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59 %%EndProcSet |
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60 %%BeginProcSet: pstricks.pro 0 0 |
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61 %! |
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62 % PostScript prologue for pstricks.tex. |
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63 % Version 97 patch 4, 04/05/10 |
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64 % For distribution, see pstricks.tex. |
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65 % |
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66 /tx@Dict 200 dict def tx@Dict begin |
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67 /ADict 25 dict def |
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68 /CM { matrix currentmatrix } bind def |
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69 /SLW /setlinewidth load def |
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70 /CLW /currentlinewidth load def |
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71 /CP /currentpoint load def |
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72 /ED { exch def } bind def |
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73 /L /lineto load def |
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74 /T /translate load def |
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75 /TMatrix { } def |
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76 /RAngle { 0 } def |
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77 /Atan { /atan load stopped { pop pop 0 } if } def |
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78 /Div { dup 0 eq { pop } { div } ifelse } def |
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79 /NET { neg exch neg exch T } def |
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80 /Pyth { dup mul exch dup mul add sqrt } def |
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81 /PtoC { 2 copy cos mul 3 1 roll sin mul } def |
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82 /PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } |
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83 def |
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84 /PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def |
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85 } { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } |
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86 /pathforall load stopped { pop pop pop pop } if z } def |
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87 /STP { .996264 dup scale } def |
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88 /STV { SDict begin normalscale end STP } def |
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89 % |
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90 %%-------------- DG begin patch 15 ---------------%% |
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91 %/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def |
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92 %PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y |
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93 %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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94 %/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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95 %0 } ifelse setdash stroke } def |
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96 /DashLine { |
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97 dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse |
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98 /b ED /x1 ED /y1 ED /x ED /y ED |
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99 /z y x add y1 add x1 add def |
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100 /Coef b a .5 sub 2 mul y mul sub z Div round |
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101 z mul a .5 sub 2 mul y mul add b exch Div def |
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102 /y y Coef mul def /x x Coef mul def /y1 y1 Coef mul def /x1 x1 Coef mul def |
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103 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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104 { [ 1 0] 0 } ifelse setdash stroke |
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105 } def |
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106 %%-------------- DG end patch 15 ---------------%% |
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107 /DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt |
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108 { /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y add |
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109 def } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if |
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110 ] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1 |
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111 setlinecap stroke } def |
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112 /LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch |
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113 2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 |
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114 % DG/SR modification begin - Dec. 12, 1997 - Patch 2 |
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115 %itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a |
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116 itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a |
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117 % DG/SR modification end |
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118 Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict |
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119 /setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 |
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120 % DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) |
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121 % a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } |
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122 % def |
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123 a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore |
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124 pop pop } def |
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125 % DG/SR modification end |
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126 /BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg |
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127 exch 3 index sub exch Atan rotate newpath } def |
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128 /EndArrow { @mtrx setmatrix CP grestore end } def |
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129 /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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130 scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill |
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131 grestore } def |
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132 /Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0 |
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133 CLW moveto } def |
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134 /Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 |
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135 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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136 CLW moveto } def |
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137 /RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW |
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138 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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139 curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } |
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140 def |
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141 /SD { 0 360 arc fill } def |
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142 /EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS |
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143 CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def |
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144 /Shadow { [ { /moveto load } { /lineto load } { /curveto load } { |
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145 /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto |
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146 load } if ] cvx newpath 3 1 roll T exec } def |
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147 /NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch |
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148 cvi def } def |
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149 /NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if |
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150 f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def |
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151 /Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub |
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152 def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def |
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153 /Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } |
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154 ifelse { pop } repeat a } def |
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155 /CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq |
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156 and { pop pop /n n 1 sub def } if } def |
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157 /Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } |
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158 repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 |
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159 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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160 moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto |
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161 Lineto pop pop closepath } ifelse } def |
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162 /Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul |
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163 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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164 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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165 div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx |
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166 setmatrix } def |
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167 % DG modification begin - Jan. 15, 1997 |
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168 %/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { |
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169 %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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170 %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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171 %d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx |
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172 %setmatrix } def |
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173 /Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup |
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174 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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175 div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 |
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176 d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx |
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177 % DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) |
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178 % setmatrix } def |
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179 setmatrix pop } def |
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180 % DG/SR modification end |
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181 /CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth |
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182 def } def |
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183 /CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth |
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184 def } def |
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185 /CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 |
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186 def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp |
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187 mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos |
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188 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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189 /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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190 m mul neg def } def |
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191 /IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } |
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192 ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } |
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193 def |
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194 /BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def |
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195 /NC { CC x1 y1 x2 y2 x y curveto } def |
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196 /EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def |
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197 /BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def |
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198 /NAC { x2 y2 x y curveto CC x1 y1 } def |
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199 /EAC { x2 y2 x y ArrowB curveto pop pop } def |
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200 /OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def |
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201 n { NC } repeat EOC } ifelse } def |
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202 /AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload |
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203 /Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop |
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204 pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def |
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205 /ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { |
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206 CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } |
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207 repeat closepath pop pop } ifelse } def |
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208 /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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209 /ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def |
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210 /SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } |
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211 def |
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212 /FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix |
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213 rotate matrix concatmatrix exch findfont exch makefont setfont } def |
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214 /Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto |
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215 x1 y1 lineto closepath } def |
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216 /OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 |
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217 y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div |
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218 exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse |
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219 /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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220 x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } |
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221 ifelse } def |
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222 /Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add |
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223 /y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { |
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224 pop pop Rect } { OvalFrame } ifelse } def |
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225 /BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop |
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226 } if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] |
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227 aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def |
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228 /OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 |
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229 2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } |
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230 ifelse } def |
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231 /ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { |
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232 6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def |
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233 /BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 |
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234 sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } |
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235 def |
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236 /Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 |
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237 sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA |
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238 x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 |
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239 y0 x0 2 mul x1 sub y1 ] def } def |
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240 /Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } |
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241 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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242 /dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div |
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243 round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div |
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244 round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub |
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245 0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def |
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246 /Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } |
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247 if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } |
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248 { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add |
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249 exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n |
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250 div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 |
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251 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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252 dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { |
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253 pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup |
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254 stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} |
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255 {z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i |
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256 w add def } repeat grestore gsave n 0 gt |
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257 % DG/SR modification begin - Nov. 7, 1997 - Patch 1 |
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258 %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } |
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259 { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } |
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260 % DG/SR modification end |
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261 { 2 setlinecap } ifelse /i y1 def /f x1 dx mul |
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262 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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263 div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop |
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264 1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs |
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265 dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt |
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266 {z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g |
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267 exch t L stroke /i i h add def } repeat grestore } def |
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268 /ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 |
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269 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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270 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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271 mul neg d } def |
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272 /Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def |
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273 /Rot { CP CP translate 3 -1 roll neg rotate NET } def |
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274 /RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } |
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275 def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle |
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276 dup a add ] cvx def } def |
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277 /RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] |
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278 cvx def } def |
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279 /PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def |
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280 /PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def |
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281 /PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def |
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282 /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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283 abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b |
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284 div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { |
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285 h1 abs h sub dup s mul abs } ifelse } def |
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286 /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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287 mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q |
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288 { x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add |
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289 exch } def |
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290 /BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible |
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291 /IfVisible true def } if } { IfVisible { Invisible /IfVisible false def |
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292 } if } ifelse } def |
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293 /InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def |
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294 /Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit |
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295 neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def |
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296 /IfVisible true def } def |
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297 end |
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298 % END pstricks.pro |
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299 |
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301 %%BeginProcSet: pst-dots.pro 0 0 |
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302 %!PS-Adobe-2.0 |
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303 %%Title: Dot Font for PSTricks |
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304 %%Creator: Timothy Van Zandt <tvz@Princeton.EDU> |
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305 %%Creation Date: May 7, 1993 |
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306 %% Version 97 patch 1, 99/12/16 |
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307 %% Modified by Etienne Riga <etienne.riga@skynet.be> - Dec. 16, 1999 |
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308 %% to add /Diamond, /SolidDiamond and /BoldDiamond |
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309 10 dict dup begin |
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310 /FontType 3 def |
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311 /FontMatrix [ .001 0 0 .001 0 0 ] def |
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312 /FontBBox [ 0 0 0 0 ] def |
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313 /Encoding 256 array def |
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314 0 1 255 { Encoding exch /.notdef put } for |
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315 Encoding |
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316 dup (b) 0 get /Bullet put |
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317 dup (c) 0 get /Circle put |
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318 dup (C) 0 get /BoldCircle put |
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319 dup (u) 0 get /SolidTriangle put |
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320 dup (t) 0 get /Triangle put |
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321 dup (T) 0 get /BoldTriangle put |
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322 dup (r) 0 get /SolidSquare put |
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323 dup (s) 0 get /Square put |
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324 dup (S) 0 get /BoldSquare put |
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325 dup (q) 0 get /SolidPentagon put |
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326 dup (p) 0 get /Pentagon put |
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327 dup (P) 0 get /BoldPentagon put |
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328 % DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga |
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329 dup (l) 0 get /SolidDiamond put |
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330 dup (d) 0 get /Diamond put |
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331 (D) 0 get /BoldDiamond put |
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332 % DG/SR modification end |
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333 /Metrics 13 dict def |
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334 Metrics begin |
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335 /Bullet 1000 def |
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336 /Circle 1000 def |
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337 /BoldCircle 1000 def |
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338 /SolidTriangle 1344 def |
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339 /Triangle 1344 def |
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340 /BoldTriangle 1344 def |
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341 /SolidSquare 886 def |
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342 /Square 886 def |
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343 /BoldSquare 886 def |
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344 /SolidPentagon 1093.2 def |
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345 /Pentagon 1093.2 def |
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346 /BoldPentagon 1093.2 def |
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347 % DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga |
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348 /SolidDiamond 1008 def |
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349 /Diamond 1008 def |
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350 /BoldDiamond 1008 def |
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351 % DG/SR modification end |
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352 /.notdef 0 def |
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353 end |
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354 /BBoxes 13 dict def |
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355 BBoxes begin |
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356 /Circle { -550 -550 550 550 } def |
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357 /BoldCircle /Circle load def |
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358 /Bullet /Circle load def |
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359 /Triangle { -571.5 -330 571.5 660 } def |
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360 /BoldTriangle /Triangle load def |
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361 /SolidTriangle /Triangle load def |
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362 /Square { -450 -450 450 450 } def |
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363 /BoldSquare /Square load def |
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364 /SolidSquare /Square load def |
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365 /Pentagon { -546.6 -465 546.6 574.7 } def |
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366 /BoldPentagon /Pentagon load def |
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367 /SolidPentagon /Pentagon load def |
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368 % DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga |
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369 /Diamond { -428.5 -742.5 428.5 742.5 } def |
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370 /BoldDiamond /Diamond load def |
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371 /SolidDiamond /Diamond load def |
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372 % DG/SR modification end |
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373 /.notdef { 0 0 0 0 } def |
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374 end |
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375 /CharProcs 20 dict def |
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376 CharProcs begin |
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377 /Adjust { |
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378 2 copy dtransform floor .5 add exch floor .5 add exch idtransform |
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379 3 -1 roll div 3 1 roll exch div exch scale |
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380 } def |
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381 /CirclePath { 0 0 500 0 360 arc closepath } def |
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382 /Bullet { 500 500 Adjust CirclePath fill } def |
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383 /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath |
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384 eofill } def |
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385 /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath |
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386 eofill } def |
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387 /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def |
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388 /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto |
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389 closepath } def |
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390 /SolidTriangle { TrianglePath fill } def |
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391 /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def |
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392 /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def |
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393 /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto |
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394 -450 -450 lineto closepath } def |
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395 /SolidSquare { SquarePath fill } def |
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396 /Square { SquarePath .89 .89 scale SquarePath eofill } def |
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397 /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def |
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398 /PentagonPath { |
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399 -337.8 -465 moveto |
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400 337.8 -465 lineto |
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401 546.6 177.6 lineto |
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402 0 574.7 lineto |
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403 -546.6 177.6 lineto |
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404 closepath |
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405 } def |
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406 /SolidPentagon { PentagonPath fill } def |
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407 /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def |
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408 /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def |
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409 % DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga |
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410 /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto |
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411 428.5 0 lineto closepath } def |
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412 /SolidDiamond { DiamondPath fill } def |
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413 /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def |
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414 /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def |
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415 % DG/SR modification end |
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416 /.notdef { } def |
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417 end |
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418 /BuildGlyph { |
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419 exch |
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420 begin |
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421 Metrics 1 index get exec 0 |
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422 BBoxes 3 index get exec |
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423 setcachedevice |
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424 CharProcs begin load exec end |
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425 end |
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426 } def |
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427 /BuildChar { |
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428 1 index /Encoding get exch get |
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429 1 index /BuildGlyph get exec |
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430 } bind def |
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431 end |
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432 /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: 8r.enc 0 0 |
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437 % File 8r.enc TeX Base 1 Encoding Revision 2.0 2002-10-30 |
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438 % |
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439 % @@psencodingfile@{ |
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440 % author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry, |
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441 % W. Schmidt, P. Lehman", |
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442 % version = "2.0", |
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443 % date = "30 October 2002", |
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444 % filename = "8r.enc", |
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445 % email = "tex-fonts@@tug.org", |
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446 % docstring = "This is the encoding vector for Type1 and TrueType |
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447 % fonts to be used with TeX. This file is part of the |
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448 % PSNFSS bundle, version 9" |
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449 % @} |
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450 % |
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451 % The idea is to have all the characters normally included in Type 1 fonts |
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452 % available for typesetting. This is effectively the characters in Adobe |
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453 % Standard encoding, ISO Latin 1, Windows ANSI including the euro symbol, |
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454 % MacRoman, and some extra characters from Lucida. |
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455 % |
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456 % Character code assignments were made as follows: |
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457 % |
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458 % (1) the Windows ANSI characters are almost all in their Windows ANSI |
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459 % positions, because some Windows users cannot easily reencode the |
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460 % fonts, and it makes no difference on other systems. The only Windows |
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461 % ANSI characters not available are those that make no sense for |
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462 % typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen |
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463 % (173). quotesingle and grave are moved just because it's such an |
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464 % irritation not having them in TeX positions. |
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465 % |
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466 % (2) Remaining characters are assigned arbitrarily to the lower part |
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467 % of the range, avoiding 0, 10 and 13 in case we meet dumb software. |
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468 % |
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469 % (3) Y&Y Lucida Bright includes some extra text characters; in the |
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470 % hopes that other PostScript fonts, perhaps created for public |
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471 % consumption, will include them, they are included starting at 0x12. |
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472 % These are /dotlessj /ff /ffi /ffl. |
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473 % |
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474 % (4) hyphen appears twice for compatibility with both ASCII and Windows. |
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475 % |
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476 % (5) /Euro was assigned to 128, as in Windows ANSI |
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477 % |
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478 % (6) Missing characters from MacRoman encoding incorporated as follows: |
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479 % |
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480 % PostScript MacRoman TeXBase1 |
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481 % -------------- -------------- -------------- |
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482 % /notequal 173 0x16 |
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483 % /infinity 176 0x17 |
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484 % /lessequal 178 0x18 |
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485 % /greaterequal 179 0x19 |
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486 % /partialdiff 182 0x1A |
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487 % /summation 183 0x1B |
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488 % /product 184 0x1C |
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489 % /pi 185 0x1D |
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490 % /integral 186 0x81 |
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491 % /Omega 189 0x8D |
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492 % /radical 195 0x8E |
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493 % /approxequal 197 0x8F |
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494 % /Delta 198 0x9D |
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495 % /lozenge 215 0x9E |
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496 % |
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497 /TeXBase1Encoding [ |
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498 % 0x00 |
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499 /.notdef /dotaccent /fi /fl |
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500 /fraction /hungarumlaut /Lslash /lslash |
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501 /ogonek /ring /.notdef /breve |
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502 /minus /.notdef /Zcaron /zcaron |
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503 % 0x10 |
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504 /caron /dotlessi /dotlessj /ff |
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505 /ffi /ffl /notequal /infinity |
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506 /lessequal /greaterequal /partialdiff /summation |
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507 /product /pi /grave /quotesingle |
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508 % 0x20 |
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509 /space /exclam /quotedbl /numbersign |
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510 /dollar /percent /ampersand /quoteright |
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511 /parenleft /parenright /asterisk /plus |
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512 /comma /hyphen /period /slash |
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513 % 0x30 |
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514 /zero /one /two /three |
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515 /four /five /six /seven |
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516 /eight /nine /colon /semicolon |
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517 /less /equal /greater /question |
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518 % 0x40 |
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519 /at /A /B /C |
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520 /D /E /F /G |
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521 /H /I /J /K |
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522 /L /M /N /O |
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523 % 0x50 |
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524 /P /Q /R /S |
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525 /T /U /V /W |
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526 /X /Y /Z /bracketleft |
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527 /backslash /bracketright /asciicircum /underscore |
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528 % 0x60 |
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529 /quoteleft /a /b /c |
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530 /d /e /f /g |
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531 /h /i /j /k |
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532 /l /m /n /o |
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533 % 0x70 |
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534 /p /q /r /s |
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535 /t /u /v /w |
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536 /x /y /z /braceleft |
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537 /bar /braceright /asciitilde /.notdef |
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538 % 0x80 |
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539 /Euro /integral /quotesinglbase /florin |
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540 /quotedblbase /ellipsis /dagger /daggerdbl |
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541 /circumflex /perthousand /Scaron /guilsinglleft |
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542 /OE /Omega /radical /approxequal |
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543 % 0x90 |
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544 /.notdef /.notdef /.notdef /quotedblleft |
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545 /quotedblright /bullet /endash /emdash |
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546 /tilde /trademark /scaron /guilsinglright |
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547 /oe /Delta /lozenge /Ydieresis |
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548 % 0xA0 |
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549 /.notdef /exclamdown /cent /sterling |
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550 /currency /yen /brokenbar /section |
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551 /dieresis /copyright /ordfeminine /guillemotleft |
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552 /logicalnot /hyphen /registered /macron |
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553 % 0xD0 |
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554 /degree /plusminus /twosuperior /threesuperior |
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555 /acute /mu /paragraph /periodcentered |
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556 /cedilla /onesuperior /ordmasculine /guillemotright |
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557 /onequarter /onehalf /threequarters /questiondown |
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558 % 0xC0 |
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559 /Agrave /Aacute /Acircumflex /Atilde |
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560 /Adieresis /Aring /AE /Ccedilla |
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561 /Egrave /Eacute /Ecircumflex /Edieresis |
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562 /Igrave /Iacute /Icircumflex /Idieresis |
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563 % 0xD0 |
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564 /Eth /Ntilde /Ograve /Oacute |
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565 /Ocircumflex /Otilde /Odieresis /multiply |
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566 /Oslash /Ugrave /Uacute /Ucircumflex |
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567 /Udieresis /Yacute /Thorn /germandbls |
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568 % 0xE0 |
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569 /agrave /aacute /acircumflex /atilde |
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570 /adieresis /aring /ae /ccedilla |
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571 /egrave /eacute /ecircumflex /edieresis |
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572 /igrave /iacute /icircumflex /idieresis |
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573 % 0xF0 |
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574 /eth /ntilde /ograve /oacute |
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575 /ocircumflex /otilde /odieresis /divide |
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576 /oslash /ugrave /uacute /ucircumflex |
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577 /udieresis /yacute /thorn /ydieresis |
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578 ] def |
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579 |
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580 |
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581 %%EndProcSet |
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582 %%BeginProcSet: texps.pro 0 0 |
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583 %! |
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584 TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 |
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585 index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll |
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586 exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]FontType 0 |
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587 ne{/Metrics exch def dict begin Encoding{exch dup type/integertype ne{ |
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588 pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get |
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589 div def}ifelse}forall Metrics/Metrics currentdict end def}{{1 index type |
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590 /nametype eq{exit}if exch pop}loop}ifelse[2 index currentdict end |
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591 definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{dup |
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592 sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll |
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594 exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}if} |
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595 forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}def |
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596 end |
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597 |
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598 %%EndProcSet |
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599 %%BeginProcSet: special.pro 0 0 |
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600 %! |
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601 TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N |
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602 /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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603 /rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N |
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604 /@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ |
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605 /hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho |
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606 X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B |
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607 /@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ |
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608 /urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known |
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609 {userdict/md get type/dicttype eq{userdict begin md length 10 add md |
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610 maxlength ge{/md md dup length 20 add dict copy def}if end md begin |
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611 /letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S |
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612 atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ |
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613 itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll |
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614 transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll |
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615 curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf |
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616 pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} |
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617 if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 |
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621 neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ |
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656 |
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678 setcmykcolor}DC/Magenta{0 1 0 0 setcmykcolor}DC/VioletRed{0 0.81 0 0 |
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680 0 0.02 setcmykcolor}DC/RedViolet{0.07 0.90 0 0.34 setcmykcolor}DC |
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2597 0 TeXcolorgray eop end |
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2598 %%Page: 5 5 |
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2741 Fx(-terms)2042 1501 y Fz(M)9 b Fx(,)28 b(all)g Fz(\034)48 |
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2742 b Fv(2)38 b Fp(ty)d Fx(and)28 b(all)g(conte)n(xts)g Fz(x)38 |
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2744 b(holds:)2100 1758 y Fv(8)p Fz(x)14 b Fo(\000)g Fz(a)g(\034)5 |
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2746 Fz(a)k Fo(:)g Fz(\034)9 b Fo(\))24 b Fv(2)f Fo(\000)g |
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2747 Fv(\))g Fz(P)35 b Fo(\000)23 b(\()p Fp(var)10 b Fo(\()p |
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2750 1981 y Fo(\000)g Fv(`)g Fz(M)32 b Fo(:)23 b Fz(\034)33 |
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2751 b Fv(!)23 b Fz(\033)f Fv(^)c Fo(\()p Fv(8)p Fz(z)t(:)45 |
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2752 b(P)35 b Fo(\000)23 b Fz(M)32 b Fo(\()p Fz(\034)h Fv(!)23 |
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2753 b Fz(\033)s Fo(\))h Fz(z)t Fo(\))e Fv(^)2183 2080 y Fo(\000)h |
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2754 Fv(`)g Fz(N)32 b Fo(:)23 b Fz(\034)28 b Fv(^)19 b Fo(\()p |
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2755 Fv(8)p Fz(z)t(:)45 b(P)35 b Fo(\000)23 b Fz(N)32 b(\034)g(z)t |
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2756 Fo(\))46 b Fv(\))2183 2180 y Fz(P)35 b Fo(\000)23 b(\()p |
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2757 Fp(app)7 b Fo(\()p Fz(M)t(;)14 b(N)9 b Fo(\)\))24 b Fz(\033)i(x)2100 |
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2758 2303 y Fv(8)p Fz(x)14 b(a)g Fo(\000)g Fz(M)22 b(\034)h(\033)n(:)2183 |
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2760 b Fv(^)h Fo(\()p Fz(a)k Fo(:)g Fz(\034)5 b(;)14 b Fo(\000\))23 |
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2762 y Fo(\()p Fv(8)p Fz(z)t(:)c(P)35 b Fo(\()p Fz(a)23 b |
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2764 Fo(\))46 b Fv(\))2183 2602 y Fz(P)35 b Fo(\000)23 b(\()p |
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2765 Fp(lam)8 b Fo(\()p Fz(a;)14 b(M)9 b Fo(\)\))23 b(\()p |
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2766 Fz(\034)33 b Fv(!)23 b Fz(\033)s Fo(\))h Fz(x)p 2059 |
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2767 2652 1959 4 v 2578 2726 a Fo(\000)f Fv(`)g Fz(M)31 b |
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2768 Fo(:)23 b Fz(\034)56 b Fv(\))46 b Fz(P)35 b Fo(\000)23 |
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2769 b Fz(M)32 b(\034)h(x)p 0 TeXcolorgray 2042 2892 a Fx(Pr)l(oof.)p |
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2772 (goal)g(by)f(aiming)h(to)g(pro)o(v)o(e)2062 3157 y Fv(8)p |
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2773 Fz(\031)26 b Fo(\000)14 b Fz(M)22 b(\034)i Fo(\()p Fz(x)f |
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2774 Fv(2)h Fx(fs-pset)p Fo(\))p Fz(:)46 b Fo(\()23 b Fz(:)14 |
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2775 b(:)g(:)23 b Fo(\))h Fv(\))f Fz(P)35 b Fo(\()p Fz(\031)3417 |
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2776 3166 y Fj(\001)3455 3157 y Fo(\000\))24 b(\()p Fz(\031)3645 |
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2777 3166 y Fj(\001)3683 3157 y Fz(M)9 b Fo(\))23 b Fz(\034)33 |
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2780 3497 y Fj(\001)2826 3488 y Fo(\000\))23 b(\()p Fp(var)10 |
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2781 b Fo(\()p Fz(\031)3172 3497 y Fj(\001)3211 3488 y Fz(a)p |
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2782 Fo(\)\))23 b Fz(\034)33 b(x)2042 3654 y FC(while)22 b(kno)n(wing)e |
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2783 (that)i Fp(valid)11 b Fo(\(\000\))23 b FC(and)e Fo(\()p |
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2785 b FC(hold.)f(V)-9 b(alidity)2042 3754 y(of)37 b(conte)o(xts)f(is)j |
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2789 Fo(:)h Fz(\034)9 b Fo(\))24 b Fv(2)f Fo(\000)18 b FC(we)g(can)g(infer)f |
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2790 Fo(\()p Fz(\031)3563 3862 y Fj(\001)3601 3853 y Fz(a)23 |
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2791 b Fo(:)g Fz(\034)9 b Fo(\))25 b Fv(2)e Fz(\031)3944 3862 |
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2795 b Fo(\(\000\))19 b Fv(^)g Fo(\()p Fz(a)k Fo(:)g Fz(\034)9 |
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2796 b Fo(\))24 b Fv(2)f Fo(\000)g Fv(\))g Fz(P)35 b Fo(\000)23 |
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2797 b Fp(var)10 b Fo(\()p Fz(a)p Fo(\))23 b Fz(\034)33 b(x)2042 |
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2798 4284 y FC(to)20 b(obtain)f Fz(P)35 b Fo(\()p Fz(\031)2525 |
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2800 b Fo(\()p Fz(\031)2910 4293 y Fj(\001)2949 4284 y Fz(a)p |
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2801 Fo(\)\))23 b Fz(\034)33 b(x)p FC(.)2141 4384 y(The)16 |
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2805 4658 y Fj(\001)2590 4649 y Fo(\000\))23 b(\()p Fp(lam)7 |
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2806 b Fo(\()p Fz(\031)2949 4658 y Fj(\001)2988 4649 y Fz(a;)14 |
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2807 b(\031)3119 4658 y Fj(\001)3157 4649 y Fz(M)9 b Fo(\)\))24 |
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2808 b(\()p Fz(\034)33 b Fv(!)23 b Fz(\033)s Fo(\))g Fz(x)2042 |
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2809 4815 y FC(under)c(the)h(assumption)f(that)2398 4973 y |
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2810 Fo(\()p Fz(i)p Fo(\))83 b Fz(a)23 b Fo(#)g(\000)2369 |
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2811 5073 y(\()p Fz(ii)p Fo(\))83 b Fz(a)23 b Fo(:)g Fz(\034)5 |
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2812 b(;)14 b Fo(\000)23 b Fv(`)g Fz(M)31 b Fo(:)23 b Fz(\033)2340 |
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2813 5172 y Fo(\()p Fz(iii)p Fo(\))83 b Fv(8)p Fz(\031)16 |
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2814 b(x:)24 b(P)34 b Fo(\()p Fz(\031)2947 5181 y Fj(\001)2986 |
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2816 b(\()p Fz(\031)3431 5181 y Fj(\001)3470 5172 y Fz(M)9 |
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2817 b Fo(\))23 b Fz(\033)j(x)3938 5073 y FC(\(8\))2042 5330 |
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2819 (are)i(\002nitely)f(sup-)2042 5430 y(ported)22 b(and)h(by)h(assumption) |
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2820 e(also)i Fz(x)p FC(,)h(there)e(e)o(xists)h(by)g(Lem.)f(4)h(an)p |
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2821 0 TeXcolorgray 0 TeXcolorgray eop end |
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2822 %%Page: 6 6 |
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2823 TeXDict begin 6 5 bop 0 TeXcolorgray 0 TeXcolorgray 0 |
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2824 TeXcolorgray -150 66 a FC(atom)29 b Fz(c)g FC(with)h |
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2826 y Fz(a;)14 b(\031)725 75 y Fj(\001)763 66 y Fz(M)t(;)g(\031)935 |
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2827 75 y Fj(\001)974 66 y Fo(\000)p Fz(;)g(x)p Fo(\))p FC(.)30 |
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2829 y(infer)1 314 y Fv(8)p Fz(x:)23 b(P)35 b Fo(\(\()p Fz(c)28 |
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2830 b(\031)407 323 y Fj(\001)445 314 y Fz(a)p Fo(\))521 323 |
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2831 y Fj(\001)560 314 y Fz(\031)610 323 y Fj(\001)648 314 |
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2839 620 y Fj(\001)731 611 y Fz(\031)781 620 y Fj(\001)819 |
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2840 611 y Fo(\000\))23 b(\(\()p Fz(c)28 b(\031)1104 620 y |
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2842 611 y Fz(\031)1307 620 y Fj(\001)1346 611 y Fz(M)9 b |
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2843 Fo(\))23 b Fz(\034)32 b(x)140 b FC(\(9\))-150 759 y(From)22 |
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2844 b Fo(\()p Fz(i)p Fo(\))h FC(and)f(Lem.)g(2)p Fo(\()p |
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2846 y Fj(\001)1172 759 y Fz(a)k Fo(#)h Fz(\031)1390 768 y |
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2847 Fj(\001)1429 759 y Fo(\000)p FC(.)22 b(W)m(ith)h Fz(c)k |
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2848 Fo(#)-150 859 y Fz(\031)-100 868 y Fj(\001)-62 859 y |
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2849 Fo(\000)17 b FC(we)f(can)g(infer)f(using)g(Lem.)h(2)p |
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2850 Fo(\()p Fz(ii)p Fo(\))g FC(that)g Fo(\()p Fz(c)27 b(\031)1277 |
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2851 868 y Fj(\001)1316 859 y Fz(a)p Fo(\))1392 868 y Fj(\001)1430 |
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2852 859 y Fz(\031)1480 868 y Fj(\001)1519 859 y Fo(\000)c(=)f |
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2853 Fz(\031)1731 868 y Fj(\001)1770 859 y Fo(\000)p FC(,)-150 |
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2854 958 y(and)e(hence)f(simplify)h(\(9\))f(further)g(to)187 |
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2855 1106 y Fv(8)p Fz(x:)j(P)35 b Fo(\()p Fz(c)23 b Fo(:)h |
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2856 Fz(\034)5 b(;)14 b(\031)680 1115 y Fj(\001)718 1106 y |
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2857 Fo(\000\))23 b(\(\()p Fz(c)28 b(\031)1003 1115 y Fj(\001)1042 |
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2858 1106 y Fz(a)p Fo(\))1118 1115 y Fj(\001)1156 1106 y Fz(\031)1206 |
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2859 1115 y Fj(\001)1245 1106 y Fz(M)9 b Fo(\))23 b Fz(\034)32 |
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2860 b(x)199 b FC(\(10\))-150 1255 y(By)28 b(equi)n(v)n(ariance)c(of)j(the)g |
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2861 (typing)f(relation)h(\(7\))n(,)h(we)f(can)g(use)h Fo(\()p |
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2862 Fz(ii)p Fo(\))-150 1354 y FC(and)20 b(infer)152 1503 |
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2863 y Fo(\()p Fz(c)28 b(\031)298 1512 y Fj(\001)337 1503 |
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2864 y Fz(a)p Fo(\))413 1512 y Fj(\001)451 1503 y Fz(\031)501 |
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2865 1512 y Fj(\001)539 1503 y Fo(\()p Fz(a)c Fo(:)f Fz(\034)5 |
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2866 b(;)14 b Fo(\000\))23 b Fv(`)g Fo(\()p Fz(c)28 b(\031)1090 |
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2867 1512 y Fj(\001)1128 1503 y Fz(a)p Fo(\))1204 1512 y Fj(\001)1243 |
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2868 1503 y Fz(\031)1293 1512 y Fj(\001)1331 1503 y Fz(M)k |
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2869 Fo(:)23 b Fz(\033)-150 1651 y FC(which)d(is)306 1750 |
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2870 y Fo(\()p Fz(c)j Fo(:)g Fz(\034)5 b(;)14 b(\031)571 1759 |
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2871 y Fj(\001)609 1750 y Fo(\000\))24 b Fv(`)e Fo(\()p Fz(c)28 |
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2872 b(\031)936 1759 y Fj(\001)975 1750 y Fz(a)p Fo(\))1051 |
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2873 1759 y Fj(\001)1089 1750 y Fz(\031)1139 1759 y Fj(\001)1178 |
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2874 1750 y Fz(M)j Fo(:)24 b Fz(\033)320 b FC(\(11\))-150 |
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2875 1879 y(No)n(w)38 b(we)h(can)f(use)g Fz(c)56 b Fo(#)h |
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2878 2127 y Fz(P)35 b Fo(\()p Fz(\031)256 2136 y Fj(\001)294 |
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2879 2127 y Fo(\000\))24 b(\()p Fz(l)r(am)p Fo(\()p Fz(c;)14 |
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2880 b Fo(\()p Fz(c)27 b(\031)828 2136 y Fj(\001)866 2127 |
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2881 y Fz(a)p Fo(\))942 2136 y Fj(\001)981 2127 y Fz(\031)1031 |
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2882 2136 y Fj(\001)1069 2127 y Fz(M)9 b Fo(\)\))24 b(\()p |
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2883 Fz(\034)33 b Fv(!)23 b Fz(\033)s Fo(\))g Fz(x)-150 2275 |
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2884 y FC(Because)f Fz(c)j Fo(#)g Fz(\031)354 2284 y Fj(\001)393 |
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2885 2275 y Fz(a)d FC(and)e Fz(c)26 b Fo(#)f Fz(\031)806 2284 |
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2886 y Fj(\001)845 2275 y Fz(M)9 b FC(,)21 b(we)h(kno)n(w)e(by)h(\(5\))o(,)h |
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2887 (ho)n(we)n(v)o(er)m(,)-150 2375 y(that)135 2523 y Fz(l)r(am)p |
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2888 Fo(\()p Fz(c;)14 b Fo(\()p Fz(c)27 b(\031)529 2532 y |
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2889 Fj(\001)567 2523 y Fz(a)p Fo(\))643 2532 y Fj(\001)682 |
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2890 2523 y Fz(\031)732 2532 y Fj(\001)770 2523 y Fz(M)9 b |
|
2891 Fo(\))23 b(=)g Fz(l)r(am)p Fo(\()p Fz(\031)1229 2532 |
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2892 y Fj(\001)1267 2523 y Fz(a;)14 b(\031)1398 2532 y Fj(\001)1436 |
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2893 2523 y Fz(M)9 b Fo(\))-150 2671 y FC(and)20 b(we)g(are)g(done.)p |
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2894 1782 2671 4 57 v 1786 2619 50 4 v 1786 2671 V 1835 2671 |
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2895 4 57 v -50 2831 a(W)m(ith)g(this)h(induction)d(principle)h(at)i(our)f |
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2897 (is)h(simple.)p 0 TeXcolorgray -150 3089 a Fx(Pr)l(oof)f(of)g(the)h(W) |
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2898 -8 b(eak)o(ening)19 b(Lemma.)p 0 TeXcolorgray 28 w FC(Perform)49 |
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2899 b(a)h(rule)g(induction)-150 3189 y(o)o(v)o(er)19 b Fo(\000)68 |
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2900 3201 y Fu(1)128 3189 y Fv(`)k Fz(M)31 b Fo(:)24 b Fz(\034)30 |
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2901 b FC(using)20 b(the)g(induction)e(hypothesis)211 3337 |
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2902 y Fo(\000)263 3349 y Fu(1)324 3337 y Fv(\022)k Fo(\000)463 |
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2903 3349 y Fu(2)523 3337 y Fv(\))i Fp(valid)10 b Fo(\(\000)892 |
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2904 3349 y Fu(2)929 3337 y Fo(\))24 b Fv(\))f Fo(\000)1143 |
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2905 3349 y Fu(2)1203 3337 y Fv(`)g Fz(M)31 b Fo(:)23 b Fz(\034)-150 |
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2906 3485 y FC(That)d(is,)h(we)f(instantiate)g(Thm.)g(1)g(with)-96 |
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2907 3620 y Fz(P)107 b Fo(=)83 b Fz(\025)p Fo(\000)312 3632 |
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2908 y Fu(1)363 3620 y Fz(M)23 b(\034)g Fo(\000)578 3632 y |
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2909 Fu(2)615 3620 y Fz(:)46 b Fo(\000)736 3632 y Fu(1)797 |
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2910 3620 y Fv(\022)22 b Fo(\000)936 3632 y Fu(2)996 3620 |
|
2911 y Fv(\))i Fp(valid)10 b Fo(\(\000)1365 3632 y Fu(2)1402 |
|
2912 3620 y Fo(\))24 b Fv(\))f Fo(\000)1616 3632 y Fu(2)1676 |
|
2913 3620 y Fv(`)g Fz(M)31 b Fo(:)23 b Fz(\034)-90 3719 y |
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2914 Fo(\000)102 b(=)83 b(\000)264 3731 y Fu(1)-108 3819 y |
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2915 Fz(M)91 b Fo(=)83 b Fz(M)-87 3919 y(\034)115 b Fo(=)83 |
|
2916 b Fz(\034)-87 4018 y(x)104 b Fo(=)83 b(\000)264 4030 |
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2917 y Fu(2)-150 4158 y FC(where)16 b Fo(\000)122 4170 y Fu(2)182 |
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2918 4158 y Fv(2)24 b Fx(fs-pset)17 b FC(by)f(Lem.)h(3.)f(This)h(gi)n(v)o |
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2919 (es)g(the)f(follo)n(wing)g(three)-150 4257 y(sub-goals:)-150 |
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2920 4398 y Fo(\(1\))47 b Fp(valid)11 b Fo(\(\000)266 4368 |
|
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3704 Fb(Lectur)m(e)2209 4143 y(Notes)19 b(in)g(Computer)g(Science)p |
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3706 eop end |
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3707 %%Trailer |
|
3708 |
|
3709 userdict /end-hook known{end-hook}if |
|
3710 %%EOF |