)4643 5550 y(bound)f(variables)h(are)f
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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(chosen)h(to)f(be)g(different)h(from)g(the)f(free)g(variables.)4643
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8331
5853 y Fz(2.1.14.)83 b(Moral)p 4643 5896 1281 9 v Fx(:)69
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8332
b(Using)55 b(conventions)h(2.1.12)g(and)g(2.1.13)g(one)f(can)h(work)g
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8333
(with)4643 6073 y Fw(\025)p Fx(-terms)f(in)h(the)f(naive)g(way.)p
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Fw(x)d Fv(6\021)g Fw(y)p Black 63 w Fx(and)p Blue 55
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8367
w Fw(x)g Fv(62)h Fw(F)33 b(V)53 b Fu(\()p Fw(L)p Fu(\))p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8368
Black Fx(,)j(then)p Blue 5081 2226 a Fw(M)24 b Fu([)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8369
Fw(x)66 b Fu(:=)f Fw(N)24 b Fu(][)p Fw(y)74 b Fu(:=)66
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8370
b Fw(L)p Fu(])g Fv(\021)f Fw(M)24 b Fu([)p Fw(y)73 b
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8371
Fu(:=)66 b Fw(L)p Fu(][)p Fw(x)g Fu(:=)g Fw(N)24 b Fu([)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Fw(y)73 b Fu(:=)66 b Fw(L)p Fu(]])p Black Fx(.)p 1 1 0.8
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8375
Blue 56 w Fw(M)p Black 24 w Fx(.)4553 2919 y Fv(\017)100
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8376
b Fz(Case)80 b(1:)p Blue 70 w Fw(M)p Black 79 w Fx(is)56
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8377
b(a)f(variable.)4830 3201 y(Case)h(1.1.)p Blue 88 w Fw(M)90
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8378
b Fv(\021)65 b Fw(x)p Black Fx(.)k(Then)56 b(both)f(sides)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8379
Black 56 w(equal)p Black Blue 54 w Fw(N)24 b Fu([)p Fw(y)74
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8380
b Fu(:=)65 b Fw(L)p Fu(])p Black 56 w Fx(since)p Blue
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8381
56 w Fw(x)h Fv(6\021)g Fw(y)p Black 8 w Fx(.)4830 3483
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8382
y(Case)56 b(1.2.)p Blue 59 w Fw(M)90 b Fv(\021)65 b Fw(y)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8383
Black 8 w Fx(.)k(Then)56 b(both)f(sides)p Black 56 w(equal)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8384
Black Blue 54 w Fw(L)p Black Fx(,)g(for)p Blue 56 w Fw(x)66
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8385
b Fv(62)h Fw(F)33 b(V)53 b Fu(\()p Fw(L)p Fu(\))p Black
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8386
5633 3765 a Fx(implies)p Blue 56 w Fw(L)p Fu([)p Fw(x)66
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8387
b Fu(:=)g Fw(:)39 b(:)h(:)p Fu(])66 b Fv(\021)g Fw(L)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8388
Black Fx(.)4830 4047 y(Case)56 b(1.3.)p Blue 59 w Fw(M)90
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8389
b Fv(\021)65 b Fw(z)75 b Fv(6\021)65 b Fw(x;)40 b(y)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8390
Black 8 w Fx(.)69 b(Then)55 b(both)g(sides)p Black 56
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8391
w(equal)p Black Blue 55 w Fw(z)p Black 9 w Fx(.)4553
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8392
4329 y Fv(\017)100 b Fz(Case)108 b(2:)p Blue 106 w Fw(M)127
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8393
b Fv(\021)103 b Fw(\025z)9 b(:M)6807 4360 y Ft(1)p Black
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8394
6910 4329 a Fx(.)p Black 74 w(By)74 b(the)g(variable)g(convention)g(we)
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8395
g(may)g(assume)4772 4549 y(that)p Blue 43 w Fw(z)g Fv(6\021)66
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8396
b Fw(x;)40 b(y)p Black 52 w Fx(and)p Blue 44 w Fw(z)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8397
Black 53 w Fx(is)45 b(not)e(free)h(in)p Blue 45 w Fw(N)10
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8398
b(;)40 b(L)p Black Black Fx(.)65 b(Then)45 b(by)f(induction)g
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8399
(hypothesis)p Blue 5198 4831 a Fu(\()p Fw(\025z)9 b(:M)5855
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8400
4862 y Ft(1)5958 4831 y Fu(\)[)p Fw(x)66 b Fu(:=)g Fw(N)24
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8401
b Fu(][)p Fw(y)74 b Fu(:=)65 b Fw(L)p Fu(])p Black Blue
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8402
4895 5130 a Fv(\021)p Black Blue 118 w Fw(\025z)9 b(:)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8403
Fu(\()p Fw(M)5855 5161 y Ft(1)5958 5130 y Fu([)p Fw(x)66
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8404
b Fu(:=)g Fw(N)24 b Fu(][)p Fw(y)73 b Fu(:=)66 b Fw(L)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Fu(]\))p Black Blue 4895 5430 a Fv(\021)p Black Blue
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8406
118 w Fw(\025z)9 b(:)p Fu(\()p Fw(M)5855 5461 y Ft(1)5958
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8407
5430 y Fu([)p Fw(y)73 b Fu(:=)66 b Fw(L)p Fu(][)p Fw(x)g
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8408
Fu(:=)g Fw(N)24 b Fu([)p Fw(y)73 b Fu(:=)66 b Fw(L)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8409
Fu(]]\))p Black Blue 4895 5729 a Fv(\021)p Black Blue
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8410
118 w Fu(\()p Fw(\025z)9 b(:M)5855 5760 y Ft(1)5958 5729
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8411
y Fu(\)[)p Fw(y)74 b Fu(:=)66 b Fw(L)p Fu(][)p Fw(x)g
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8412
Fu(:=)f Fw(N)24 b Fu([)p Fw(y)74 b Fu(:=)66 b Fw(L)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8413
Fu(]])p Black Fx(.)4553 6029 y Fv(\017)100 b Fz(Case)81
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8414
b(3:)p Blue 71 w Fw(M)91 b Fv(\021)68 b Fw(M)6345 6060
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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y Ft(1)6448 6029 y Fw(M)6684 6060 y Ft(2)p Black 6788
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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6029 a Fx(.)j(The)57 b(statement)e(follows)g(again)h(from)h(the)e
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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a 0 TeXcolorgray 0 TeXcolorgray 4585 1909 a
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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SDict begin H.R end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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 4585 1909
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8442
SDict begin [ /View [/XYZ H.V] /Dest (page.1) cvn H.B /DEST pdfmark
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8445
SDict begin [ {ThisPage}<</Trans << /S /R >> >> /PUT pdfmark end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8446
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8447
0 TeXcolorgray Black 1 1 0.8 TeXcolorrgb 1 1 0.8 TeXcolorrgb
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8448
4561 2414 6035 718 v 1 1 0.8 TeXcolorrgb Black 4623 1915
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8449
a Fz(Substitution)79 b(Lemma:)69 b Fx(If)p Blue 56 w
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8450
Fw(x)d Fv(6\021)g Fw(y)p Black 63 w Fx(and)p Blue 55
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8451
w Fw(x)g Fv(62)h Fw(F)33 b(V)53 b Fu(\()p Fw(L)p Fu(\))p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8452
Black Fx(,)j(then)p Blue 5081 2226 a Fw(M)24 b Fu([)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8453
Fw(x)66 b Fu(:=)f Fw(N)24 b Fu(][)p Fw(y)74 b Fu(:=)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8454
b Fw(L)p Fu(])g Fv(\021)f Fw(M)24 b Fu([)p Fw(y)73 b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8455
Fu(:=)66 b Fw(L)p Fu(][)p Fw(x)g Fu(:=)g Fw(N)24 b Fu([)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8456
Fw(y)73 b Fu(:=)66 b Fw(L)p Fu(]])p Black Fx(.)p 1 1 0.8
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8457
TeXcolorrgb Black 4582 2638 a Fz(Proof:)j Fx(By)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8458
55 w(induction)56 b(on)f(the)g(structure)f(of)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8459
Blue 56 w Fw(M)p Black 24 w Fx(.)4553 2919 y Fv(\017)100
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8460
b Fz(Case)80 b(1:)p Blue 70 w Fw(M)p Black 79 w Fx(is)56
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8461
b(a)f(variable.)4830 3201 y(Case)h(1.1.)p Blue 88 w Fw(M)90
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8462
b Fv(\021)65 b Fw(x)p Black Fx(.)k(Then)56 b(both)f(sides)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8463
Black 56 w(equal)p Black Blue 54 w Fw(N)24 b Fu([)p Fw(y)74
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8464
b Fu(:=)65 b Fw(L)p Fu(])p Black 56 w Fx(since)p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8465
56 w Fw(x)h Fv(6\021)g Fw(y)p Black 8 w Fx(.)4830 3483
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8466
y(Case)56 b(1.2.)p Blue 59 w Fw(M)90 b Fv(\021)65 b Fw(y)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8467
Black 8 w Fx(.)k(Then)56 b(both)f(sides)p Black 56 w(equal)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8468
Black Blue 54 w Fw(L)p Black Fx(,)g(for)p Blue 56 w Fw(x)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8469
b Fv(62)h Fw(F)33 b(V)53 b Fu(\()p Fw(L)p Fu(\))p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8470
5633 3765 a Fx(implies)p Blue 56 w Fw(L)p Fu([)p Fw(x)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8471
b Fu(:=)g Fw(:)39 b(:)h(:)p Fu(])66 b Fv(\021)g Fw(L)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8472
Black Fx(.)4830 4047 y(Case)56 b(1.3.)p Blue 59 w Fw(M)90
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8473
b Fv(\021)65 b Fw(z)75 b Fv(6\021)65 b Fw(x;)40 b(y)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8474
Black 8 w Fx(.)69 b(Then)55 b(both)g(sides)p Black 56
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8475
w(equal)p Black Blue 55 w Fw(z)p Black 9 w Fx(.)4553
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8476
4329 y Fv(\017)100 b Fz(Case)108 b(2:)p Blue 106 w Fw(M)127
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8477
b Fv(\021)103 b Fw(\025z)9 b(:M)6807 4360 y Ft(1)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8478
6910 4329 a Fx(.)p Black 74 w(By)74 b(the)g(variable)g(convention)g(we)
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8479
g(may)g(assume)4772 4549 y(that)p Blue 43 w Fw(z)g Fv(6\021)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8480
b Fw(x;)40 b(y)p Black 52 w Fx(and)p Blue 44 w Fw(z)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8481
Black 53 w Fx(is)45 b(not)e(free)h(in)p Blue 45 w Fw(N)10
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8482
b(;)40 b(L)p Black Black Fx(.)65 b(Then)45 b(by)f(induction)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8483
(hypothesis)p Blue 5198 4831 a Fu(\()p Fw(\025z)9 b(:M)5855
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8484
4862 y Ft(1)5958 4831 y Fu(\)[)p Fw(x)66 b Fu(:=)g Fw(N)24
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8485
b Fu(][)p Fw(y)74 b Fu(:=)65 b Fw(L)p Fu(])p Black Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8486
4895 5130 a Fv(\021)p Black Blue 118 w Fw(\025z)9 b(:)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8487
Fu(\()p Fw(M)5855 5161 y Ft(1)5958 5130 y Fu([)p Fw(x)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8488
b Fu(:=)g Fw(N)24 b Fu(][)p Fw(y)73 b Fu(:=)66 b Fw(L)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8489
Fu(]\))p Black Blue 4895 5430 a Fv(\021)p Black Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8490
118 w Fw(\025z)9 b(:)p Fu(\()p Fw(M)5855 5461 y Ft(1)5958
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8491
5430 y Fu([)p Fw(y)73 b Fu(:=)66 b Fw(L)p Fu(][)p Fw(x)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8492
Fu(:=)g Fw(N)24 b Fu([)p Fw(y)73 b Fu(:=)66 b Fw(L)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8493
Fu(]]\))p Black Blue 4895 5729 a Fv(\021)p Black Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8494
118 w Fu(\()p Fw(\025z)9 b(:M)5855 5760 y Ft(1)5958 5729
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8495
y Fu(\)[)p Fw(y)74 b Fu(:=)66 b Fw(L)p Fu(][)p Fw(x)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8496
Fu(:=)f Fw(N)24 b Fu([)p Fw(y)74 b Fu(:=)66 b Fw(L)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8497
Fu(]])p Black Fx(.)4553 6029 y Fv(\017)100 b Fz(Case)81
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8498
b(3:)p Blue 71 w Fw(M)91 b Fv(\021)68 b Fw(M)6345 6060
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8499
y Ft(1)6448 6029 y Fw(M)6684 6060 y Ft(2)p Black 6788
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8500
6029 a Fx(.)j(The)57 b(statement)e(follows)g(again)h(from)h(the)e
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8501
(induc-)4772 6249 y(tion)f(hypothesis.)4243 b(\223)40
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8502
b Fs(\003)f Fx(\224)p Red Black 1 1 0.8 TeXcolorrgb Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8503
6145 4735 a @beginspecial @setspecial
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8504
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8505
3.8 neg 72.07573 neg 220.0411 77.07573 .5 Frame  gsave 1 1 0.8  setrgbcolor
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8506
fill grestore gsave 0.8 SLW TeXDict begin Red end 0 setlinecap stroke
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8507
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8509
@endspecial -1359
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8510
x(Remember:)69 b(only)54 b(if)p Blue 56 w Fw(y)74 b Fv(6)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8511
Fu(=)65 b Fw(x)p Black 56 w Fx(and)p Blue 56 w Fw(x)h
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8512
Fv(62)g Fw(F)33 b(V)53 b Fu(\()p Fw(N)24 b Fu(\))p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8513
56 w Fx(then)p Blue 6331 3722 a Fu(\()p Fw(\025y)8 b(:M)24
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8514
b Fu(\)[)p Fw(x)65 b Fu(:=)h Fw(N)24 b Fu(])66 b(=)f
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8515
Fw(\025y)8 b(:)p Fu(\()p Fw(M)24 b Fu([)p Fw(x)66 b Fu(:=)f
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8516
Fw(N)24 b Fu(]\))p Black Blue 6571 4186 a(\()p Fw(\025z)9
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8517
b(:M)7228 4216 y Ft(1)7331 4186 y Fu(\)[)p Fw(x)67 b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8518
Fu(:=)e Fw(N)24 b Fu(][)p Fw(y)74 b Fu(:=)65 b Fw(L)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8519
Fu(])p Black Blue 6269 4565 a Fv(\021)p Black Blue 117
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8520
w Fu(\()p Fw(\025z)9 b(:)p Fu(\()p Fw(M)7320 4596 y Ft(1)7423
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8521
4565 y Fu([)p Fw(x)67 b Fu(:=)e Fw(N)24 b Fu(]\)\)[)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8522
Fw(y)74 b Fu(:=)66 b Fw(L)p Fu(])p Black 10361 4443 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8523
Ft(1)10289 4565 y Fv( )p Blue 6269 4944 a(\021)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8524
Blue 117 w Fw(\025z)9 b(:)p Fu(\()p Fw(M)7228 4975 y
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8525
Ft(1)7331 4944 y Fu([)p Fw(x)66 b Fu(:=)g Fw(N)24 b Fu(][)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8526
Fw(y)73 b Fu(:=)66 b Fw(L)p Fu(]\))p Black 10361 4822
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8527
a Ft(2)10289 4944 y Fv( )p Blue 6269 5244 a(\021)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8528
Blue 117 w Fw(\025z)9 b(:)p Fu(\()p Fw(M)7228 5275 y
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8529
Ft(1)7331 5244 y Fu([)p Fw(y)74 b Fu(:=)65 b Fw(L)p Fu(][)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8530
Fw(x)h Fu(:=)g Fw(N)24 b Fu([)p Fw(y)74 b Fu(:=)65 b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8531
Fw(L)p Fu(]]\))p Black 395 w Fx(IH)p Blue 6269 5623 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8532
Fv(\021)p Black Blue 117 w Fu(\()p Fw(\025z)9 b(:)p Fu(\()p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8533
Fw(M)7320 5654 y Ft(1)7423 5623 y Fu([)p Fw(y)74 b Fu(:=)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8534
b Fw(L)p Fu(]\)\)[)p Fw(x)h Fu(:=)e Fw(N)24 b Fu([)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8535
Fw(y)74 b Fu(:=)65 b Fw(L)p Fu(]]\))p Black 10361 5501
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8536
a Ft(2)10289 5623 y Fv(!)p Red 52 w Fz(!)p Black Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8537
6269 6002 a Fv(\021)p Black Blue 117 w Fu(\()p Fw(\025z)9
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8538
b(:M)7228 6033 y Ft(1)7331 6002 y Fu(\)[)p Fw(y)74 b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8539
Fu(:=)66 b Fw(L)p Fu(][)p Fw(x)g Fu(:=)g Fw(N)24 b Fu([)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8540
Fw(y)73 b Fu(:=)66 b Fw(L)p Fu(]])p Black Fx(.)10361
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8541
5880 y Ft(1)10289 6002 y Fv(!)p 0 TeXcolorgray 10797
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8542
5925 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8543
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8544
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8545
b(5.)h(December)e(2005)h(\226)h(p.3)f(\(6/6\))p 0 TeXcolorgray
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8546
4360 6416 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8547
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8549
%%Page: 4 9
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8550
TeXDict begin 4 8 bop 0 TeXcolorgray 4360 6416 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8551
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8552
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8553
6416 a 4585 1909 a
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8554
SDict begin /product where{pop product(Distiller)search{pop pop pop
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8555
version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8556
closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8557
grestore}if}{pop}ifelse}{pop}ifelse}if end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8558
 4585 1909 a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8559
SDict begin H.S end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8560
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8561
a 0 TeXcolorgray 0 TeXcolorgray 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8562
SDict begin H.R end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8563
 4585 1909
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
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a 4585 1909 a
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Christian Urban <urbanc@in.tum.de>
parents:
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  8565
SDict begin [ /View [/XYZ H.V] /Dest (page.1) cvn H.B /DEST pdfmark
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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  8568
SDict begin [ {ThisPage}<</Trans << /S /R >> >> /PUT pdfmark end
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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1909 a
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8571
SDict begin [ /Page 9/View [ /XYZ null null null ] /Title (\mbox {Formal Proof in Isabelle})
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Christian Urban <urbanc@in.tum.de>
parents:
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  8572
/OUT pdfmark end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8573
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8574
b(Pr)-9 b(oof)128 b(in)g(Isabelle)p 0 TeXcolorgray Black
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8575
Blue 4481 2336 a Fx(lemma)p Black 56 w(forget:)p Blue
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8576
4481 2578 a(assumes)p Black 56 w(a:)69 b(\224)p OliveGreen
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8577
Fw(x)d Fu(#)g Fw(L)p Black Fx(\224)p Blue 4481 2820 a(shows)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8578
Black 56 w(\224)p OliveGreen Fw(L)p Fu([)p Fw(x)26 b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8579
Fu(::=)g Fw(N)e Fu(])67 b(=)f Fw(L)p Black Fx(\224)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8580
Blue 4481 3061 a(using)p Black 56 w(a)p Blue 55 w(by)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8581
Black 55 w(\(nominal)p 6097 3061 56 9 v 67 w(induct)95
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8582
b Fw(L)g Fx(avoiding:)109 b Fw(x)135 b(N)118 b Fx(rule:)108
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8583
b(lam)p 9281 3061 V 67 w(induct\))5392 3303 y(\(auto)55
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8584
b(simp)h(add:)p Black 138 w(abs)p 7146 3303 V 67 w(fresh)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8585
Black Black 88 w(fresh)p 8265 3303 V 68 w(atm)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8586
16 w(\))p Blue 4481 3662 a(lemma)p Black 56 w(fresh)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8587
5566 3662 V 68 w(fact:)p Blue 4481 3904 a(\002xes)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8588
56 w(x)30 b(::)i(\224)p OliveGreen(name)p Black(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8589
Blue 4481 4146 a(assumes)p Black 56 w(a:)69 b(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8590
OliveGreen Fw(x)d Fu(#)g Fw(M)p Black 24 w Fx(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8591
Blue 55 w(and)p Black 87 w(b:)j(\224)p OliveGreen Fw(x)e
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8592
Fu(#)e Fw(N)p Black 24 w Fx(\224)p Blue 4481 4387 a(shows)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8593
Black 56 w(\224)p OliveGreen Fw(x)i Fu(#)f Fw(M)24 b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8594
Fu([)p Fw(y)34 b Fu(::=)26 b Fw(N)e Fu(])p Black Fx(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8595
Blue 4481 4629 a(using)p Black 56 w(a)55 b(b)p Blue 56
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8596
w(by)p Black 55 w(\(nominal)p 6263 4629 V 67 w(induct)95
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8597
b Fw(M)118 b Fx(avoiding:)109 b Fw(x)135 b(y)142 b(N)119
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8598
b Fx(rule:)108 b(lam)p 9815 4629 V 66 w(induct\))5557
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8599
4871 y(\(auto)54 b(simp)i(add:)109 b(abs)p 7281 4871
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8600
V 68 w(fresh)96 b(fresh)p 8409 4871 V 68 w(atm\))p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8601
4481 5230 a(lemma)p Black 56 w(subst)p 5559 5230 V 67
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8602
w(lemma:)p Blue 4481 5471 a(assumes)p Black 56 w(a:)69
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8603
b(\224)p OliveGreen Fw(x)d Fv(6)p Fu(=)g Fw(y)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8604
8 w Fx(\224)p Blue 55 w(and)p Black 87 w(b:)j(\224)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8605
OliveGreen Fw(x)d Fu(#)g Fw(L)p Black Fx(\224)p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8606
4481 5713 a(shows)p Black 56 w(\224)p OliveGreen Fw(M)24
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8607
b Fu([)p Fw(x)i Fu(::=)g Fw(N)e Fu(][)p Fw(y)34 b Fu(::=)26
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8608
b Fw(L)p Fu(])67 b(=)e Fw(M)24 b Fu([)p Fw(y)34 b Fu(::=)26
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8609
b Fw(L)p Fu(][)p Fw(x)g Fu(::=)g Fw(N)e Fu([)p Fw(y)34
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8610
b Fu(::=)26 b Fw(L)p Fu(]])p Black Fx(\224)p Blue 4481
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8611
5955 a(using)p Black 56 w(a)55 b(b)p Blue 56 w(by)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8612
55 w(\(nominal)p 6263 5955 V 67 w(induct)95 b Fw(M)118
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8613
b Fx(avoiding:)109 b Fw(x)135 b(y)142 b(N)158 b(L)95
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8614
b Fx(rule:)108 b(lam)p 10105 5955 V 67 w(induct\))5557
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8615
6196 y(\(auto)54 b(simp)i(add:)109 b(forget)94 b(fresh)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8616
8132 6196 V 68 w(fact\))p 0 TeXcolorgray 10797 5925 a
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8619
10797 5925 a 0.5 TeXcolorgray 8969 6307 a FB(Cambridge,)27
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8620
b(5.)g(December)g(2005)g(\226)g(p.4)h(\(1/3\))p 0 TeXcolorgray
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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6416 a 4585 1909 a
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8629
SDict begin /product where{pop product(Distiller)search{pop pop pop
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Christian Urban <urbanc@in.tum.de>
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diff changeset
  8630
version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8633
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8634
SDict begin H.S end
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Christian Urban <urbanc@in.tum.de>
parents:
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8636
a 0 TeXcolorgray 0 TeXcolorgray 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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SDict begin H.R end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8638
 4585 1909
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8639
a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8640
SDict begin [ /View [/XYZ H.V] /Dest (page.1) cvn H.B /DEST pdfmark
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8641
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8642
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8643
SDict begin [ {ThisPage}<</Trans << /S /R >> >> /PUT pdfmark end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8644
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8645
4872 2027 a FH(F)-13 b(ormal)129 b(Pr)-9 b(oof)128 b(in)g(Isabelle)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8646
0 TeXcolorgray Black Blue 4481 2336 a Fx(lemma)p Black
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8647
56 w(forget:)p Blue 4481 2578 a(assumes)p Black 56 w(a:)69
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8648
b(\224)p OliveGreen Fw(x)d Fu(#)g Fw(L)p Black Fx(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8649
Blue 4481 2820 a(shows)p Black 56 w(\224)p OliveGreen
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8650
Fw(L)p Fu([)p Fw(x)26 b Fu(::=)g Fw(N)e Fu(])67 b(=)f
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8651
Fw(L)p Black Fx(\224)p Blue 4481 3061 a(using)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8652
56 w(a)p Blue 55 w(by)p Black 55 w(\(nominal)p 6097 3061
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8653
56 9 v 67 w(induct)95 b Fw(L)g Fx(avoiding:)109 b Fw(x)135
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8654
b(N)118 b Fx(rule:)108 b(lam)p 9281 3061 V 67 w(induct\))5392
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8655
3303 y(\(auto)55 b(simp)h(add:)p Red 138 w(abs)p 7146
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8656
3303 V 67 w(fresh)p Black Red 88 w(fresh)p 8265 3303
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8657
V 68 w(atm)p Black 16 w(\))p Blue 4481 3662 a(lemma)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8658
Black 56 w(fresh)p 5566 3662 V 68 w(fact:)p Blue 4481
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8659
3904 a(\002xes)p Black 56 w(x)30 b(::)i(\224)p OliveGreen(name)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8660
Black(\224)p Blue 4481 4146 a(assumes)p Black 56 w(a:)69
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8661
b(\224)p OliveGreen Fw(x)d Fu(#)g Fw(M)p Black 24 w Fx(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8662
Blue 55 w(and)p Black 87 w(b:)j(\224)p OliveGreen Fw(x)e
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8663
Fu(#)e Fw(N)p Black 24 w Fx(\224)p Blue 4481 4387 a(shows)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8664
Black 56 w(\224)p OliveGreen Fw(x)i Fu(#)f Fw(M)24 b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8665
Fu([)p Fw(y)34 b Fu(::=)26 b Fw(N)e Fu(])p Black Fx(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8666
Blue 4481 4629 a(using)p Black 56 w(a)55 b(b)p Blue 56
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8667
w(by)p Black 55 w(\(nominal)p 6263 4629 V 67 w(induct)95
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8668
b Fw(M)118 b Fx(avoiding:)109 b Fw(x)135 b(y)142 b(N)119
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8669
b Fx(rule:)108 b(lam)p 9815 4629 V 66 w(induct\))5557
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8670
4871 y(\(auto)54 b(simp)i(add:)109 b(abs)p 7281 4871
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8671
V 68 w(fresh)96 b(fresh)p 8409 4871 V 68 w(atm\))p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8672
4481 5230 a(lemma)p Black 56 w(subst)p 5559 5230 V 67
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8673
w(lemma:)p Blue 4481 5471 a(assumes)p Black 56 w(a:)69
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8674
b(\224)p OliveGreen Fw(x)d Fv(6)p Fu(=)g Fw(y)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8675
8 w Fx(\224)p Blue 55 w(and)p Black 87 w(b:)j(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8676
OliveGreen Fw(x)d Fu(#)g Fw(L)p Black Fx(\224)p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8677
4481 5713 a(shows)p Black 56 w(\224)p OliveGreen Fw(M)24
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8678
b Fu([)p Fw(x)i Fu(::=)g Fw(N)e Fu(][)p Fw(y)34 b Fu(::=)26
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8679
b Fw(L)p Fu(])67 b(=)e Fw(M)24 b Fu([)p Fw(y)34 b Fu(::=)26
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8680
b Fw(L)p Fu(][)p Fw(x)g Fu(::=)g Fw(N)e Fu([)p Fw(y)34
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8681
b Fu(::=)26 b Fw(L)p Fu(]])p Black Fx(\224)p Blue 4481
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8682
5955 a(using)p Black 56 w(a)55 b(b)p Blue 56 w(by)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8683
55 w(\(nominal)p 6263 5955 V 67 w(induct)95 b Fw(M)118
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8684
b Fx(avoiding:)109 b Fw(x)135 b(y)142 b(N)158 b(L)95
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8685
b Fx(rule:)108 b(lam)p 10105 5955 V 67 w(induct\))5557
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8686
6196 y(\(auto)54 b(simp)i(add:)109 b(forget)94 b(fresh)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8687
8132 6196 V 68 w(fact\))p Red Black 1 1 0.8 TeXcolorrgb
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8688
Black 5703 4570 a @beginspecial @setspecial
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8689
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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3.8 neg 33.08267 neg 239.95796 38.08269 .5 Frame  gsave 1 1 0.8  setrgbcolor
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8694
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8695
-561 x(abs)p 6009 4009 V 67 w(fresh:)p Black Black Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8696
6281 4278 a Fu(\()p Fw(x)67 b Fu(#)e Fx(Lam)41 b Fu([)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8697
Fw(y)8 b Fu(])p Fw(:M)24 b Fu(\))105 b(=)g(\()p Fw(x)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8698
b Fu(=)g Fw(y)36 b Fv(_)28 b Fw(x)66 b Fu(#)g Fw(M)24
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8699
b Fu(\))p Black 5703 4578 a Fx(fresh)p 6196 4578 V 68
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8700
w(atm:)p Black Black Blue 6281 4848 a Fu(\()p Fw(x)67
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8701
b Fu(#)e Fw(y)8 b Fu(\))66 b(=)g(\()p Fw(x)h Fv(6)p Fu(=)e
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8702
Fw(y)8 b Fu(\))p Black 6281 5122 a Fx(provided)p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8703
56 w Fw(y)p Black 63 w Fx(is)56 b(an)f(atom)p 0 TeXcolorgray
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8704
10797 5925 a
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8705
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8706
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8707
a FB(Cambridge,)27 b(5.)h(December)e(2005)h(\226)h(p.4)f(\(2/3\))p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8708
0 TeXcolorgray 4360 6416 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8710
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8711
%%Page: 4 11
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8713
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8714
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8715
6416 a 4585 1909 a
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8716
SDict begin /product where{pop product(Distiller)search{pop pop pop
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8717
version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8720
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8721
SDict begin H.S end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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a 0 TeXcolorgray 0 TeXcolorgray 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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SDict begin H.R end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8725
 4585 1909
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8726
a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8727
SDict begin [ /View [/XYZ H.V] /Dest (page.1) cvn H.B /DEST pdfmark
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8728
end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8729
 4585 1909 a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8730
SDict begin [ {ThisPage}<</Trans << /S /R >> >> /PUT pdfmark end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8731
 4585 1909 a Gray
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8732
4872 2027 a FH(F)-13 b(ormal)129 b(Pr)-9 b(oof)128 b(in)g(Isabelle)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8733
0 TeXcolorgray Black Blue 4481 2336 a Fx(lemma)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8734
56 w(forget:)p Blue 4481 2578 a(assumes)p Black 56 w(a:)69
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8735
b(\224)p OliveGreen Fw(x)d Fu(#)g Fw(L)p Black Fx(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8736
Blue 4481 2820 a(shows)p Black 56 w(\224)p OliveGreen
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8737
Fw(L)p Fu([)p Fw(x)26 b Fu(::=)g Fw(N)e Fu(])67 b(=)f
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8738
Fw(L)p Black Fx(\224)p Blue 4481 3061 a(using)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8739
56 w(a)p Blue 55 w(by)p Black 55 w(\(nominal)p 6097 3061
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8740
56 9 v 67 w(induct)95 b Fw(L)g Fx(avoiding:)109 b Fw(x)135
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8741
b(N)118 b Fx(rule:)108 b(lam)p 9281 3061 V 67 w(induct\))5392
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8742
3303 y(\(auto)55 b(simp)h(add:)p Black 138 w(abs)p 7146
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8743
3303 V 67 w(fresh)p Black Black 88 w(fresh)p 8265 3303
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8744
V 68 w(atm)p Black 16 w(\))p Blue 4481 3662 a(lemma)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8745
Black 56 w(fresh)p 5566 3662 V 68 w(fact:)p Blue 4481
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8746
3904 a(\002xes)p Black 56 w(x)30 b(::)i(\224)p OliveGreen(name)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8747
Black(\224)p Blue 4481 4146 a(assumes)p Black 56 w(a:)69
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8748
b(\224)p OliveGreen Fw(x)d Fu(#)g Fw(M)p Black 24 w Fx(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8749
Blue 55 w(and)p Black 87 w(b:)j(\224)p OliveGreen Fw(x)e
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8750
Fu(#)e Fw(N)p Black 24 w Fx(\224)p Blue 4481 4387 a(shows)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8751
Black 56 w(\224)p OliveGreen Fw(x)i Fu(#)f Fw(M)24 b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8752
Fu([)p Fw(y)34 b Fu(::=)26 b Fw(N)e Fu(])p Black Fx(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8753
Blue 4481 4629 a(using)p Black 56 w(a)55 b(b)p Blue 56
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8754
w(by)p Black 55 w(\(nominal)p 6263 4629 V 67 w(induct)95
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8755
b Fw(M)118 b Fx(avoiding:)109 b Fw(x)135 b(y)142 b(N)119
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8756
b Fx(rule:)108 b(lam)p 9815 4629 V 66 w(induct\))5557
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8757
4871 y(\(auto)54 b(simp)i(add:)109 b(abs)p 7281 4871
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8758
V 68 w(fresh)96 b(fresh)p 8409 4871 V 68 w(atm\))p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8759
4481 5230 a(lemma)p Black 56 w(subst)p 5559 5230 V 67
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8760
w(lemma:)p Blue 4481 5471 a(assumes)p Black 56 w(a:)69
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8761
b(\224)p OliveGreen Fw(x)d Fv(6)p Fu(=)g Fw(y)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8762
8 w Fx(\224)p Blue 55 w(and)p Black 87 w(b:)j(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8763
OliveGreen Fw(x)d Fu(#)g Fw(L)p Black Fx(\224)p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8764
4481 5713 a(shows)p Black 56 w(\224)p OliveGreen Fw(M)24
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8765
b Fu([)p Fw(x)i Fu(::=)g Fw(N)e Fu(][)p Fw(y)34 b Fu(::=)26
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8766
b Fw(L)p Fu(])67 b(=)e Fw(M)24 b Fu([)p Fw(y)34 b Fu(::=)26
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8767
b Fw(L)p Fu(][)p Fw(x)g Fu(::=)g Fw(N)e Fu([)p Fw(y)34
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8768
b Fu(::=)26 b Fw(L)p Fu(]])p Black Fx(\224)p Blue 4481
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8769
5955 a(using)p Black 56 w(a)55 b(b)p Blue 56 w(by)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8770
55 w(\(nominal)p 6263 5955 V 67 w(induct)95 b Fw(M)118
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8771
b Fx(avoiding:)109 b Fw(x)135 b(y)142 b(N)158 b(L)95
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8772
b Fx(rule:)108 b(lam)p 10105 5955 V 67 w(induct\))5557
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8773
6196 y(\(auto)54 b(simp)i(add:)109 b(forget)94 b(fresh)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8774
8132 6196 V 68 w(fact\))p 0 TeXcolorgray 10797 5925 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8775
 0 setgray
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8776
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8777
10797 5925 a 0.5 TeXcolorgray 8954 6307 a FB(Cambridge,)27
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8778
b(5.)h(December)e(2005)h(\226)h(p.4)f(\(3/3\))p 0 TeXcolorgray
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8779
4360 6416 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8780
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8781
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8782
%%Page: 5 12
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8783
TeXDict begin 5 11 bop 0 TeXcolorgray 4360 6416 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8784
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8785
 4360
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8786
6416 a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8787
SDict begin /product where{pop product(Distiller)search{pop pop pop
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8788
version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8789
closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8790
grestore}if}{pop}ifelse}{pop}ifelse}if end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8791
 4585 1909 a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8792
SDict begin H.S end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8793
 4585 1909
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8794
a 0 TeXcolorgray 0 TeXcolorgray 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8795
SDict begin H.R end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8796
 4585 1909
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8797
a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8798
SDict begin [ /View [/XYZ H.V] /Dest (page.1) cvn H.B /DEST pdfmark
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8799
end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8800
 4585 1909 a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8801
SDict begin [ {ThisPage}<</Trans << /S /R >> >> /PUT pdfmark end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8802
 4585 1909 a 4585
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8803
1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8804
SDict begin [ /Page 12/View [ /XYZ null null null ] /Title (Weakening Lemma)
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8805
/OUT pdfmark end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8806
 4585 1909 a Gray 5408 2027 a FH(W)-33 b(eak)-5
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8807
b(ening)127 b(Lemma)p 0 TeXcolorgray Black 1 1 0.8 TeXcolorrgb
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8808
1 1 0.8 TeXcolorrgb 4599 2987 6249 713 v 1 1 0.8 TeXcolorrgb
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8809
Black 4785 2525 a Fp(Weakening)144 b(Lemma:)k Fn(If)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8810
Blue 100 w Fm(\000)7535 2562 y Fl(1)7791 2525 y Fk(`)e
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8811
Fj(t)f Fm(:)h Fj(\033)p Black 109 w Fn(and)p Blue 99
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8812
w Fm(\000)9490 2562 y Fl(2)p Black 9701 2525 a Fn(is)100
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8813
b(a)g(valid)4785 2785 y(super-context)67 b(of)p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8814
67 w Fm(\000)6794 2822 y Fl(1)p Black 6905 2785 a Fn(,)f(then)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8815
Blue 66 w Fm(\000)7740 2822 y Fl(2)7930 2785 y Fk(`)79
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8816
b Fj(t)g Fm(:)h Fj(\033)p Black 9 w Fn(.)p 1 1 0.8 TeXcolorrgb
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8817
Black Black Green Black Green Black OliveGreen Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8818
4893 3401 a @beginspecial @setspecial
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8819
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8820
0.0 0.0 9.14807 9.14807 .5 Frame  gsave 2.0 -45. PtoC Shadow TeXDict
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8821
begin OliveGreen end gsave fill grestore stroke grestore gsave TeXDict
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8822
begin Green end gsave fill grestore stroke grestore gsave TeXDict begin
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8823
Green end fill grestore gsave 0.0 SLW TeXDict begin Green end 0 setlinecap
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8824
stroke  grestore end
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8825
 
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8826
@endspecial Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8827
284 w Fp(valid)p 5177 3447 487 10 v 1 w Fn(:)i(no)67
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8828
b(variable)g(has)g(two)f(assigned)i(types)p Black Green
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8829
Black Green Black OliveGreen Black 4893 3837 a @beginspecial
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8830
@setspecial
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  8831
 tx@Dict begin STP newpath 0.0 SLW TeXDict begin Green end  0. true
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
  9114
y Ft(2)5678 2845 y Fv(`)f Fw(t)g Fu(:)g Fw(\033)p Black
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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8 w Fx(\224)p Blue 4728 3096 a(using)p Black 52 w(a)55
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9116
b(b)h(c)p Blue 4728 3347 a(apply)p Black 55 w(\(nominal)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9117
5937 3347 V 68 w(induct)f Fu(\000)6730 3378 y Ft(1)6889
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9118
3347 y Fw(t)g(\033)63 b Fx(avoiding:)69 b Fu(\000)8194
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9119
3378 y Ft(2)8353 3347 y Fx(rule:)f(typing)p 9358 3347
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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V 67 w(induct\))p Blue 4728 3598 a(apply)p Black 55 w(\(auto)55
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b(simp)h(add:)69 b(sc)p 6799 3598 V 68 w(def\))p Blue
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Christian Urban <urbanc@in.tum.de>
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4728 3849 a(done)p Black 0 TeXcolorgray 10797 5925 a
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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10797 5925 a 0.5 TeXcolorgray 8969 6307 a FB(Cambridge,)27
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Christian Urban <urbanc@in.tum.de>
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b(5.)g(December)g(2005)g(\226)g(p.9)h(\(1/2\))p 0 TeXcolorgray
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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6198 2343 56 9 v 67 w(lemma:)p Blue 4725 2594 a(assumes)p
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Christian Urban <urbanc@in.tum.de>
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Black 107 w(a:)52 b(\224)p OliveGreen Fu(\000)5958 2625
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Christian Urban <urbanc@in.tum.de>
parents:
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y Ft(1)6128 2594 y Fv(`)66 b Fw(t)g Fu(:)g Fw(\033)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
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Black 8 w Fx(\224)p Blue 55 w(and)p Black 107 w(b:)52
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b(\224)p OliveGreen Fu(\000)7742 2625 y Ft(1)7912 2594
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
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y Fv(\034)66 b Fu(\000)8359 2625 y Ft(2)p Black 8463
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
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2594 a Fx(\224)p Blue 55 w(and)p Black 107 w(c:)53 b(\224)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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OliveGreen(valid)66 b Fu(\000)9881 2625 y Ft(2)p Black
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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9985 2594 a Fx(\224)p Blue 4725 2845 a(shows)p Black
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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52 w(\224)p OliveGreen Fu(\000)5505 2876 y Ft(2)5675
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9163
2845 y Fv(`)g Fw(t)g Fu(:)g Fw(\033)p Black 8 w Fx(\224)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Blue 4725 3096 a(using)p Black 51 w(a)55 b(b)h(c)p Blue
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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V 67 w(induct)g Fu(\000)6764 3378 y Ft(1)6923 3347 y
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Christian Urban <urbanc@in.tum.de>
parents:
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Fw(t)f(\033)63 b Fx(avoiding:)69 b Fu(\000)8228 3378
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Christian Urban <urbanc@in.tum.de>
parents:
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y Ft(2)8387 3347 y Fx(rule:)f(typing)p 9392 3347 V 66
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Christian Urban <urbanc@in.tum.de>
parents:
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w(induct\))p Blue 4842 3598 a(case)p Black 56 w(\(t3)55
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9170
b Fw(a)66 b Fu(\000)5944 3629 y Ft(1)6048 3598 y Fw(\034)93
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b(\033)74 b(t)p Fx(\))p Orchid 55 w(\(*)56 b(lambda-case)g(*\))p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9172
Black Blue 4842 3849 a(have)p Black 52 w(a1:)c(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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OliveGreen Fu(\000)5790 3880 y Ft(1)5960 3849 y Fv(\034)65
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9174
b Fu(\000)6406 3880 y Ft(2)p Black 6510 3849 a Fx(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Blue 55 w(by)p Black 56 w(fact)p Blue 4842 4100 a(have)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9176
Black 52 w(a2:)53 b(\224)p OliveGreen(valid)e Fu(\000)6268
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9177
4131 y Ft(2)p Black 6372 4100 a Fx(\224)p Blue 56 w(by)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Black 55 w(fact)p Blue 4842 4351 a(have)p Black 56 w(ih:)69
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b(\224)p OliveGreen -155 x Ff(V)5860 4351 y Fu(\000)6003
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9180
4382 y Ft(3)6107 4351 y Fw(:)d Fu(\()p Fw(a;)39 b(\034)28
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9181
b Fu(\))e(::)g(\000)7122 4382 y Ft(1)7253 4351 y Fv(\034)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9182
Fu(\000)7660 4382 y Ft(3)7790 4351 y Fu(=)-40 b Fv(\))26
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9183
b Fx(valid)67 b Fu(\000)8806 4382 y Ft(3)8936 4351 y
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9184
Fu(=)-40 b Fv(\))26 b Fu(\000)9488 4382 y Ft(3)9658 4351
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9185
y Fv(`)66 b Fw(t)f Fu(:)h Fw(\033)p Black 8 w Fx(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Blue 55 w(by)p Black 56 w(fact)p Blue 4842 4602 a(have)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9187
Black 56 w(fc:)k(\224)p OliveGreen Fw(a)65 b Fu(#)h(\000)6282
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9188
4633 y Ft(2)p Black 6386 4602 a Fx(\224)p Blue 56 w(by)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Black 55 w(fact)p Blue 4842 4852 a(have)p Black 56 w(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9190
OliveGreen Fu(\()p Fw(a;)40 b(\034)28 b Fu(\))e(::)g(\000)6249
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9191
4883 y Ft(1)6419 4852 y Fv(\034)65 b Fu(\()p Fw(a;)40
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b(\034)28 b Fu(\))e(::)g(\000)7606 4883 y Ft(2)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9193
7710 4852 a Fx(\224)p Blue 56 w(using)p Black 55 w(a1)55
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b(sc)p 8759 4852 V 68 w(def)p Blue 55 w(by)p Black 56
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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w(simp)p Blue 4842 5103 a(moreover)p Black Blue 4842
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9196
5354 a(have)p Black 56 w(\224)p OliveGreen(valid)h Fu(\()p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9197
Fw(a;)39 b(\034)28 b Fu(\))e(::)g(\000)6701 5385 y Ft(2)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Black 6806 5354 a Fx(\224)p Blue 55 w(using)p Black 55
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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w(a2)56 b(fc)p Blue 56 w(by)p Black 56 w(force)p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9200
4842 5605 a(ultimately)e(have)p Black 51 w(\224)p OliveGreen
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9201
Fu(\()p Fw(a;)40 b(\034)28 b Fu(\))e(::)g(\000)7163 5636
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9202
y Ft(2)7333 5605 y Fv(`)67 b Fw(t)e Fu(:)h Fw(\033)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Black 8 w Fx(\224)p Blue 55 w(using)p Black 55 w(ih)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Blue 56 w(by)p Black 55 w(simp)p Blue 4842 5856 a(with)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9205
Black 52 w(fc)p Blue 52 w(show)p Black 52 w(\224)p OliveGreen
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9206
Fu(\000)6199 5887 y Ft(2)6369 5856 y Fv(`)g Fx(Lam)h
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9207
Fu([)p Fw(a)p Fu(])p Fw(:t)e Fu(:)h Fw(\034)93 b Fv(!)66
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b Fw(\033)p Black 8 w Fx(\224)p Blue 51 w(by)p Black
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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55 w(force)p Blue 4725 6107 a(qed)51 b(by)p Black 51
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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w(\(auto)k(simp)h(add:)69 b(sc)p 6917 6107 V 68 w(def\))p
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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  9235
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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1 1 0.8 TeXcolorrgb Black 4661 1866 a Fz(Reducibility)71
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Christian Urban <urbanc@in.tum.de>
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diff changeset
  9246
b(Lemma:)c Fx(Let)p Blue 49 w Fw(t)p Black 49 w Fx(be)50
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9247
b(any)f(term)g(\(not)g(assumed)h(to)f(be)g(reducible\),)4661
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9248
2086 y(and)63 b(suppose)g(all)f(the)g(free)h(variables)h(of)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9249
Blue 63 w Fw(t)p Black 62 w Fx(are)f(among)p Blue 62
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9250
w Fw(x)9152 2117 y Ft(1)p Black 9256 2086 a Fx(,.)34
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9251
b(.)f(.)h(,)p Blue Fw(x)9733 2117 y Fr(n)p Black 9925
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9252
2086 a Fx(of)63 b(types)p Blue 4661 2307 a Fw(U)4826
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9253
2338 y Ft(1)p Black 4930 2307 a Fx(,.)34 b(.)f(.)g(,)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9254
Blue Fw(U)5435 2338 y Fr(n)p Black 5565 2307 a Fx(.)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9255
b(If)p Blue 44 w Fw(u)6058 2338 y Ft(1)p Black 6162 2307
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9256
a Fx(,.)33 b(.)h(.)f(,)p Blue Fw(u)6643 2338 y Fr(n)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9257
Black 6817 2307 a Fx(are)44 b(reducible)h(terms)f(of)h(types)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9258
Blue 44 w Fw(U)9478 2338 y Ft(1)p Black 9582 2307 a Fx(,.)34
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9259
b(.)f(.)g(,)p Blue Fw(U)10087 2338 y Fr(n)p Black 10262
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9260
2307 a Fx(then)p Blue 4661 2535 a Fw(t)p Fu([)p Fw(x)4949
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9261
2566 y Ft(1)5119 2535 y Fu(:=)65 b Fw(u)5576 2566 y Ft(1)5680
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9262
2535 y Fw(;)39 b(:)h(:)g(:)f(;)h(x)6344 2566 y Fr(n)6539
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9263
2535 y Fu(:=)66 b Fw(u)6997 2566 y Fr(n)7126 2535 y Fu(])p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9264
Black 55 w Fx(is)56 b(reducible.)p 1 1 0.8 TeXcolorrgb
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9265
Black 4582 2887 a Fz(Proof:)69 b Fx(By)55 b(induction)h(on)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9266
Blue 55 w Fw(t)p Black Fx(.)68 b(We)56 b(write)p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9267
55 w Fw(t)p Fu([)p Fw(x)p 7785 2920 137 9 v 66 w Fu(:=)65
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9268
b Fw(u)p 8303 2920 141 9 v Fu(])p Black 55 w Fx(for)56
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9269
b(the)f(substitution.)4553 3169 y Fv(\017)100 b Fz(Case)80
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9270
b(1)p Blue 56 w Fw(t)p Black 55 w Fx(is)p Blue 56 w Fw(x)5908
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9271
3200 y Fr(i)p Black 5986 3169 a Fx(:)4772 3421 y(one)87
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9272
b(has)i(to)e(check)j(the)d(tautology)e(\223if)p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9273
89 w Fw(u)8128 3452 y Fr(i)p Black 8294 3421 a Fx(is)j(reducible,)97
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9274
b(then)p Blue 88 w Fw(u)10102 3452 y Fr(i)p Black 10267
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9275
3421 a Fx(is)89 b(re-)4772 3642 y(ducible\224;)55 b(details)g(are)h
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9276
(left)e(to)h(the)g(reader.)4553 3953 y Fv(\017)100 b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9277
Fz(Case)80 b(2)p Blue 56 w Fw(t)p Black 55 w Fx(is)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9278
Blue 56 w Fw(w)45 b(v)p Black 8 w Fx(:)4772 4206 y(by)55
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9279
b(induction)g(hypothesis)p Blue 55 w Fw(w)6 b Fu([)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9280
Fw(x)p 7103 4239 137 9 v 65 w Fu(:=)66 b Fw(u)p 7621
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9281
4239 141 9 v Fu(])p Black 55 w Fx(and)p Blue 55 w Fw(v)8
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9282
b Fu([)p Fw(x)p 8430 4239 137 9 v 66 w Fu(:=)66 b Fw(u)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9283
8949 4239 141 9 v -1 w Fu(])p Black 56 w Fx(are)55 b(reducible,)g(and)
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9284
4772 4434 y(so)70 b(\(by)g(de\002nition\))p Blue 70 w
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9285
Fw(w)6 b Fu([)p Fw(x)p 6574 4467 137 9 v 95 w Fu(:=)95
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9286
b Fw(u)p 7151 4467 141 9 v Fu(]\()p Fw(v)8 b Fu([)p Fw(x)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9287
7641 4467 137 9 v 96 w Fu(:=)95 b Fw(u)p 8219 4467 141
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9288
9 v Fu(]\))p Black Fx(;)78 b(but)70 b(this)g(term)g(is)h(nothing)4772
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9289
4662 y(other)54 b(than)p Blue 56 w Fw(t)p Fu([)p Fw(x)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9290
5905 4695 137 9 v 66 w Fu(:=)65 b Fw(u)p 6423 4695 141
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9291
9 v Fu(])p Black Fx(.)4553 4973 y Fv(\017)100 b Fz(Case)80
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9292
b(3)p Blue 56 w Fw(t)p Black 55 w Fx(is)p Blue 56 w Fw(\025y)8
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9293
b(:w)p Black 60 w Fx(of)56 b(type)p Blue 54 w Fw(V)119
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9294
b Fv(!)65 b Fw(W)p Black 33 w Fx(:)4772 5225 y(by)59
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9295
b(induction)g(hypothesis,)p Blue 61 w Fw(w)6 b Fu([)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9296
Fw(x)p 7168 5258 137 9 v 73 w Fu(:=)74 b Fw(u)p 7702
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9297
5258 141 9 v -1 w(;)40 b(y)81 b Fu(:=)74 b Fw(v)8 b Fu(])p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9298
Black 59 w Fx(is)60 b(reducible)f(for)g(all)p Blue 59
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9299
w Fw(v)p Black 67 w Fx(of)4772 5453 y(type)p Blue 72
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9300
w Fw(V)p Black 53 w Fx(.)122 b(Lemma)6252 5453 y
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9301
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9302
3.13422 } false /N@A 16 {InitRnode } NewNode end end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9303
 6252
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9304
5453 a Fx(6.3.2)75 b(says)f(that)p Blue 73 w Fw(t)p Fu([)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9305
Fw(x)p 7807 5486 137 9 v 101 w Fu(:=)102 b Fw(u)p 8397
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9306
5486 141 9 v -1 w Fu(])g(=)f Fw(\025y)8 b(:)p Fu(\()p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9307
Fw(w)e Fu([)p Fw(x)p 9662 5486 137 9 v 101 w Fu(:=)102
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9308
b Fw(u)p 10252 5486 141 9 v -1 w Fu(]\))p Black 74 w
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9309
Fx(is)4772 5674 y(reducible.)4755 b(\223)40 b Fs(\003)f
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9310
Fx(\224)p 0 TeXcolorgray 10797 5925 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9311
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9312
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9313
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9314
(\226)h(p.10)f(\(1/2\))p 0 TeXcolorgray 4360 6416 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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6416 a eop end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9318
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9321
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9322
6416 a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9323
SDict begin /product where{pop product(Distiller)search{pop pop pop
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9324
version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9325
closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9326
grestore}if}{pop}ifelse}{pop}ifelse}if end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9327
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9328
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9330
a 0 TeXcolorgray 0 TeXcolorgray 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9331
SDict begin H.R end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9332
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9333
a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9334
SDict begin [ /View [/XYZ H.V] /Dest (page.1) cvn H.B /DEST pdfmark
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9335
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9336
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9337
SDict begin [ {ThisPage}<</Trans << /S /R >> >> /PUT pdfmark end
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9338
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9339
0 TeXcolorgray Black 1 1 0.8 TeXcolorrgb 1 1 0.8 TeXcolorrgb
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9340
4599 2664 6119 1016 v 1 1 0.8 TeXcolorrgb Black 4661
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9341
1866 a Fz(Reducibility)71 b(Lemma:)c Fx(Let)p Blue 49
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9342
w Fw(t)p Black 49 w Fx(be)50 b(any)f(term)g(\(not)g(assumed)h(to)f(be)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9343
(reducible\),)4661 2086 y(and)63 b(suppose)g(all)f(the)g(free)h
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9344
(variables)h(of)p Blue 63 w Fw(t)p Black 62 w Fx(are)f(among)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9345
Blue 62 w Fw(x)9152 2117 y Ft(1)p Black 9256 2086 a Fx(,.)34
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9346
b(.)f(.)h(,)p Blue Fw(x)9733 2117 y Fr(n)p Black 9925
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9347
2086 a Fx(of)63 b(types)p Blue 4661 2307 a Fw(U)4826
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9348
2338 y Ft(1)p Black 4930 2307 a Fx(,.)34 b(.)f(.)g(,)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9349
Blue Fw(U)5435 2338 y Fr(n)p Black 5565 2307 a Fx(.)66
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9350
b(If)p Blue 44 w Fw(u)6058 2338 y Ft(1)p Black 6162 2307
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9351
a Fx(,.)33 b(.)h(.)f(,)p Blue Fw(u)6643 2338 y Fr(n)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9352
Black 6817 2307 a Fx(are)44 b(reducible)h(terms)f(of)h(types)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9353
Blue 44 w Fw(U)9478 2338 y Ft(1)p Black 9582 2307 a Fx(,.)34
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9354
b(.)f(.)g(,)p Blue Fw(U)10087 2338 y Fr(n)p Black 10262
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9355
2307 a Fx(then)p Blue 4661 2535 a Fw(t)p Fu([)p Fw(x)4949
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9356
2566 y Ft(1)5119 2535 y Fu(:=)65 b Fw(u)5576 2566 y Ft(1)5680
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9357
2535 y Fw(;)39 b(:)h(:)g(:)f(;)h(x)6344 2566 y Fr(n)6539
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9358
2535 y Fu(:=)66 b Fw(u)6997 2566 y Fr(n)7126 2535 y Fu(])p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9359
Black 55 w Fx(is)56 b(reducible.)p 1 1 0.8 TeXcolorrgb
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9360
Black 4582 2887 a Fz(Proof:)69 b Fx(By)55 b(induction)h(on)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9361
Blue 55 w Fw(t)p Black Fx(.)68 b(We)56 b(write)p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9362
55 w Fw(t)p Fu([)p Fw(x)p 7785 2920 137 9 v 66 w Fu(:=)65
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9363
b Fw(u)p 8303 2920 141 9 v Fu(])p Black 55 w Fx(for)56
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9364
b(the)f(substitution.)4553 3169 y Fv(\017)100 b Fz(Case)80
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9365
b(1)p Blue 56 w Fw(t)p Black 55 w Fx(is)p Blue 56 w Fw(x)5908
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9366
3200 y Fr(i)p Black 5986 3169 a Fx(:)4772 3421 y(one)87
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9367
b(has)i(to)e(check)j(the)d(tautology)e(\223if)p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9368
89 w Fw(u)8128 3452 y Fr(i)p Black 8294 3421 a Fx(is)j(reducible,)97
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9369
b(then)p Blue 88 w Fw(u)10102 3452 y Fr(i)p Black 10267
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9370
3421 a Fx(is)89 b(re-)4772 3642 y(ducible\224;)55 b(details)g(are)h
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9371
(left)e(to)h(the)g(reader.)4553 3953 y Fv(\017)100 b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9372
Fz(Case)80 b(2)p Blue 56 w Fw(t)p Black 55 w Fx(is)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9373
Blue 56 w Fw(w)45 b(v)p Black 8 w Fx(:)4772 4206 y(by)55
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9374
b(induction)g(hypothesis)p Blue 55 w Fw(w)6 b Fu([)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9375
Fw(x)p 7103 4239 137 9 v 65 w Fu(:=)66 b Fw(u)p 7621
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9376
4239 141 9 v Fu(])p Black 55 w Fx(and)p Blue 55 w Fw(v)8
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9377
b Fu([)p Fw(x)p 8430 4239 137 9 v 66 w Fu(:=)66 b Fw(u)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9378
8949 4239 141 9 v -1 w Fu(])p Black 56 w Fx(are)55 b(reducible,)g(and)
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9379
4772 4434 y(so)70 b(\(by)g(de\002nition\))p Blue 70 w
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9380
Fw(w)6 b Fu([)p Fw(x)p 6574 4467 137 9 v 95 w Fu(:=)95
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9381
b Fw(u)p 7151 4467 141 9 v Fu(]\()p Fw(v)8 b Fu([)p Fw(x)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9382
7641 4467 137 9 v 96 w Fu(:=)95 b Fw(u)p 8219 4467 141
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9383
9 v Fu(]\))p Black Fx(;)78 b(but)70 b(this)g(term)g(is)h(nothing)4772
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9384
4662 y(other)54 b(than)p Blue 56 w Fw(t)p Fu([)p Fw(x)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9385
5905 4695 137 9 v 66 w Fu(:=)65 b Fw(u)p 6423 4695 141
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9386
9 v Fu(])p Black Fx(.)4553 4973 y Fv(\017)100 b Fz(Case)80
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9387
b(3)p Blue 56 w Fw(t)p Black 55 w Fx(is)p Blue 56 w Fw(\025y)8
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9388
b(:w)p Black 60 w Fx(of)56 b(type)p Blue 54 w Fw(V)119
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9389
b Fv(!)65 b Fw(W)p Black 33 w Fx(:)4772 5225 y(by)59
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9390
b(induction)g(hypothesis,)p Blue 61 w Fw(w)6 b Fu([)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9391
Fw(x)p 7168 5258 137 9 v 73 w Fu(:=)74 b Fw(u)p 7702
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9392
5258 141 9 v -1 w(;)40 b(y)81 b Fu(:=)74 b Fw(v)8 b Fu(])p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9393
Black 59 w Fx(is)60 b(reducible)f(for)g(all)p Blue 59
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9394
w Fw(v)p Black 67 w Fx(of)4772 5453 y(type)p Blue 72
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9395
w Fw(V)p Black 53 w Fx(.)122 b(Lemma)6252 5453 y
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5453 a Fx(6.3.2)75 b(says)f(that)p Blue 73 w Fw(t)p Fu([)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9400
Fw(x)p 7807 5486 137 9 v 101 w Fu(:=)102 b Fw(u)p 8397
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9401
5486 141 9 v -1 w Fu(])g(=)f Fw(\025y)8 b(:)p Fu(\()p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9402
Fw(w)e Fu([)p Fw(x)p 9662 5486 137 9 v 101 w Fu(:=)102
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9403
b Fw(u)p 10252 5486 141 9 v -1 w Fu(]\))p Black 74 w
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9404
Fx(is)4772 5674 y(reducible.)4755 b(\223)40 b Fs(\003)f
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Fx(\224)5891 5955 y
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9415
@endspecial -118
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9416
x Fx(Lemma)56 b(6.3.2:)71 b(If)55 b(for)h(all)f(reducible)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9417
Blue 55 w Fw(u)p Black 55 w Fx(of)g(type)p Blue 55 w
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9418
Fw(U)p Black 24 w Fx(,)p Blue 5969 6065 a Fw(v)8 b Fu([)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9419
Fw(x)66 b Fu(:=)g Fw(u)p Fu(])p Black 55 w Fx(is)55 b(reducible,)h
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9420
(then)f(so)g(is)p Blue 56 w Fw(\025x:v)p Black 8 w Fx(.)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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8912 6307 a FB(Cambridge,)27 b(5.)h(December)f(2005)f(\226)i(p.10)f
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
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diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9450
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9455
w(Rd:)p Blue 4481 2049 a(assumes)p Black 56 w(a:)69 b(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9456
OliveGreen Fu(\000)d Fv(`)g Fw(t)g Fu(:)g Fw(\034)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9457
28 w Fx(\224)p Blue 4893 2291 a(and)p Black 55 w(b:)k(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9458
OliveGreen Fv(8)p Fw(x)39 b(\033)-6 b(:)67 b Fu(\()p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9459
Fw(x;)40 b(\033)8 b Fu(\))26 b Fv(2)g Fx(set)40 b Fu(\000)65
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9460
b Fv(\000)-39 b(!)65 b Fw(x)26 b Fv(2)g Fx(dom)q Fu(\()p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9461
Fw(\022)7 b Fu(\))54 b Fv(^)f Fw(\022)7 b Fv(h)p Fw(x)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9462
Fv(i)26 b(2)g Fw(R)q(d)10126 2322 y Fr(\033)p Black 10255
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9463
2291 a Fx(\224)p Blue 4481 2532 a(shows)p Black 56 w(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9464
OliveGreen Fw(t)p Fu([)p Fw(\022)7 b Fu(])66 b Fv(2)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9465
Fw(R)q(d)6060 2563 y Fr(\034)p Black 6178 2532 a Fx(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9466
Blue 4481 2774 a(using)p Black 56 w(a)55 b(b)p Blue 56
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9467
w(proof)p Black 55 w(\(nominal)p 6534 2774 V 67 w(induct)h
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9468
Fw(t)f Fx(avoiding:)69 b Fu(\000)55 b Fw(\034)83 b(\022)101
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9469
b Fx(rule:)108 b(lam)p 9550 2774 V 67 w(induct\))p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9470
4481 3016 a(case)p Black 56 w(\(Lam)j Fw(a)f(t)p Fx(\))p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9471
Blue 4658 3257 a(have)p Black 55 w(ih:)70 b(\224)p OliveGreen
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9472
-155 x Ff(V)5675 3257 y Fu(\000)40 b Fw(\034)67 b(\022)7
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9473
b(:)65 b Fu(\000)h Fv(`)g Fw(t)g Fu(:)g Fw(\034)94 b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9474
Fu(=)-40 b Fv(\))p Black OliveGreen 4658 3499 a Fu(\()p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9475
Fv(8)p Fw(x)40 b(\033)-6 b(:)66 b Fu(\()p Fw(x;)40 b(\033)8
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9476
b Fu(\))26 b Fv(2)g Fx(set)40 b Fu(\000)26 b Fv(\000)-40
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9477
b(!)26 b Fw(x)g Fv(2)g Fx(dom)q Fu(\()p Fw(\022)7 b Fu(\))44
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9478
b Fv(^)f Fw(\022)7 b Fv(h)p Fw(x)p Fv(i)26 b(2)g Fw(R)q(d)9220
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9479
3530 y Fr(\033)9349 3499 y Fu(\))67 b(=)-40 b Fv(\))65
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9480
b Fw(t)p Fu([)p Fw(\022)7 b Fu(])26 b Fv(2)g Fw(R)q(d)10814
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9481
3530 y Fr(\034)p Black 10933 3499 a Fx(\224)p Blue 4658
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9482
3741 a(and)p Black 55 w Fw(\022)p 5148 3741 V 74 w Fx(cond:)69
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9483
b(\224)p OliveGreen Fv(8)p Fw(x)40 b(\033)-6 b(:)66 b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9484
Fu(\()p Fw(x;)40 b(\033)8 b Fu(\))26 b Fv(2)g Fx(set)40
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9485
b Fu(\000)26 b Fv(\000)-39 b(!)26 b Fw(x)g Fv(2)g Fx(dom)q
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9486
Fu(\()p Fw(\022)7 b Fu(\))53 b Fv(^)g Fw(\022)7 b Fv(h)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9487
Fw(x)p Fv(i)26 b(2)g Fw(R)q(d)10290 3772 y Fr(\033)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9488
Black 10419 3741 a Fx(\224)p Blue 4658 3982 a(and)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9489
55 w(fr:)70 b(\224)p OliveGreen Fw(a)c Fu(#)g(\000)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9490
Black Fx(\224)51 b(\224)p OliveGreen Fw(a)66 b Fu(#)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9491
Fw(\022)p Black 7 w Fx(\224)p Blue 4658 4224 a(and)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9492
Black 55 w(\224)p OliveGreen Fu(\000)g Fv(`)g Fx(Lam)40
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9493
b Fu([)p Fw(a)p Fu(])p Fw(:t)66 b Fu(:)g Fw(\034)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9494
28 w Fx(\224)p Blue 55 w(by)p Black 55 w(fact)p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9495
4658 4466 a(hence)p Black 52 w(\224)p OliveGreen Fv(9)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9496
Fw(\034)5526 4497 y Ft(1)5629 4466 y Fw(\034)5737 4497
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9497
y Ft(2)5841 4466 y Fw(:\034)54 b Fu(=)26 b Fw(\034)6388
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9498
4497 y Ft(1)6478 4466 y Fv(!)-13 b Fw(\034)6811 4497
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9499
y Ft(2)6954 4466 y Fv(^)40 b Fu(\()p Fw(a;)f(\034)7588
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9500
4497 y Ft(1)7692 4466 y Fu(\))26 b(::)g(\000)g Fv(`)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9501
Fw(t)g Fu(:)g Fw(\034)8620 4497 y Ft(2)p Black 8726 4466
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9502
a Fx(\224)p Blue 52 w(using)p Black 52 w(t3)p 9550 4466
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9503
V 67 w(elim)52 b(fr)p Blue 52 w(by)p Black 52 w(simp)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9504
Blue 4658 4707 a(then)j(obtain)p Black OliveGreen 55
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9505
w Fw(\034)5810 4738 y Ft(1)p Black OliveGreen 5969 4707
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9506
a Fw(\034)6077 4738 y Ft(2)p Black Blue 6236 4707 a Fx(where)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9507
Black 55 w Fw(\034)p 6965 4707 V 94 w Fx(inst:)70 b(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9508
OliveGreen Fw(\034)53 b Fu(=)26 b Fw(\034)8025 4738 y
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9509
Ft(1)8116 4707 y Fv(!)-13 b Fw(\034)8449 4738 y Ft(2)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9510
Black 8552 4707 a Fx(\224)p Blue 6244 4949 a(and)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9511
56 w(ty:)68 b(\224)p OliveGreen Fu(\()p Fw(a;)40 b(\034)7419
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9512
4980 y Ft(1)7523 4949 y Fu(\)#\000)26 b Fv(`)g Fw(t)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9513
Fu(:)g Fw(\034)8465 4980 y Ft(2)p Black 8570 4949 a Fx(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9514
Blue 55 w(by)p Black 56 w(blast)p Blue 4658 5191 a(from)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9515
Black 56 w(ih)p Blue 55 w(have)p Black 56 w(\224)p OliveGreen
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9516
Fv(8)p Fw(s)66 b Fv(2)g Fw(R)q(d)6715 5222 y Fr(\034)6803
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9517
5242 y Fe(1)6902 5191 y Fw(:t)p Fu([)p Fw(\022)7 b Fu(][)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9518
Fw(a)26 b Fu(::=)g Fw(s)p Fu(])65 b Fv(2)i Fw(R)q(d)8648
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9519
5222 y Fr(\034)8736 5242 y Fe(2)p Black 8835 5191 a Fx(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9520
Blue 55 w(using)p Black 55 w(fr)56 b(ty)f Fw(\022)p 10066
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9521
5191 V 74 w Fx(cond)p Blue 4893 5432 a(by)p Black 55
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9522
w(\(force)h(dest:)68 b(fresh)p 6762 5432 V 68 w(context)54
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9523
b(simp)j(add:)69 b(psubts)p 9015 5432 V 67 w(subst\))p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9524
Blue 4658 5674 a(hence)p Black 55 w(\224)p OliveGreen(Lam)40
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9525
b Fu([)p Fw(a)p Fu(])p Fw(:)p Fu(\()p Fw(t)p Fu([)p Fw(\022)7
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9526
b Fu(]\))66 b Fv(2)h Fw(R)q(d)7122 5705 y Fr(\034)7210
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9527
5726 y Fe(1)7298 5705 y Fd(!)p Fr(\034)7573 5726 y Fe(2)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9528
Black 7672 5674 a Fx(\224)p Blue 56 w(by)p Black 55 w(\(simp)56
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9529
b(only:)69 b(abs)p 9345 5674 V 67 w(Rd\))59 b(\226\224Lem.)d(6.3.2\224)
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9530
p Blue 4481 5916 a(thus)p Black 56 w(\224)p OliveGreen
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9531
Fu(\()p Fx(Lam)40 b Fu([)p Fw(a)p Fu(])p Fw(:t)p Fu(\)[)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9532
Fw(\022)7 b Fu(])65 b Fv(2)i Fw(R)q(d)6824 5947 y Fr(\034)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9533
Black 6942 5916 a Fx(\224)p Blue 55 w(using)p Black 56
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9534
w(fr)56 b Fw(\034)p 7946 5916 V 94 w Fx(inst)p Blue 56
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9535
w(by)p Black 55 w(simp)p Blue 4481 6157 a(qed)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9536
55 w(\(force)g(dest!:)69 b(t1)p 6186 6157 V 66 w(elim)55
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9537
b(t2)p 6857 6157 V 67 w(elim\)+)p Red Black 1 1 0.8 TeXcolorrgb
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9544
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9545
-338 x Fz(Reducibility)79 b(Lemma:)69 b Fx(Let)p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9546
55 w Fw(t)p Black 54 w Fx(be)55 b(any)g(term)g(\(not)f(assumed)h(to)f
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9547
(be)h(reducible\),)4643 3822 y(and)g(suppose)h(all)f(the)g(free)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9548
(variables)h(of)p Blue 56 w Fw(t)p Black 55 w Fx(are)f(among)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9549
Blue 55 w Fw(x)9060 3853 y Ft(1)p Black 9164 3822 a Fx(,.)34
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9550
b(.)f(.)h(,)p Blue Fw(x)9641 3853 y Fr(n)p Black 9826
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9551
3822 a Fx(of)55 b(types)p Blue 4643 4043 a Fw(U)4808
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9552
4074 y Ft(1)p Black 4912 4043 a Fx(,.)34 b(.)f(.)g(,)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9553
Blue Fw(U)5417 4074 y Fr(n)p Black 5547 4043 a Fx(.)69
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9554
b(If)p Blue 56 w Fw(u)6055 4074 y Ft(1)p Black 6158 4043
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9555
a Fx(,.)34 b(.)f(.)h(,)p Blue Fw(u)6640 4074 y Fr(n)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9556
Black 6824 4043 a Fx(are)56 b(reducible)f(terms)g(of)h(types)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9557
Blue 55 w Fw(U)9540 4074 y Ft(1)p Black 9644 4043 a Fx(,.)33
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9558
b(.)h(.)f(,)p Blue Fw(U)10149 4074 y Fr(n)p Black 4643
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9559
4271 a Fx(then)p Blue 55 w Fw(t)p Fu([)p Fw(x)5380 4302
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9560
y Ft(1)5550 4271 y Fu(:=)65 b Fw(u)6007 4302 y Ft(1)6111
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9561
4271 y Fw(;)40 b(:)f(:)h(:)f(;)h(x)6775 4302 y Fr(n)6970
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9562
4271 y Fu(:=)66 b Fw(u)7428 4302 y Fr(n)7557 4271 y Fu(])p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9563
Black 55 w Fx(is)56 b(reducible.)p 0 TeXcolorgray 10797
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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5925 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b(5.)h(December)e(2005)h(\226)h(p.11)f(\(1/2\))p 0 TeXcolorgray
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9575
6416 a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9580
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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a 4585 1909 a
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9587
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9589
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9590
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9592
0 TeXcolorgray Black Blue 4481 1807 a Fx(lemma)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9593
56 w(all)p 5281 1807 56 9 v 66 w(Rd:)p Blue 4481 2049
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9594
a(assumes)p Black 56 w(a:)69 b(\224)p OliveGreen Fu(\000)d
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9595
Fv(`)g Fw(t)g Fu(:)g Fw(\034)p Black 28 w Fx(\224)p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9596
4893 2291 a(and)p Black 55 w(b:)k(\224)p OliveGreen Fv(8)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9597
Fw(x)39 b(\033)-6 b(:)67 b Fu(\()p Fw(x;)40 b(\033)8
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9598
b Fu(\))26 b Fv(2)g Fx(set)40 b Fu(\000)65 b Fv(\000)-39
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9599
b(!)65 b Fw(x)26 b Fv(2)g Fx(dom)q Fu(\()p Fw(\022)7
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9600
b Fu(\))54 b Fv(^)f Fw(\022)7 b Fv(h)p Fw(x)p Fv(i)26
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9601
b(2)g Fw(R)q(d)10126 2322 y Fr(\033)p Black 10255 2291
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9602
a Fx(\224)p Blue 4481 2532 a(shows)p Black 56 w(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9603
OliveGreen Fw(t)p Fu([)p Fw(\022)7 b Fu(])66 b Fv(2)g
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9604
Fw(R)q(d)6060 2563 y Fr(\034)p Black 6178 2532 a Fx(\224)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9605
Blue 4481 2774 a(using)p Black 56 w(a)55 b(b)p Blue 56
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9606
w(proof)p Black 55 w(\(nominal)p 6534 2774 V 67 w(induct)h
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9607
Fw(t)f Fx(avoiding:)69 b Fu(\000)55 b Fw(\034)83 b(\022)101
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9608
b Fx(rule:)108 b(lam)p 9550 2774 V 67 w(induct\))p Blue
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9609
4481 3016 a(case)p Black 56 w(\(Lam)j Fw(a)f(t)p Fx(\))p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9610
Blue 4658 3257 a(have)p Black 55 w(ih:)70 b(\224)p OliveGreen
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9611
-155 x Ff(V)5675 3257 y Fu(\000)40 b Fw(\034)67 b(\022)7
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9612
b(:)65 b Fu(\000)h Fv(`)g Fw(t)g Fu(:)g Fw(\034)94 b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9613
Fu(=)-40 b Fv(\))p Black OliveGreen 4658 3499 a Fu(\()p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9614
Fv(8)p Fw(x)40 b(\033)-6 b(:)66 b Fu(\()p Fw(x;)40 b(\033)8
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9615
b Fu(\))26 b Fv(2)g Fx(set)40 b Fu(\000)26 b Fv(\000)-40
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9616
b(!)26 b Fw(x)g Fv(2)g Fx(dom)q Fu(\()p Fw(\022)7 b Fu(\))44
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9617
b Fv(^)f Fw(\022)7 b Fv(h)p Fw(x)p Fv(i)26 b(2)g Fw(R)q(d)9220
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9618
3530 y Fr(\033)9349 3499 y Fu(\))67 b(=)-40 b Fv(\))65
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9619
b Fw(t)p Fu([)p Fw(\022)7 b Fu(])26 b Fv(2)g Fw(R)q(d)10814
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9620
3530 y Fr(\034)p Black 10933 3499 a Fx(\224)p Blue 4658
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9621
3741 a(and)p Black 55 w Fw(\022)p 5148 3741 V 74 w Fx(cond:)69
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9622
b(\224)p OliveGreen Fv(8)p Fw(x)40 b(\033)-6 b(:)66 b
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9623
Fu(\()p Fw(x;)40 b(\033)8 b Fu(\))26 b Fv(2)g Fx(set)40
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9624
b Fu(\000)26 b Fv(\000)-39 b(!)26 b Fw(x)g Fv(2)g Fx(dom)q
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9625
Fu(\()p Fw(\022)7 b Fu(\))53 b Fv(^)g Fw(\022)7 b Fv(h)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9626
Fw(x)p Fv(i)26 b(2)g Fw(R)q(d)10290 3772 y Fr(\033)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9627
Black 10419 3741 a Fx(\224)p Blue 4658 3982 a(and)p Black
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9628
55 w(fr:)70 b(\224)p OliveGreen Fw(a)c Fu(#)g(\000)p
345dd18f020e added slides
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9629
Black Fx(\224)51 b(\224)p OliveGreen Fw(a)66 b Fu(#)g
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Christian Urban <urbanc@in.tum.de>
parents:
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Fw(\022)p Black 7 w Fx(\224)p Blue 4658 4224 a(and)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Black 55 w(\224)p OliveGreen Fu(\000)g Fv(`)g Fx(Lam)40
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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b Fu([)p Fw(a)p Fu(])p Fw(:t)66 b Fu(:)g Fw(\034)p Black
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Christian Urban <urbanc@in.tum.de>
parents:
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28 w Fx(\224)p Blue 55 w(by)p Black 55 w(fact)p Blue
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Fw(\034)5526 4497 y Ft(1)5629 4466 y Fw(\034)5737 4497
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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y Ft(2)5841 4466 y Fw(:\034)54 b Fu(=)26 b Fw(\034)6388
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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4497 y Ft(1)6478 4466 y Fv(!)-13 b Fw(\034)6811 4497
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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y Ft(2)6954 4466 y Fv(^)40 b Fu(\()p Fw(a;)f(\034)7588
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  9639
4497 y Ft(1)7692 4466 y Fu(\))26 b(::)g(\000)g Fv(`)g
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Fw(t)g Fu(:)g Fw(\034)8620 4497 y Ft(2)p Black 8726 4466
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Christian Urban <urbanc@in.tum.de>
parents:
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a Fx(\224)p Blue 52 w(using)p Black 52 w(t3)p 9550 4466
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Christian Urban <urbanc@in.tum.de>
parents:
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V 67 w(elim)52 b(fr)p Blue 52 w(by)p Black 52 w(simp)p
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Christian Urban <urbanc@in.tum.de>
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Blue 4658 4707 a(then)j(obtain)p Black OliveGreen 55
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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w Fw(\034)5810 4738 y Ft(1)p Black OliveGreen 5969 4707
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Christian Urban <urbanc@in.tum.de>
parents:
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a Fw(\034)6077 4738 y Ft(2)p Black Blue 6236 4707 a Fx(where)p
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Christian Urban <urbanc@in.tum.de>
parents:
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Black 55 w Fw(\034)p 6965 4707 V 94 w Fx(inst:)70 b(\224)p
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Fu(:)g Fw(\034)8465 4980 y Ft(2)p Black 8570 4949 a Fx(\224)p
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Fv(8)p Fw(s)66 b Fv(2)g Fw(R)q(d)6715 5222 y Fr(\034)6803
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Fw(a)26 b Fu(::=)g Fw(s)p Fu(])65 b Fv(2)i Fw(R)q(d)8648
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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b Fu([)p Fw(a)p Fu(])p Fw(:)p Fu(\()p Fw(t)p Fu([)p Fw(\022)7
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Christian Urban <urbanc@in.tum.de>
parents:
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b Fu(]\))66 b Fv(2)h Fw(R)q(d)7122 5705 y Fr(\034)7210
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Black 7672 5674 a Fx(\224)p Blue 56 w(by)p Black 55 w(\(simp)56
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Christian Urban <urbanc@in.tum.de>
parents:
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b(only:)69 b(abs)p 9345 5674 V 67 w(Rd\))59 b(\226\224Lem.)d(6.3.2\224)
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Fu(\()p Fx(Lam)40 b Fu([)p Fw(a)p Fu(])p Fw(:t)p Fu(\)[)p
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Fw(\022)7 b Fu(])65 b Fv(2)i Fw(R)q(d)6824 5947 y Fr(\034)p
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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%%Trailer
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Christian Urban <urbanc@in.tum.de>
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%%EOF