14
|
1 |
%!PS-Adobe-2.0
|
|
2 |
%%Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software
|
|
3 |
%%Title: a04-urban.dvi
|
|
4 |
%%Pages: 8
|
|
5 |
%%PageOrder: Ascend
|
|
6 |
%%BoundingBox: 0 0 595 842
|
|
7 |
%%DocumentFonts: Times-Bold Times-Roman Times-BoldItalic Times-Italic
|
|
8 |
%%DocumentPaperSizes: a4
|
|
9 |
%%EndComments
|
|
10 |
%DVIPSWebPage: (www.radicaleye.com)
|
|
11 |
%DVIPSCommandLine: dvips a04-urban.dvi -o a04-urban.ps
|
|
12 |
%DVIPSParameters: dpi=600
|
|
13 |
%DVIPSSource: TeX output 2007.02.24:0557
|
|
14 |
%%BeginProcSet: tex.pro 0 0
|
|
15 |
%!
|
|
16 |
/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S
|
|
17 |
N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72
|
|
18 |
mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0
|
|
19 |
0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{
|
|
20 |
landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize
|
|
21 |
mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[
|
|
22 |
matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round
|
|
23 |
exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{
|
|
24 |
statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0]
|
|
25 |
N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin
|
|
26 |
/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array
|
|
27 |
/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2
|
|
28 |
array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N
|
|
29 |
df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A
|
|
30 |
definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get
|
|
31 |
}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub}
|
|
32 |
B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr
|
|
33 |
1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S
|
|
34 |
/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy
|
|
35 |
setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask
|
|
36 |
restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn
|
|
37 |
/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put
|
|
38 |
}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{
|
|
39 |
bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A
|
|
40 |
mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{
|
|
41 |
SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{
|
|
42 |
userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X
|
|
43 |
1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4
|
|
44 |
index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N
|
|
45 |
/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{
|
|
46 |
/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)
|
|
47 |
(LaserWriter 16/600)]{A length product length le{A length product exch 0
|
|
48 |
exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse
|
|
49 |
end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask
|
|
50 |
grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot}
|
|
51 |
imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round
|
|
52 |
exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto
|
|
53 |
fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p
|
|
54 |
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}
|
|
55 |
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{
|
|
56 |
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
|
|
57 |
rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end
|
|
58 |
|
|
59 |
%%EndProcSet
|
|
60 |
%%BeginProcSet: pstricks.pro 0 0
|
|
61 |
%!
|
|
62 |
% PostScript prologue for pstricks.tex.
|
|
63 |
% Version 97 patch 4, 04/05/10
|
|
64 |
% For distribution, see pstricks.tex.
|
|
65 |
%
|
|
66 |
/tx@Dict 200 dict def tx@Dict begin
|
|
67 |
/ADict 25 dict def
|
|
68 |
/CM { matrix currentmatrix } bind def
|
|
69 |
/SLW /setlinewidth load def
|
|
70 |
/CLW /currentlinewidth load def
|
|
71 |
/CP /currentpoint load def
|
|
72 |
/ED { exch def } bind def
|
|
73 |
/L /lineto load def
|
|
74 |
/T /translate load def
|
|
75 |
/TMatrix { } def
|
|
76 |
/RAngle { 0 } def
|
|
77 |
/Atan { /atan load stopped { pop pop 0 } if } def
|
|
78 |
/Div { dup 0 eq { pop } { div } ifelse } def
|
|
79 |
/NET { neg exch neg exch T } def
|
|
80 |
/Pyth { dup mul exch dup mul add sqrt } def
|
|
81 |
/PtoC { 2 copy cos mul 3 1 roll sin mul } def
|
|
82 |
/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def }
|
|
83 |
def
|
|
84 |
/PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
|
|
85 |
} { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ }
|
|
86 |
/pathforall load stopped { pop pop pop pop } if z } def
|
|
87 |
/STP { .996264 dup scale } def
|
|
88 |
/STV { SDict begin normalscale end STP } def
|
|
89 |
%
|
|
90 |
%%-------------- DG begin patch 15 ---------------%%
|
|
91 |
%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def
|
|
92 |
%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y
|
|
93 |
%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul
|
|
94 |
%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ]
|
|
95 |
%0 } ifelse setdash stroke } def
|
|
96 |
/DashLine {
|
|
97 |
dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse
|
|
98 |
/b ED /x1 ED /y1 ED /x ED /y ED
|
|
99 |
/z y x add y1 add x1 add def
|
|
100 |
/Coef b a .5 sub 2 mul y mul sub z Div round
|
|
101 |
z mul a .5 sub 2 mul y mul add b exch Div def
|
|
102 |
/y y Coef mul def /x x Coef mul def /y1 y1 Coef mul def /x1 x1 Coef mul def
|
|
103 |
x1 0 gt y1 0 gt x 0 gt y 0 gt and { [ y x y1 x1 ] 1 a sub y mul}
|
|
104 |
{ [ 1 0] 0 } ifelse setdash stroke
|
|
105 |
} def
|
|
106 |
%%-------------- DG end patch 15 ---------------%%
|
|
107 |
/DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt
|
|
108 |
{ /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y add
|
|
109 |
def } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if
|
|
110 |
] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1
|
|
111 |
setlinecap stroke } def
|
|
112 |
/LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch
|
|
113 |
2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25
|
|
114 |
% DG/SR modification begin - Dec. 12, 1997 - Patch 2
|
|
115 |
%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
|
|
116 |
itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
|
|
117 |
% DG/SR modification end
|
|
118 |
Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict
|
|
119 |
/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1
|
|
120 |
% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
|
|
121 |
% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }
|
|
122 |
% def
|
|
123 |
a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore
|
|
124 |
pop pop } def
|
|
125 |
% DG/SR modification end
|
|
126 |
/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg
|
|
127 |
exch 3 index sub exch Atan rotate newpath } def
|
|
128 |
/EndArrow { @mtrx setmatrix CP grestore end } def
|
|
129 |
/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1
|
|
130 |
scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill
|
|
131 |
grestore } def
|
|
132 |
/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0
|
|
133 |
CLW moveto } def
|
|
134 |
/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2
|
|
135 |
div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0
|
|
136 |
CLW moveto } def
|
|
137 |
/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW
|
|
138 |
2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0
|
|
139 |
curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto }
|
|
140 |
def
|
|
141 |
/SD { 0 360 arc fill } def
|
|
142 |
/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS
|
|
143 |
CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def
|
|
144 |
/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
|
|
145 |
/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
|
|
146 |
load } if ] cvx newpath 3 1 roll T exec } def
|
|
147 |
/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch
|
|
148 |
cvi def } def
|
|
149 |
/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if
|
|
150 |
f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
|
|
151 |
/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub
|
|
152 |
def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def
|
|
153 |
/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }
|
|
154 |
ifelse { pop } repeat a } def
|
|
155 |
/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
|
|
156 |
and { pop pop /n n 1 sub def } if } def
|
|
157 |
/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }
|
|
158 |
repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1
|
|
159 |
ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1
|
|
160 |
moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto
|
|
161 |
Lineto pop pop closepath } ifelse } def
|
|
162 |
/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul
|
|
163 |
neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add
|
|
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
|
|
165 |
div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
|
|
166 |
setmatrix } def
|
|
167 |
% DG modification begin - Jan. 15, 1997
|
|
168 |
%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {
|
|
169 |
%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
|
|
170 |
%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0
|
|
171 |
%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
|
|
172 |
%setmatrix } def
|
|
173 |
/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup
|
|
174 |
CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
|
|
175 |
div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0
|
|
176 |
d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
|
|
177 |
% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
|
|
178 |
% setmatrix } def
|
|
179 |
setmatrix pop } def
|
|
180 |
% DG/SR modification end
|
|
181 |
/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
|
|
182 |
def } def
|
|
183 |
/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
|
|
184 |
def } def
|
|
185 |
/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
|
|
186 |
def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
|
|
187 |
mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos
|
|
188 |
abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def
|
|
189 |
/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul
|
|
190 |
m mul neg def } def
|
|
191 |
/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }
|
|
192 |
ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }
|
|
193 |
def
|
|
194 |
/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
|
|
195 |
/NC { CC x1 y1 x2 y2 x y curveto } def
|
|
196 |
/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
|
|
197 |
/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
|
|
198 |
/NAC { x2 y2 x y curveto CC x1 y1 } def
|
|
199 |
/EAC { x2 y2 x y ArrowB curveto pop pop } def
|
|
200 |
/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def
|
|
201 |
n { NC } repeat EOC } ifelse } def
|
|
202 |
/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload
|
|
203 |
/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop
|
|
204 |
pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def
|
|
205 |
/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {
|
|
206 |
CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }
|
|
207 |
repeat closepath pop pop } ifelse } def
|
|
208 |
/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
|
|
209 |
/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
|
|
210 |
/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }
|
|
211 |
def
|
|
212 |
/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix
|
|
213 |
rotate matrix concatmatrix exch findfont exch makefont setfont } def
|
|
214 |
/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
|
|
215 |
x1 y1 lineto closepath } def
|
|
216 |
/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
|
|
217 |
y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
|
|
218 |
exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse
|
|
219 |
/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto
|
|
220 |
x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }
|
|
221 |
ifelse } def
|
|
222 |
/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add
|
|
223 |
/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {
|
|
224 |
pop pop Rect } { OvalFrame } ifelse } def
|
|
225 |
/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop
|
|
226 |
} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]
|
|
227 |
aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
|
|
228 |
/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6
|
|
229 |
2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }
|
|
230 |
ifelse } def
|
|
231 |
/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {
|
|
232 |
6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def
|
|
233 |
/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1
|
|
234 |
sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }
|
|
235 |
def
|
|
236 |
/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
|
|
237 |
sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
|
|
238 |
x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
|
|
239 |
y0 x0 2 mul x1 sub y1 ] def } def
|
|
240 |
/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 }
|
|
241 |
if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if
|
|
242 |
/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div
|
|
243 |
round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div
|
|
244 |
round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub
|
|
245 |
0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def
|
|
246 |
/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def }
|
|
247 |
if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def }
|
|
248 |
{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
|
|
249 |
exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n
|
|
250 |
div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1
|
|
251 |
dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt {
|
|
252 |
dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {
|
|
253 |
pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup
|
|
254 |
stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}
|
|
255 |
{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i
|
|
256 |
w add def } repeat grestore gsave n 0 gt
|
|
257 |
% DG/SR modification begin - Nov. 7, 1997 - Patch 1
|
|
258 |
%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
|
|
259 |
{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
|
|
260 |
% DG/SR modification end
|
|
261 |
{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul
|
|
262 |
n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n
|
|
263 |
div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop
|
|
264 |
1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs
|
|
265 |
dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt
|
|
266 |
{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g
|
|
267 |
exch t L stroke /i i h add def } repeat grestore } def
|
|
268 |
/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0
|
|
269 |
1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add
|
|
270 |
exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
|
|
271 |
mul neg d } def
|
|
272 |
/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
|
|
273 |
/Rot { CP CP translate 3 -1 roll neg rotate NET } def
|
|
274 |
/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }
|
|
275 |
def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle
|
|
276 |
dup a add ] cvx def } def
|
|
277 |
/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]
|
|
278 |
cvx def } def
|
|
279 |
/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
|
|
280 |
/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
|
|
281 |
/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
|
|
282 |
/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
|
|
283 |
abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
|
|
284 |
div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
|
|
285 |
h1 abs h sub dup s mul abs } ifelse } def
|
|
286 |
/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
|
|
287 |
mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
|
|
288 |
{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
|
|
289 |
exch } def
|
|
290 |
/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
|
|
291 |
/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
|
|
292 |
} if } ifelse } def
|
|
293 |
/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
|
|
294 |
/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
|
|
295 |
neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
|
|
296 |
/IfVisible true def } def
|
|
297 |
end
|
|
298 |
% END pstricks.pro
|
|
299 |
|
|
300 |
%%EndProcSet
|
|
301 |
%%BeginProcSet: pst-dots.pro 0 0
|
|
302 |
%!PS-Adobe-2.0
|
|
303 |
%%Title: Dot Font for PSTricks
|
|
304 |
%%Creator: Timothy Van Zandt <tvz@Princeton.EDU>
|
|
305 |
%%Creation Date: May 7, 1993
|
|
306 |
%% Version 97 patch 1, 99/12/16
|
|
307 |
%% Modified by Etienne Riga <etienne.riga@skynet.be> - Dec. 16, 1999
|
|
308 |
%% to add /Diamond, /SolidDiamond and /BoldDiamond
|
|
309 |
10 dict dup begin
|
|
310 |
/FontType 3 def
|
|
311 |
/FontMatrix [ .001 0 0 .001 0 0 ] def
|
|
312 |
/FontBBox [ 0 0 0 0 ] def
|
|
313 |
/Encoding 256 array def
|
|
314 |
0 1 255 { Encoding exch /.notdef put } for
|
|
315 |
Encoding
|
|
316 |
dup (b) 0 get /Bullet put
|
|
317 |
dup (c) 0 get /Circle put
|
|
318 |
dup (C) 0 get /BoldCircle put
|
|
319 |
dup (u) 0 get /SolidTriangle put
|
|
320 |
dup (t) 0 get /Triangle put
|
|
321 |
dup (T) 0 get /BoldTriangle put
|
|
322 |
dup (r) 0 get /SolidSquare put
|
|
323 |
dup (s) 0 get /Square put
|
|
324 |
dup (S) 0 get /BoldSquare put
|
|
325 |
dup (q) 0 get /SolidPentagon put
|
|
326 |
dup (p) 0 get /Pentagon put
|
|
327 |
dup (P) 0 get /BoldPentagon put
|
|
328 |
% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga
|
|
329 |
dup (l) 0 get /SolidDiamond put
|
|
330 |
dup (d) 0 get /Diamond put
|
|
331 |
(D) 0 get /BoldDiamond put
|
|
332 |
% DG/SR modification end
|
|
333 |
/Metrics 13 dict def
|
|
334 |
Metrics begin
|
|
335 |
/Bullet 1000 def
|
|
336 |
/Circle 1000 def
|
|
337 |
/BoldCircle 1000 def
|
|
338 |
/SolidTriangle 1344 def
|
|
339 |
/Triangle 1344 def
|
|
340 |
/BoldTriangle 1344 def
|
|
341 |
/SolidSquare 886 def
|
|
342 |
/Square 886 def
|
|
343 |
/BoldSquare 886 def
|
|
344 |
/SolidPentagon 1093.2 def
|
|
345 |
/Pentagon 1093.2 def
|
|
346 |
/BoldPentagon 1093.2 def
|
|
347 |
% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga
|
|
348 |
/SolidDiamond 1008 def
|
|
349 |
/Diamond 1008 def
|
|
350 |
/BoldDiamond 1008 def
|
|
351 |
% DG/SR modification end
|
|
352 |
/.notdef 0 def
|
|
353 |
end
|
|
354 |
/BBoxes 13 dict def
|
|
355 |
BBoxes begin
|
|
356 |
/Circle { -550 -550 550 550 } def
|
|
357 |
/BoldCircle /Circle load def
|
|
358 |
/Bullet /Circle load def
|
|
359 |
/Triangle { -571.5 -330 571.5 660 } def
|
|
360 |
/BoldTriangle /Triangle load def
|
|
361 |
/SolidTriangle /Triangle load def
|
|
362 |
/Square { -450 -450 450 450 } def
|
|
363 |
/BoldSquare /Square load def
|
|
364 |
/SolidSquare /Square load def
|
|
365 |
/Pentagon { -546.6 -465 546.6 574.7 } def
|
|
366 |
/BoldPentagon /Pentagon load def
|
|
367 |
/SolidPentagon /Pentagon load def
|
|
368 |
% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga
|
|
369 |
/Diamond { -428.5 -742.5 428.5 742.5 } def
|
|
370 |
/BoldDiamond /Diamond load def
|
|
371 |
/SolidDiamond /Diamond load def
|
|
372 |
% DG/SR modification end
|
|
373 |
/.notdef { 0 0 0 0 } def
|
|
374 |
end
|
|
375 |
/CharProcs 20 dict def
|
|
376 |
CharProcs begin
|
|
377 |
/Adjust {
|
|
378 |
2 copy dtransform floor .5 add exch floor .5 add exch idtransform
|
|
379 |
3 -1 roll div 3 1 roll exch div exch scale
|
|
380 |
} def
|
|
381 |
/CirclePath { 0 0 500 0 360 arc closepath } def
|
|
382 |
/Bullet { 500 500 Adjust CirclePath fill } def
|
|
383 |
/Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath
|
|
384 |
eofill } def
|
|
385 |
/BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath
|
|
386 |
eofill } def
|
|
387 |
/BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def
|
|
388 |
/TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto
|
|
389 |
closepath } def
|
|
390 |
/SolidTriangle { TrianglePath fill } def
|
|
391 |
/Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def
|
|
392 |
/BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def
|
|
393 |
/SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto
|
|
394 |
-450 -450 lineto closepath } def
|
|
395 |
/SolidSquare { SquarePath fill } def
|
|
396 |
/Square { SquarePath .89 .89 scale SquarePath eofill } def
|
|
397 |
/BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def
|
|
398 |
/PentagonPath {
|
|
399 |
-337.8 -465 moveto
|
|
400 |
337.8 -465 lineto
|
|
401 |
546.6 177.6 lineto
|
|
402 |
0 574.7 lineto
|
|
403 |
-546.6 177.6 lineto
|
|
404 |
closepath
|
|
405 |
} def
|
|
406 |
/SolidPentagon { PentagonPath fill } def
|
|
407 |
/Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def
|
|
408 |
/BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def
|
|
409 |
% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga
|
|
410 |
/DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto
|
|
411 |
428.5 0 lineto closepath } def
|
|
412 |
/SolidDiamond { DiamondPath fill } def
|
|
413 |
/Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def
|
|
414 |
/BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def
|
|
415 |
% DG/SR modification end
|
|
416 |
/.notdef { } def
|
|
417 |
end
|
|
418 |
/BuildGlyph {
|
|
419 |
exch
|
|
420 |
begin
|
|
421 |
Metrics 1 index get exec 0
|
|
422 |
BBoxes 3 index get exec
|
|
423 |
setcachedevice
|
|
424 |
CharProcs begin load exec end
|
|
425 |
end
|
|
426 |
} def
|
|
427 |
/BuildChar {
|
|
428 |
1 index /Encoding get exch get
|
|
429 |
1 index /BuildGlyph get exec
|
|
430 |
} bind def
|
|
431 |
end
|
|
432 |
/PSTricksDotFont exch definefont pop
|
|
433 |
%END pst-dots.pro
|
|
434 |
|
|
435 |
%%EndProcSet
|
|
436 |
%%BeginProcSet: 8r.enc 0 0
|
|
437 |
% File 8r.enc TeX Base 1 Encoding Revision 2.0 2002-10-30
|
|
438 |
%
|
|
439 |
% @@psencodingfile@{
|
|
440 |
% author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry,
|
|
441 |
% W. Schmidt, P. Lehman",
|
|
442 |
% version = "2.0",
|
|
443 |
% date = "30 October 2002",
|
|
444 |
% filename = "8r.enc",
|
|
445 |
% email = "tex-fonts@@tug.org",
|
|
446 |
% docstring = "This is the encoding vector for Type1 and TrueType
|
|
447 |
% fonts to be used with TeX. This file is part of the
|
|
448 |
% PSNFSS bundle, version 9"
|
|
449 |
% @}
|
|
450 |
%
|
|
451 |
% The idea is to have all the characters normally included in Type 1 fonts
|
|
452 |
% available for typesetting. This is effectively the characters in Adobe
|
|
453 |
% Standard encoding, ISO Latin 1, Windows ANSI including the euro symbol,
|
|
454 |
% MacRoman, and some extra characters from Lucida.
|
|
455 |
%
|
|
456 |
% Character code assignments were made as follows:
|
|
457 |
%
|
|
458 |
% (1) the Windows ANSI characters are almost all in their Windows ANSI
|
|
459 |
% positions, because some Windows users cannot easily reencode the
|
|
460 |
% fonts, and it makes no difference on other systems. The only Windows
|
|
461 |
% ANSI characters not available are those that make no sense for
|
|
462 |
% typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen
|
|
463 |
% (173). quotesingle and grave are moved just because it's such an
|
|
464 |
% irritation not having them in TeX positions.
|
|
465 |
%
|
|
466 |
% (2) Remaining characters are assigned arbitrarily to the lower part
|
|
467 |
% of the range, avoiding 0, 10 and 13 in case we meet dumb software.
|
|
468 |
%
|
|
469 |
% (3) Y&Y Lucida Bright includes some extra text characters; in the
|
|
470 |
% hopes that other PostScript fonts, perhaps created for public
|
|
471 |
% consumption, will include them, they are included starting at 0x12.
|
|
472 |
% These are /dotlessj /ff /ffi /ffl.
|
|
473 |
%
|
|
474 |
% (4) hyphen appears twice for compatibility with both ASCII and Windows.
|
|
475 |
%
|
|
476 |
% (5) /Euro was assigned to 128, as in Windows ANSI
|
|
477 |
%
|
|
478 |
% (6) Missing characters from MacRoman encoding incorporated as follows:
|
|
479 |
%
|
|
480 |
% PostScript MacRoman TeXBase1
|
|
481 |
% -------------- -------------- --------------
|
|
482 |
% /notequal 173 0x16
|
|
483 |
% /infinity 176 0x17
|
|
484 |
% /lessequal 178 0x18
|
|
485 |
% /greaterequal 179 0x19
|
|
486 |
% /partialdiff 182 0x1A
|
|
487 |
% /summation 183 0x1B
|
|
488 |
% /product 184 0x1C
|
|
489 |
% /pi 185 0x1D
|
|
490 |
% /integral 186 0x81
|
|
491 |
% /Omega 189 0x8D
|
|
492 |
% /radical 195 0x8E
|
|
493 |
% /approxequal 197 0x8F
|
|
494 |
% /Delta 198 0x9D
|
|
495 |
% /lozenge 215 0x9E
|
|
496 |
%
|
|
497 |
/TeXBase1Encoding [
|
|
498 |
% 0x00
|
|
499 |
/.notdef /dotaccent /fi /fl
|
|
500 |
/fraction /hungarumlaut /Lslash /lslash
|
|
501 |
/ogonek /ring /.notdef /breve
|
|
502 |
/minus /.notdef /Zcaron /zcaron
|
|
503 |
% 0x10
|
|
504 |
/caron /dotlessi /dotlessj /ff
|
|
505 |
/ffi /ffl /notequal /infinity
|
|
506 |
/lessequal /greaterequal /partialdiff /summation
|
|
507 |
/product /pi /grave /quotesingle
|
|
508 |
% 0x20
|
|
509 |
/space /exclam /quotedbl /numbersign
|
|
510 |
/dollar /percent /ampersand /quoteright
|
|
511 |
/parenleft /parenright /asterisk /plus
|
|
512 |
/comma /hyphen /period /slash
|
|
513 |
% 0x30
|
|
514 |
/zero /one /two /three
|
|
515 |
/four /five /six /seven
|
|
516 |
/eight /nine /colon /semicolon
|
|
517 |
/less /equal /greater /question
|
|
518 |
% 0x40
|
|
519 |
/at /A /B /C
|
|
520 |
/D /E /F /G
|
|
521 |
/H /I /J /K
|
|
522 |
/L /M /N /O
|
|
523 |
% 0x50
|
|
524 |
/P /Q /R /S
|
|
525 |
/T /U /V /W
|
|
526 |
/X /Y /Z /bracketleft
|
|
527 |
/backslash /bracketright /asciicircum /underscore
|
|
528 |
% 0x60
|
|
529 |
/quoteleft /a /b /c
|
|
530 |
/d /e /f /g
|
|
531 |
/h /i /j /k
|
|
532 |
/l /m /n /o
|
|
533 |
% 0x70
|
|
534 |
/p /q /r /s
|
|
535 |
/t /u /v /w
|
|
536 |
/x /y /z /braceleft
|
|
537 |
/bar /braceright /asciitilde /.notdef
|
|
538 |
% 0x80
|
|
539 |
/Euro /integral /quotesinglbase /florin
|
|
540 |
/quotedblbase /ellipsis /dagger /daggerdbl
|
|
541 |
/circumflex /perthousand /Scaron /guilsinglleft
|
|
542 |
/OE /Omega /radical /approxequal
|
|
543 |
% 0x90
|
|
544 |
/.notdef /.notdef /.notdef /quotedblleft
|
|
545 |
/quotedblright /bullet /endash /emdash
|
|
546 |
/tilde /trademark /scaron /guilsinglright
|
|
547 |
/oe /Delta /lozenge /Ydieresis
|
|
548 |
% 0xA0
|
|
549 |
/.notdef /exclamdown /cent /sterling
|
|
550 |
/currency /yen /brokenbar /section
|
|
551 |
/dieresis /copyright /ordfeminine /guillemotleft
|
|
552 |
/logicalnot /hyphen /registered /macron
|
|
553 |
% 0xD0
|
|
554 |
/degree /plusminus /twosuperior /threesuperior
|
|
555 |
/acute /mu /paragraph /periodcentered
|
|
556 |
/cedilla /onesuperior /ordmasculine /guillemotright
|
|
557 |
/onequarter /onehalf /threequarters /questiondown
|
|
558 |
% 0xC0
|
|
559 |
/Agrave /Aacute /Acircumflex /Atilde
|
|
560 |
/Adieresis /Aring /AE /Ccedilla
|
|
561 |
/Egrave /Eacute /Ecircumflex /Edieresis
|
|
562 |
/Igrave /Iacute /Icircumflex /Idieresis
|
|
563 |
% 0xD0
|
|
564 |
/Eth /Ntilde /Ograve /Oacute
|
|
565 |
/Ocircumflex /Otilde /Odieresis /multiply
|
|
566 |
/Oslash /Ugrave /Uacute /Ucircumflex
|
|
567 |
/Udieresis /Yacute /Thorn /germandbls
|
|
568 |
% 0xE0
|
|
569 |
/agrave /aacute /acircumflex /atilde
|
|
570 |
/adieresis /aring /ae /ccedilla
|
|
571 |
/egrave /eacute /ecircumflex /edieresis
|
|
572 |
/igrave /iacute /icircumflex /idieresis
|
|
573 |
% 0xF0
|
|
574 |
/eth /ntilde /ograve /oacute
|
|
575 |
/ocircumflex /otilde /odieresis /divide
|
|
576 |
/oslash /ugrave /uacute /ucircumflex
|
|
577 |
/udieresis /yacute /thorn /ydieresis
|
|
578 |
] def
|
|
579 |
|
|
580 |
|
|
581 |
%%EndProcSet
|
|
582 |
%%BeginProcSet: texps.pro 0 0
|
|
583 |
%!
|
|
584 |
TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2
|
|
585 |
index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll
|
|
586 |
exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]FontType 0
|
|
587 |
ne{/Metrics exch def dict begin Encoding{exch dup type/integertype ne{
|
|
588 |
pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get
|
|
589 |
div def}ifelse}forall Metrics/Metrics currentdict end def}{{1 index type
|
|
590 |
/nametype eq{exit}if exch pop}loop}ifelse[2 index currentdict end
|
|
591 |
definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{dup
|
|
592 |
sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll
|
|
593 |
mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[
|
|
594 |
exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}if}
|
|
595 |
forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}def
|
|
596 |
end
|
|
597 |
|
|
598 |
%%EndProcSet
|
|
599 |
%%BeginProcSet: special.pro 0 0
|
|
600 |
%!
|
|
601 |
TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N
|
|
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
|
|
603 |
/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N
|
|
604 |
/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{
|
|
605 |
/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho
|
|
606 |
X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B
|
|
607 |
/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{
|
|
608 |
/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known
|
|
609 |
{userdict/md get type/dicttype eq{userdict begin md length 10 add md
|
|
610 |
maxlength ge{/md md dup length 20 add dict copy def}if end md begin
|
|
611 |
/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S
|
|
612 |
atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{
|
|
613 |
itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll
|
|
614 |
transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll
|
|
615 |
curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf
|
|
616 |
pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}
|
|
617 |
if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1
|
|
618 |
-1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3
|
|
619 |
get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip
|
|
620 |
yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub
|
|
621 |
neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{
|
|
622 |
noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop
|
|
623 |
90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get
|
|
624 |
neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr
|
|
625 |
1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr
|
|
626 |
2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4
|
|
627 |
-1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S
|
|
628 |
TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{
|
|
629 |
Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale
|
|
630 |
}if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState
|
|
631 |
save N userdict maxlength dict begin/magscale true def normalscale
|
|
632 |
currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts
|
|
633 |
/psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x
|
|
634 |
psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx
|
|
635 |
psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub
|
|
636 |
TR/showpage{}N/erasepage{}N/setpagedevice{pop}N/copypage{}N/p 3 def
|
|
637 |
@MacSetUp}N/doclip{psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll
|
|
638 |
newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto
|
|
639 |
closepath clip newpath moveto}N/endTexFig{end psf$SavedState restore}N
|
|
640 |
/@beginspecial{SDict begin/SpecialSave save N gsave normalscale
|
|
641 |
currentpoint TR @SpecialDefaults count/ocount X/dcount countdictstack N}
|
|
642 |
N/@setspecial{CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs
|
|
643 |
neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate
|
|
644 |
rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse
|
|
645 |
scale llx neg lly neg TR}{rhiSeen{rhi ury lly sub div dup scale llx neg
|
|
646 |
lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx
|
|
647 |
ury lineto llx ury lineto closepath clip}if/showpage{}N/erasepage{}N
|
|
648 |
/setpagedevice{pop}N/copypage{}N newpath}N/@endspecial{count ocount sub{
|
|
649 |
pop}repeat countdictstack dcount sub{end}repeat grestore SpecialSave
|
|
650 |
restore end}N/@defspecial{SDict begin}N/@fedspecial{end}B/li{lineto}B
|
|
651 |
/rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1
|
|
652 |
setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY
|
|
653 |
moveto}N/ellipse{/endangle X/startangle X/yrad X/xrad X/savematrix
|
|
654 |
matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc
|
|
655 |
savematrix setmatrix}N end
|
|
656 |
|
|
657 |
%%EndProcSet
|
|
658 |
%%BeginProcSet: color.pro 0 0
|
|
659 |
%!
|
|
660 |
TeXDict begin/setcmykcolor where{pop}{/setcmykcolor{dup 10 eq{pop
|
|
661 |
setrgbcolor}{1 sub 4 1 roll 3{3 index add neg dup 0 lt{pop 0}if 3 1 roll
|
|
662 |
}repeat setrgbcolor pop}ifelse}B}ifelse/TeXcolorcmyk{setcmykcolor}def
|
|
663 |
/TeXcolorrgb{setrgbcolor}def/TeXcolorgrey{setgray}def/TeXcolorgray{
|
|
664 |
setgray}def/TeXcolorhsb{sethsbcolor}def/currentcmykcolor where{pop}{
|
|
665 |
/currentcmykcolor{currentrgbcolor 10}B}ifelse/DC{exch dup userdict exch
|
|
666 |
known{pop pop}{X}ifelse}B/GreenYellow{0.15 0 0.69 0 setcmykcolor}DC
|
|
667 |
/Yellow{0 0 1 0 setcmykcolor}DC/Goldenrod{0 0.10 0.84 0 setcmykcolor}DC
|
|
668 |
/Dandelion{0 0.29 0.84 0 setcmykcolor}DC/Apricot{0 0.32 0.52 0
|
|
669 |
setcmykcolor}DC/Peach{0 0.50 0.70 0 setcmykcolor}DC/Melon{0 0.46 0.50 0
|
|
670 |
setcmykcolor}DC/YellowOrange{0 0.42 1 0 setcmykcolor}DC/Orange{0 0.61
|
|
671 |
0.87 0 setcmykcolor}DC/BurntOrange{0 0.51 1 0 setcmykcolor}DC
|
|
672 |
/Bittersweet{0 0.75 1 0.24 setcmykcolor}DC/RedOrange{0 0.77 0.87 0
|
|
673 |
setcmykcolor}DC/Mahogany{0 0.85 0.87 0.35 setcmykcolor}DC/Maroon{0 0.87
|
|
674 |
0.68 0.32 setcmykcolor}DC/BrickRed{0 0.89 0.94 0.28 setcmykcolor}DC/Red{
|
|
675 |
0 1 1 0 setcmykcolor}DC/OrangeRed{0 1 0.50 0 setcmykcolor}DC/RubineRed{
|
|
676 |
0 1 0.13 0 setcmykcolor}DC/WildStrawberry{0 0.96 0.39 0 setcmykcolor}DC
|
|
677 |
/Salmon{0 0.53 0.38 0 setcmykcolor}DC/CarnationPink{0 0.63 0 0
|
|
678 |
setcmykcolor}DC/Magenta{0 1 0 0 setcmykcolor}DC/VioletRed{0 0.81 0 0
|
|
679 |
setcmykcolor}DC/Rhodamine{0 0.82 0 0 setcmykcolor}DC/Mulberry{0.34 0.90
|
|
680 |
0 0.02 setcmykcolor}DC/RedViolet{0.07 0.90 0 0.34 setcmykcolor}DC
|
|
681 |
/Fuchsia{0.47 0.91 0 0.08 setcmykcolor}DC/Lavender{0 0.48 0 0
|
|
682 |
setcmykcolor}DC/Thistle{0.12 0.59 0 0 setcmykcolor}DC/Orchid{0.32 0.64 0
|
|
683 |
0 setcmykcolor}DC/DarkOrchid{0.40 0.80 0.20 0 setcmykcolor}DC/Purple{
|
|
684 |
0.45 0.86 0 0 setcmykcolor}DC/Plum{0.50 1 0 0 setcmykcolor}DC/Violet{
|
|
685 |
0.79 0.88 0 0 setcmykcolor}DC/RoyalPurple{0.75 0.90 0 0 setcmykcolor}DC
|
|
686 |
/BlueViolet{0.86 0.91 0 0.04 setcmykcolor}DC/Periwinkle{0.57 0.55 0 0
|
|
687 |
setcmykcolor}DC/CadetBlue{0.62 0.57 0.23 0 setcmykcolor}DC
|
|
688 |
/CornflowerBlue{0.65 0.13 0 0 setcmykcolor}DC/MidnightBlue{0.98 0.13 0
|
|
689 |
0.43 setcmykcolor}DC/NavyBlue{0.94 0.54 0 0 setcmykcolor}DC/RoyalBlue{1
|
|
690 |
0.50 0 0 setcmykcolor}DC/Blue{1 1 0 0 setcmykcolor}DC/Cerulean{0.94 0.11
|
|
691 |
0 0 setcmykcolor}DC/Cyan{1 0 0 0 setcmykcolor}DC/ProcessBlue{0.96 0 0 0
|
|
692 |
setcmykcolor}DC/SkyBlue{0.62 0 0.12 0 setcmykcolor}DC/Turquoise{0.85 0
|
|
693 |
0.20 0 setcmykcolor}DC/TealBlue{0.86 0 0.34 0.02 setcmykcolor}DC
|
|
694 |
/Aquamarine{0.82 0 0.30 0 setcmykcolor}DC/BlueGreen{0.85 0 0.33 0
|
|
695 |
setcmykcolor}DC/Emerald{1 0 0.50 0 setcmykcolor}DC/JungleGreen{0.99 0
|
|
696 |
0.52 0 setcmykcolor}DC/SeaGreen{0.69 0 0.50 0 setcmykcolor}DC/Green{1 0
|
|
697 |
1 0 setcmykcolor}DC/ForestGreen{0.91 0 0.88 0.12 setcmykcolor}DC
|
|
698 |
/PineGreen{0.92 0 0.59 0.25 setcmykcolor}DC/LimeGreen{0.50 0 1 0
|
|
699 |
setcmykcolor}DC/YellowGreen{0.44 0 0.74 0 setcmykcolor}DC/SpringGreen{
|
|
700 |
0.26 0 0.76 0 setcmykcolor}DC/OliveGreen{0.64 0 0.95 0.40 setcmykcolor}
|
|
701 |
DC/RawSienna{0 0.72 1 0.45 setcmykcolor}DC/Sepia{0 0.83 1 0.70
|
|
702 |
setcmykcolor}DC/Brown{0 0.81 1 0.60 setcmykcolor}DC/Tan{0.14 0.42 0.56 0
|
|
703 |
setcmykcolor}DC/Gray{0 0 0 0.50 setcmykcolor}DC/Black{0 0 0 1
|
|
704 |
setcmykcolor}DC/White{0 0 0 0 setcmykcolor}DC end
|
|
705 |
|
|
706 |
%%EndProcSet
|
|
707 |
TeXDict begin 39139632 55387786 1000 600 600 (a04-urban.dvi)
|
|
708 |
@start
|
|
709 |
%DVIPSBitmapFont: Fa cmmi9 9 1
|
|
710 |
/Fa 1 22 df<007C000000007F800000001FE00000000FE000000007F000000007F00000
|
|
711 |
0003F800000003F800000003F800000001FC00000001FC00000001FC00000000FE000000
|
|
712 |
00FE00000000FF000000007F000000007F000000003F800000003F800000003F80000000
|
|
713 |
1FC00000001FC00000001FE00000000FE00000000FE000000007F000000007F000000007
|
|
714 |
F000000007F80000000FF80000001FF80000003DFC00000079FC000000F8FE000001F0FE
|
|
715 |
000003E0FE000007C07F00000F807F00001F007F00003E003F80007E003F8000FC003FC0
|
|
716 |
01F8001FC003F0001FC007E0000FE01FC0000FE03FC0000FE07F800007F0FF000007F0FE
|
|
717 |
000007F8FC000003F8F8000001FCF0000000FC26357CB32D>21 D
|
|
718 |
E
|
|
719 |
%EndDVIPSBitmapFont
|
|
720 |
/Fb 134[33 33 50 33 37 21 29 29 1[37 37 37 54 21 2[21
|
|
721 |
37 37 21 33 37 33 37 37 11[54 42 37 46 1[46 54 50 62
|
|
722 |
42 1[33 25 54 54 46 46 54 50 1[46 6[25 37 37 1[37 1[37
|
|
723 |
37 37 37 37 1[19 25 19 2[25 25 25 39[{TeXBase1Encoding ReEncodeFont}55
|
|
724 |
74.7198 /Times-Italic rf /Fc 105[37 27[33 37 37 54 37
|
|
725 |
37 21 29 25 37 37 37 37 58 21 37 1[21 37 37 25 33 37
|
|
726 |
33 37 33 3[25 1[25 46 2[71 54 54 46 42 50 1[42 54 54
|
|
727 |
66 46 54 29 25 54 54 42 46 54 50 50 54 6[21 37 37 37
|
|
728 |
37 37 37 37 37 37 37 21 19 25 19 2[25 25 1[58 35[42 2[{
|
|
729 |
TeXBase1Encoding ReEncodeFont}70 74.7198 /Times-Roman
|
|
730 |
rf
|
|
731 |
%DVIPSBitmapFont: Fd cmsy9 9 1
|
|
732 |
/Fd 1 16 df<001FC00000FFF80001FFFC0007FFFF000FFFFF801FFFFFC03FFFFFE03FFF
|
|
733 |
FFE07FFFFFF07FFFFFF0FFFFFFF8FFFFFFF8FFFFFFF8FFFFFFF8FFFFFFF8FFFFFFF8FFFF
|
|
734 |
FFF8FFFFFFF8FFFFFFF87FFFFFF07FFFFFF03FFFFFE03FFFFFE01FFFFFC00FFFFF8007FF
|
|
735 |
FF0001FFFC0000FFF800001FC0001D1D7CA126>15 D E
|
|
736 |
%EndDVIPSBitmapFont
|
|
737 |
/Fe 206[21 49[{TeXBase1Encoding ReEncodeFont}1 41.511
|
|
738 |
/Times-Italic rf /Ff 153[16 26 29 100[{TeXBase1Encoding ReEncodeFont}3
|
|
739 |
58.1154 /Times-Italic rf
|
|
740 |
%DVIPSBitmapFont: Fg cmtt10 10 8
|
|
741 |
/Fg 8 118 df<0003FE0000001FFFC000007FFFF00001FFFFF80003FFFFFC0007FE03FE
|
|
742 |
000FF800FF001FE0003F801FC0003F803F80001FC03F00000FC07F00000FC07E00000FE0
|
|
743 |
7E000007E0FC000007E0FFFFFFFFE0FFFFFFFFE0FFFFFFFFE0FFFFFFFFE0FFFFFFFFC0FC
|
|
744 |
00000000FE000000007E000000007E000000007F000000003F000003C03F800007E01FC0
|
|
745 |
0007E00FF0000FE007F8003FC007FF00FFC001FFFFFF8000FFFFFF00003FFFFC00000FFF
|
|
746 |
F0000001FF800023247CA32C>101 D<00000FF80000003FFE000000FFFF000001FFFF80
|
|
747 |
0003FFFF800007FC7F800007F07F80000FE03F00000FC03F00000FC00000000FC0000000
|
|
748 |
0FC00000000FC00000000FC00000000FC000007FFFFFFE00FFFFFFFF00FFFFFFFF00FFFF
|
|
749 |
FFFF007FFFFFFE00000FC00000000FC00000000FC00000000FC00000000FC00000000FC0
|
|
750 |
0000000FC00000000FC00000000FC00000000FC00000000FC00000000FC00000000FC000
|
|
751 |
00000FC00000000FC00000000FC00000000FC00000000FC00000000FC00000000FC00000
|
|
752 |
000FC00000000FC00000000FC00000000FC00000000FC00000000FC000003FFFFFF0007F
|
|
753 |
FFFFF8007FFFFFF8007FFFFFF8003FFFFFF00021337DB22C>I<00070000001FC000001F
|
|
754 |
C000003FE000003FE000003FE000001FC000001FC0000007000000000000000000000000
|
|
755 |
0000000000000000000000000000000000007FFFC0007FFFE000FFFFE0007FFFE0007FFF
|
|
756 |
E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007
|
|
757 |
E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007
|
|
758 |
E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0007FFF
|
|
759 |
FFFCFFFFFFFEFFFFFFFEFFFFFFFE7FFFFFFC1F3479B32C>105 D<7FF01FE00000FFF87F
|
|
760 |
FC0000FFF9FFFE0000FFFBFFFF00007FFFFFFF000001FFF03F800001FFC01F800001FF80
|
|
761 |
1FC00001FF000FC00001FE000FC00001FC000FC00001FC000FC00001F8000FC00001F800
|
|
762 |
0FC00001F8000FC00001F8000FC00001F8000FC00001F8000FC00001F8000FC00001F800
|
|
763 |
0FC00001F8000FC00001F8000FC00001F8000FC00001F8000FC00001F8000FC00001F800
|
|
764 |
0FC00001F8000FC00001F8000FC00001F8000FC00001F8000FC00001F8000FC0007FFFE0
|
|
765 |
FFFF00FFFFF1FFFF80FFFFF1FFFF80FFFFF1FFFF807FFFE0FFFF0029247FA32C>110
|
|
766 |
D<7FF01FE000FFF8FFF800FFFBFFFE00FFFFFFFF007FFFFFFF8001FFF07FC001FF801FE0
|
|
767 |
01FF0007F001FE0003F801FC0003F801FC0001FC01F80000FC01F80000FC01F80000FE01
|
|
768 |
F800007E01F800007E01F800007E01F800007E01F800007E01F800007E01F800007E01F8
|
|
769 |
00007E01F80000FE01FC0000FC01FC0000FC01FC0001F801FE0003F801FF0007F001FF00
|
|
770 |
0FF001FF801FE001FFE07FC001FFFFFF8001FFFFFF0001FBFFFE0001F8FFF80001F83FC0
|
|
771 |
0001F800000001F800000001F800000001F800000001F800000001F800000001F8000000
|
|
772 |
01F800000001F800000001F800000001F800000001F800000001F80000007FFFE00000FF
|
|
773 |
FFF00000FFFFF00000FFFFF000007FFFE0000027367FA32C>112
|
|
774 |
D<007FF87003FFFFF80FFFFFF81FFFFFF83FFFFFF87FC00FF87E0003F8FC0001F8F80001
|
|
775 |
F8F80001F8F80001F8FC0000F07F0000007FF000003FFFC0001FFFFE000FFFFF8003FFFF
|
|
776 |
E0007FFFF80001FFFC000007FC000000FE7800007FFC00003FFC00001FFE00001FFE0000
|
|
777 |
1FFF00003FFF80003EFFC000FEFFF007FCFFFFFFFCFFFFFFF8FFFFFFE0F8FFFF80701FFC
|
|
778 |
0020247AA32C>115 D<001E000000003F000000003F000000003F000000003F00000000
|
|
779 |
3F000000003F000000003F000000003F000000003F0000007FFFFFFF00FFFFFFFF80FFFF
|
|
780 |
FFFF80FFFFFFFF807FFFFFFF00003F000000003F000000003F000000003F000000003F00
|
|
781 |
0000003F000000003F000000003F000000003F000000003F000000003F000000003F0000
|
|
782 |
00003F000000003F000000003F000000003F000000003F000000003F0003C0003F0007E0
|
|
783 |
003F0007E0003F0007E0003F0007E0003F0007E0003F800FE0001F801FC0001FE07FC000
|
|
784 |
0FFFFF80000FFFFF000003FFFE000001FFF80000003FE000232E7EAD2C>I<7FF003FF80
|
|
785 |
00FFF807FFC000FFF807FFC000FFF807FFC0007FF803FFC00001F8000FC00001F8000FC0
|
|
786 |
0001F8000FC00001F8000FC00001F8000FC00001F8000FC00001F8000FC00001F8000FC0
|
|
787 |
0001F8000FC00001F8000FC00001F8000FC00001F8000FC00001F8000FC00001F8000FC0
|
|
788 |
0001F8000FC00001F8000FC00001F8000FC00001F8000FC00001F8000FC00001F8000FC0
|
|
789 |
0001F8000FC00001F8001FC00001F8001FC00001F8003FC00001FC007FC00000FE03FFC0
|
|
790 |
0000FFFFFFFF00007FFFFFFF80003FFFFFFF80001FFFCFFF800003FE07FF0029247FA32C
|
|
791 |
>I E
|
|
792 |
%EndDVIPSBitmapFont
|
|
793 |
%DVIPSBitmapFont: Fh cmex10 10 4
|
|
794 |
/Fh 4 84 df<000001F0000007F000000FF000003FF000007FF00001FFC00003FF800007
|
|
795 |
FF00000FFE00001FFC00003FF800007FF000007FE00000FFC00001FF800003FF800003FF
|
|
796 |
000007FE000007FE00000FFC00000FFC00001FF800001FF800003FF800003FF000003FF0
|
|
797 |
00007FF000007FE000007FE000007FE000007FE00000FFE00000FFC00000FFC00000FFC0
|
|
798 |
0000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC0
|
|
799 |
0000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC0
|
|
800 |
0000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC0
|
|
801 |
0000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC0
|
|
802 |
0000FFC00000FFC00000FFC00000FFC000001C4B607E4A>56 D<FFC00000FFC00000FFC0
|
|
803 |
0000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC0
|
|
804 |
0000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC0
|
|
805 |
0000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC0
|
|
806 |
0000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC00000FFC0
|
|
807 |
0000FFC00000FFC00000FFC00000FFC00000FFE000007FE000007FE000007FE000007FE0
|
|
808 |
00007FF000003FF000003FF000003FF800001FF800001FF800000FFC00000FFC000007FE
|
|
809 |
000007FE000003FF000003FF800001FF800000FFC000007FE000007FF000003FF800001F
|
|
810 |
FC00000FFE000007FF000003FF800001FFC000007FF000003FF000000FF0000007F00000
|
|
811 |
01F01C4B60804A>58 D<00001FF800001FF800001FF800001FF800001FF800001FF80000
|
|
812 |
1FF800001FF800001FF800001FF800001FF800001FF800001FF800001FF800001FF80000
|
|
813 |
1FF800001FF800001FF800001FF800001FF800001FF800001FF800001FF800001FF80000
|
|
814 |
1FF800001FF800001FF800001FF800001FF800001FF800001FF800001FF800001FF80000
|
|
815 |
1FF800001FF800001FF800001FF800001FF800001FF800001FF800001FF800001FF80000
|
|
816 |
1FF800003FF800003FF000003FF000003FF000003FF000007FE000007FE000007FE00000
|
|
817 |
7FC00000FFC00000FFC00001FF800001FF800001FF000003FF000003FE000007FE00000F
|
|
818 |
FC00000FF800001FF800003FF000003FE000007FC00000FF800001FF000003FE000007FC
|
|
819 |
00000FF800001FF000007FE00000FF800000FF000000FC000000FF000000FF8000007FE0
|
|
820 |
00001FF000000FF8000007FC000003FE000001FF000000FF8000007FC000003FE000003F
|
|
821 |
F000001FF800000FF800000FFC000007FE000003FE000003FF000001FF000001FF800001
|
|
822 |
FF800000FFC00000FFC000007FC000007FE000007FE000007FE000003FF000003FF00000
|
|
823 |
3FF000003FF000003FF800001FF800001FF800001FF800001FF800001FF800001FF80000
|
|
824 |
1FF800001FF800001FF800001FF800001FF800001FF800001FF800001FF800001FF80000
|
|
825 |
1FF800001FF800001FF800001FF800001FF800001FF800001FF800001FF800001FF80000
|
|
826 |
1FF800001FF800001FF800001FF800001FF800001FF800001FF800001FF800001FF80000
|
|
827 |
1FF800001FF800001FF800001FF800001FF800001FF800001FF800001FF800001FF80000
|
|
828 |
1FF81D9773804A>60 D<7800000000000780FC00000000000FC0FC00000000000FC0FC00
|
|
829 |
000000000FC0FC00000000000FC0FC00000000000FC0FC00000000000FC0FC0000000000
|
|
830 |
0FC0FC00000000000FC0FC00000000000FC0FC00000000000FC0FC00000000000FC0FC00
|
|
831 |
000000000FC0FC00000000000FC0FC00000000000FC0FC00000000000FC0FC0000000000
|
|
832 |
0FC0FC00000000000FC0FC00000000000FC0FC00000000000FC0FC00000000000FC0FC00
|
|
833 |
000000000FC0FC00000000000FC0FC00000000000FC0FC00000000000FC0FC0000000000
|
|
834 |
0FC0FC00000000000FC0FC00000000000FC0FC00000000000FC0FC00000000000FC0FC00
|
|
835 |
000000000FC0FC00000000000FC0FC00000000000FC0FC00000000000FC0FC0000000000
|
|
836 |
0FC0FC00000000000FC0FC00000000000FC0FC00000000000FC0FC00000000000FC0FC00
|
|
837 |
000000000FC0FC00000000000FC0FC00000000000FC0FC00000000000FC0FC0000000000
|
|
838 |
0FC0FC00000000000FC0FC00000000000FC0FC00000000000FC0FC00000000000FC0FC00
|
|
839 |
000000000FC0FC00000000000FC0FC00000000000FC0FC00000000000FC0FC0000000000
|
|
840 |
0FC0FC00000000000FC0FC00000000000FC0FC00000000000FC0FC00000000000FC0FC00
|
|
841 |
000000000FC0FC00000000000FC0FE00000000001FC07E00000000001F807E0000000000
|
|
842 |
1F807F00000000003F803F00000000003F003F00000000003F003F80000000007F001F80
|
|
843 |
000000007E001FC000000000FE000FE000000001FC000FF000000003FC0007F800000007
|
|
844 |
F80003FC0000000FF00001FE0000001FE00000FF8000007FC000007FC00000FF8000003F
|
|
845 |
F80007FF0000001FFF003FFE0000000FFFFFFFFC00000003FFFFFFF000000001FFFFFFE0
|
|
846 |
000000007FFFFF80000000000FFFFC000000000001FFE00000003A537B7F45>83
|
|
847 |
D E
|
|
848 |
%EndDVIPSBitmapFont
|
|
849 |
%DVIPSBitmapFont: Fi msbm10 10 2
|
|
850 |
/Fi 2 66 df<000003FF00001C00001FFFE0003C0000FFFFFC007C0001FFFFFE00FC0007
|
|
851 |
FE01FF83F8000FF0003FC7F0003F800007FFC0007F000003FF8000FC000000FF0000F800
|
|
852 |
00007E0001F0000001FE0003F0000003FF0003E0000007FF0007C000000FCF8007C00000
|
|
853 |
1F8F800F8000003F07C00F8000007E07C00F000001FC03C01F000003F803E01F000007E0
|
|
854 |
03E01E00000FC001E01E00001F8001E01E00003F0001E01E0000FE0001E01E0001FC0001
|
|
855 |
E01E0003F00001E01E0007E00001E01E000FC00001E01F001F800003E01F007F000003E0
|
|
856 |
0F00FE000003C00F81F8000007C00F83F0000007C007C7E000000F8007CFC000000F8003
|
|
857 |
FF8000001F0003FF0000003F0001FE0000003E0001F80000007C0003FC000000FC0007FF
|
|
858 |
000003F8000FFF800007F0003F8FF0003FC0007F07FE01FF8000FC01FFFFFE0000F800FF
|
|
859 |
FFFC0000F0001FFFE00000E00003FF00000036307BAF41>63 D<00000030000000000000
|
|
860 |
7800000000000078000000000000F8000000000000FC000000000000FC000000000001FE
|
|
861 |
000000000001CE000000000001CE000000000003CF000000000003870000000000078780
|
|
862 |
00000000070380000000000703C0000000000F01C0000000000F01C0000000000F81E000
|
|
863 |
0000001F80E0000000001FC0F0000000003DC0700000000039C0780000000039E0380000
|
|
864 |
000078E0380000000070F03C0000000070701C00000000F0781E00000000E0380E000000
|
|
865 |
01E0380E00000001E03C0F00000001C01C0700000003C01E0780000003C00E0380000003
|
|
866 |
800E03C0000007800F01C0000007800701C0000007000781E000000F000380E000000F00
|
|
867 |
0380F000001E0003C07000001FFFFFC07800001FFFFFC03800003FFFFFE03800003C0000
|
|
868 |
E03C00003C0000E01C00007C0000F01E00007C0000700E0000FC0000700E0000FC000078
|
|
869 |
0F0000F8000038070001F8000038078001F8000038038001F800003C03C003FC00001C01
|
|
870 |
C0039C00001C01E0079C00003C00E01F1E0000F800F8FFFFC00FFFFFFEFFFFE00FFFFFFF
|
|
871 |
FFFFC00FFFFFFE383B7EBA25>65 D E
|
|
872 |
%EndDVIPSBitmapFont
|
|
873 |
%DVIPSBitmapFont: Fj cmbsy10 14.4 1
|
|
874 |
/Fj 1 2 df<03F8000FFE001FFF003FFF807FFFC07FFFC0FFFFE0FFFFE0FFFFE0FFFFE0
|
|
875 |
FFFFE0FFFFE0FFFFE07FFFC07FFFC03FFF801FFF000FFE0003F800131377A726>1
|
|
876 |
D E
|
|
877 |
%EndDVIPSBitmapFont
|
|
878 |
/Fk 204[25 25 25 49[{TeXBase1Encoding ReEncodeFont}3
|
|
879 |
49.8132 /Times-Roman rf /Fm 206[21 49[{TeXBase1Encoding ReEncodeFont}1
|
|
880 |
41.511 /Times-Roman rf /Fn 134[42 2[42 46 28 32 37 1[46
|
|
881 |
42 46 69 23 46 1[23 46 42 28 37 46 37 46 42 9[83 2[55
|
|
882 |
46 60 2[65 2[55 5[51 1[60 60 8[28 4[42 42 42 42 42 2[21
|
|
883 |
28 42[46 2[{TeXBase1Encoding ReEncodeFont}39 83.022 /Times-Bold
|
|
884 |
rf
|
|
885 |
%DVIPSBitmapFont: Fo cmr10 10 12
|
|
886 |
/Fo 12 94 df<FFFFFFFFFFE0FFFFFFFFFFE0FFFFFFFFFFE001FF80003FE000FF000007
|
|
887 |
E000FF000003F000FF000001F000FF000000F000FF0000007000FF0000007000FF000000
|
|
888 |
3000FF0000003000FF0000003000FF0000003000FF0000003800FF0000001800FF000000
|
|
889 |
1800FF0000001800FF0000001800FF0000000000FF0000000000FF0000000000FF000000
|
|
890 |
0000FF0000000000FF0000000000FF0000000000FF0000000000FF0000000000FF000000
|
|
891 |
0000FF0000000000FF0000000000FF0000000000FF0000000000FF0000000000FF000000
|
|
892 |
0000FF0000000000FF0000000000FF0000000000FF0000000000FF0000000000FF000000
|
|
893 |
0000FF0000000000FF0000000000FF0000000000FF0000000000FF0000000000FF000000
|
|
894 |
0000FF0000000000FF0000000000FF0000000000FF0000000000FF0000000000FF000000
|
|
895 |
0001FFC0000000FFFFFFE00000FFFFFFE00000FFFFFFE000002D397DB834>0
|
|
896 |
D<0000000C000300000000001E000780000000001E000780000000003E000F8000000000
|
|
897 |
3E000F80000000003C000F00000000003C000F00000000007C001F00000000007C001F00
|
|
898 |
0000000078001E000000000078001E000000000078001E0000000000F8003E0000000000
|
|
899 |
F8003E0000000000F0003C0000000000F0003C0000000001F0007C0000000001F0007C00
|
|
900 |
00000001E000780000000001E000780000000003E000F80000000003E000F80000000003
|
|
901 |
C000F00000000003C000F00000000003C000F00000000007C001F000007FFFFFFFFFFFFF
|
|
902 |
80FFFFFFFFFFFFFFC0FFFFFFFFFFFFFFC07FFFFFFFFFFFFF8000001F0007C0000000001E
|
|
903 |
000780000000001E000780000000001E000780000000003E000F80000000003E000F8000
|
|
904 |
0000003C000F00000000003C000F00000000007C001F00000000007C001F000000000078
|
|
905 |
001E000000000078001E000000000078001E0000000000F8003E0000007FFFFFFFFFFFFF
|
|
906 |
80FFFFFFFFFFFFFFC0FFFFFFFFFFFFFFC07FFFFFFFFFFFFF800003E000F80000000003C0
|
|
907 |
00F00000000003C000F00000000003C000F00000000007C001F00000000007C001F00000
|
|
908 |
0000078001E000000000078001E0000000000F8003E0000000000F8003E0000000000F00
|
|
909 |
03C0000000000F0003C0000000001F0007C0000000001F0007C0000000001E0007800000
|
|
910 |
00001E000780000000001E000780000000003E000F80000000003E000F80000000003C00
|
|
911 |
0F00000000003C000F00000000007C001F00000000007C001F000000000078001E000000
|
|
912 |
000078001E000000000030000C000000003A4A7BB945>35 D<0000600000E00001C00003
|
|
913 |
80000700000E00001E00003C0000780000780000F00001E00001E00003C00003C00007C0
|
|
914 |
000780000F80000F00000F00001F00001E00001E00003E00003E00003E00007C00007C00
|
|
915 |
007C00007C00007C00007C0000F80000F80000F80000F80000F80000F80000F80000F800
|
|
916 |
00F80000F80000F80000F80000F80000F80000F80000F80000F80000F800007C00007C00
|
|
917 |
007C00007C00007C00007C00003E00003E00003E00001E00001E00001F00000F00000F00
|
|
918 |
000F800007800007C00003C00003C00001E00001E00000F000007800007800003C00001E
|
|
919 |
00000E000007000003800001C00000E0000060135278BD20>40 D<C00000E00000700000
|
|
920 |
3800001C00000E00000F000007800003C00003C00001E00000F00000F000007800007800
|
|
921 |
007C00003C00003E00001E00001E00001F00000F00000F00000F80000F80000F800007C0
|
|
922 |
0007C00007C00007C00007C00007C00003E00003E00003E00003E00003E00003E00003E0
|
|
923 |
0003E00003E00003E00003E00003E00003E00003E00003E00003E00003E00003E00007C0
|
|
924 |
0007C00007C00007C00007C00007C0000F80000F80000F80000F00000F00001F00001E00
|
|
925 |
001E00003E00003C00007C0000780000780000F00000F00001E00003C00003C000078000
|
|
926 |
0F00000E00001C0000380000700000E00000C0000013527CBD20>I<0001C0000003C000
|
|
927 |
0007C000001FC00000FFC000FFFFC000FFFFC000FF1FC000001FC000001FC000001FC000
|
|
928 |
001FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC000
|
|
929 |
001FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC000
|
|
930 |
001FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC000
|
|
931 |
001FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC000
|
|
932 |
001FC000001FC000001FC000001FC000001FC000003FE0007FFFFFF07FFFFFF07FFFFFF0
|
|
933 |
1C3879B72A>49 D<000FF00000007FFE000001FFFF800003E03FE0000F000FF0000E0007
|
|
934 |
F8001C0003FC00380001FE00300001FE00700000FF00600000FF00FC0000FF00FF00007F
|
|
935 |
80FF80007F80FF80007F80FF80007F80FF80007F80FF80007F807F00007F801C00007F80
|
|
936 |
0000007F80000000FF00000000FF00000000FF00000001FE00000001FC00000003FC0000
|
|
937 |
0003F800000007F000000007E00000000FE00000001FC00000003F800000003F00000000
|
|
938 |
7C00000000F800000001F000000003E000000007C00000000F800000000F000000001E00
|
|
939 |
0180003C000180007800018000F000038001E000030003C000030007800003000E000007
|
|
940 |
000FFFFFFF001FFFFFFF003FFFFFFF007FFFFFFE00FFFFFFFE00FFFFFFFE00FFFFFFFE00
|
|
941 |
21387CB72A>I<0007F80000003FFF0000007FFFC00001F80FF00003C007F800078003FC
|
|
942 |
000E0001FC000F0001FE001FE000FE001FF000FF001FF000FF001FF000FF001FF000FF00
|
|
943 |
1FF000FF000FE000FF0007C000FF00000000FE00000001FE00000001FE00000001FC0000
|
|
944 |
0003F800000003F800000007F000000007E00000000F800000007E0000001FFC0000001F
|
|
945 |
FF800000000FE000000007F000000001FC00000001FE00000000FF000000007F80000000
|
|
946 |
7F800000007FC00000007FC00000003FC00000003FE00000003FE01E00003FE07F80003F
|
|
947 |
E0FFC0003FE0FFC0003FE0FFC0003FE0FFC0003FE0FFC0003FC0FF80007FC07F80007F80
|
|
948 |
7E00007F80700000FF00380001FE001E0001FE000F8003F80007F00FF00001FFFFC00000
|
|
949 |
7FFF0000000FF80000233A7DB72A>I<1C007F00FF80FF80FF80FF80FF807F001C000000
|
|
950 |
000000000000000000000000000000000000000000000000000000000000000000001C00
|
|
951 |
7F00FF80FF80FF80FF80FF807F001C00092479A317>58 D<7FFFFFFFFFFFF8FFFFFFFFFF
|
|
952 |
FFFCFFFFFFFFFFFFFC7FFFFFFFFFFFF80000000000000000000000000000000000000000
|
|
953 |
000000000000000000000000000000000000000000000000000000000000000000000000
|
|
954 |
000000000000000000000000000000000000000000000000000000000000000000000000
|
|
955 |
0000000000007FFFFFFFFFFFF8FFFFFFFFFFFFFCFFFFFFFFFFFFFC7FFFFFFFFFFFF83616
|
|
956 |
7B9F41>61 D<000003FF00000000001FFFE000000000FC00FC00000001E0001E00000007
|
|
957 |
8000078000001E000001E000003800000070000070000000380000E00000001C0001C000
|
|
958 |
00000E000380000000070003000000000300070001FC0003800E0007FF0001C00C001F03
|
|
959 |
C000C01C007E00E000E01800FC007000603801F8003800703001F0001C00303003F0000F
|
|
960 |
E0307007E00007E0386007E00007E018600FC00007E018600FC00007E018E00FC00007E0
|
|
961 |
1CC01F800007E00CC01F800007E00CC01F800007E00CC01F800007E00CC01F800007E00C
|
|
962 |
C01F800007E00CC01F800007E00CC01F800007E00CC01F800007E00CC01F800007E00CE0
|
|
963 |
0FC00007E00C600FC00007E00C600FC00007E00C6007E00007E01C7007E00007E0183003
|
|
964 |
F0000FE0183001F0001FE0183801F8003FE0381800FC0077E0301C007E00E3F0700C001F
|
|
965 |
03C1F0E00E0007FF00FFC0070001FC003F00030000000000000380000000000001C00000
|
|
966 |
00000000E00000000000007000000000000038000000007C001E00000003FC0007800000
|
|
967 |
1FF00001E00000FF800000FC003FFC0000001FFFFF8000000003FFE00000363C7BBA41>
|
|
968 |
64 D<FFF8FFF8FFF8FFF8F000F000F000F000F000F000F000F000F000F000F000F000F0
|
|
969 |
00F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F0
|
|
970 |
00F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F0
|
|
971 |
00F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F0
|
|
972 |
00F000F000F000F000F000F000F000F000FFF8FFF8FFF8FFF80D5378BD17>91
|
|
973 |
D<FFF8FFF8FFF8FFF8007800780078007800780078007800780078007800780078007800
|
|
974 |
780078007800780078007800780078007800780078007800780078007800780078007800
|
|
975 |
780078007800780078007800780078007800780078007800780078007800780078007800
|
|
976 |
780078007800780078007800780078007800780078007800780078007800780078007800
|
|
977 |
780078007800780078007800780078FFF8FFF8FFF8FFF80D537FBD17>93
|
|
978 |
D E
|
|
979 |
%EndDVIPSBitmapFont
|
|
980 |
%DVIPSBitmapFont: Fp cmti10 10 10
|
|
981 |
/Fp 10 122 df<0000F800000007FE0000001F871C00003E03FE00007C03FE0000F801FE
|
|
982 |
0001F801FE0003F000FC0007E000FC000FE000FC000FC001FC001FC001F8001FC001F800
|
|
983 |
3F8001F8003F8003F8007F8003F0007F0003F0007F0003F0007F0007F000FF0007E000FE
|
|
984 |
0007E000FE0007E000FE000FE000FE000FC000FC000FC1C0FC000FC1C0FC001FC1C0FC00
|
|
985 |
1F83C0FC001F8380FC003F8380FC003F87807C007F87007C00FF07003E01FF0F003E038F
|
|
986 |
8E001F0F079E0007FE03FC0001F000F000222677A42A>97 D<00000001F8000000FFF800
|
|
987 |
0000FFF8000000FFF800000003F800000003F000000003F000000007F000000007F00000
|
|
988 |
0007E000000007E00000000FE00000000FE00000000FC00000000FC00000001FC0000000
|
|
989 |
1FC00000001F800000001F800000003F800000003F800000F83F000007FE3F00001F877F
|
|
990 |
00003E03FF00007C03FE0000F801FE0001F801FE0003F000FE0007E000FC000FE000FC00
|
|
991 |
0FC001FC001FC001FC001FC001F8003F8001F8003F8003F8007F8003F8007F0003F0007F
|
|
992 |
0003F0007F0007F000FF0007F000FE0007E000FE0007E000FE000FE000FE000FE000FC00
|
|
993 |
0FC1C0FC000FC1C0FC001FC1C0FC001FC3C0FC001F8380FC003F8380FC003F87807C007F
|
|
994 |
87007C00FF07003E01FF0F003E038F8E001F0F079E0007FE03FC0001F000F000253B77B9
|
|
995 |
2A>100 D<0001C00007E00007F0000FF0000FE00007E000038000000000000000000000
|
|
996 |
000000000000000000000000000000000000000000000000F00003FC00071E000E1F001C
|
|
997 |
1F001C1F00381F00383F00703F00703F00707F00F07E00E07E00E0FE0000FC0000FC0001
|
|
998 |
FC0001F80003F80003F80003F00007F00007E00007E0000FE0E00FC0E00FC1E01FC1C01F
|
|
999 |
81C01F81C01F83801F03801F07001F07001F0E000F1C0007F80001E000143879B619>
|
|
1000 |
105 D<000FC007FFC007FFC007FFC0001FC0001F80001F80003F80003F80003F00003F00
|
|
1001 |
007F00007F00007E00007E0000FE0000FE0000FC0000FC0001FC0001FC0001F80001F800
|
|
1002 |
03F80003F80003F00003F00007F00007F00007E00007E0000FE0000FE0000FC0000FC000
|
|
1003 |
1FC0001FC0001F80001F80003F80003F80003F00003F00007F00007F00007E0E007E0E00
|
|
1004 |
FE0E00FE1E00FC1C00FC1C00FC3C00FC3800F83800F878007870007CE0001FE0000F8000
|
|
1005 |
123B79B915>108 D<01E000FE0007F00007F803FF801FFC000E3C0F07C0783E001E3E3C
|
|
1006 |
03E1E01F001C1F7803F3C01F80383FF001F7800F80383FE001F7000F80783FC001FE000F
|
|
1007 |
80703FC001FE000FC0703F8001FC000FC0703F0003F8001F80F07F0003F8001F80E07E00
|
|
1008 |
03F0001F80E07E0003F0001F80007E0007F0003F8000FE0007F0003F0000FC0007E0003F
|
|
1009 |
0000FC0007E0003F0000FC000FE0007F0001FC000FE0007E0001F8000FC0007E0001F800
|
|
1010 |
0FC000FE0001F8001FC000FC0003F8001FC000FC0003F0001F8001FC1C03F0001F8001F8
|
|
1011 |
1C03F0003F8001F83C07F0003F8003F83807E0003F0003F03807E0003F0003F03807E000
|
|
1012 |
7F0003F0700FE0007F0003E0700FC0007E0003E0F00FC0007E0003E0E00FC000FE0003E1
|
|
1013 |
C01FC000FE0001E3C01F8000FC0000FF000700003800003C003E2679A444>I<00078007
|
|
1014 |
C000001FE03FF000003CF0787C000038F8E03E0000787FC03E0000707F801F000070FF00
|
|
1015 |
1F0000F0FE001F8000E0FE001F8000E0FC001F8001E1FC001F8001C1FC001F8001C1F800
|
|
1016 |
1F8001C1F8001F800003F8003F800003F8003F800003F0003F800003F0003F800007F000
|
|
1017 |
7F800007F0007F800007E0007F000007E0007F00000FE000FF00000FE000FE00000FC000
|
|
1018 |
FE00000FC001FC00001FC001FC00001FC001F800001F8003F800001F8003F000003F8007
|
|
1019 |
E000003FC00FC000003FC00F8000003FE01F0000007FE03E0000007F70FC0000007E3FF0
|
|
1020 |
0000007E0F80000000FE0000000000FE0000000000FC0000000000FC0000000001FC0000
|
|
1021 |
000001FC0000000001F80000000001F80000000003F80000000003F80000000003F00000
|
|
1022 |
000007F000000000FFFFC0000000FFFFC0000000FFFFC0000000293580A42A>112
|
|
1023 |
D<03C003F0000FF01FFC001E783C0F001C7C700F003C3EE03F80383FC03F80387F803F80
|
|
1024 |
787F803F00707F003F00707F001C00F07E000000E0FE000000E0FC000000E0FC00000000
|
|
1025 |
FC00000001FC00000001F800000001F800000001F800000003F800000003F000000003F0
|
|
1026 |
00000003F000000007F000000007E000000007E000000007E00000000FE00000000FC000
|
|
1027 |
00000FC00000000FC00000001FC00000001F800000001F800000001F800000003F800000
|
|
1028 |
003F000000000E00000000212679A423>114 D<0003800007C0000FC0000FC0000FC000
|
|
1029 |
0FC0001FC0001F80001F80001F80003F80003F00003F00003F00007F00007E007FFFFF7F
|
|
1030 |
FFFFFFFFFF00FC0000FC0000FC0001FC0001F80001F80001F80003F80003F00003F00003
|
|
1031 |
F00007F00007E00007E00007E0000FE0000FC0000FC0000FC0001FC0001F801C1F801C1F
|
|
1032 |
803C3F80383F00783F00703F00F03F00E03F01C03E03C01F07800F0F0007FC0001F00018
|
|
1033 |
3579B31C>116 D<00F0000E0003FC003F00071E007F800E1F007F801C1F007F803C1F00
|
|
1034 |
7F80381F003F80383F001F80703F000F80703F000F80707F000F80F07E000F00E07E0007
|
|
1035 |
00E0FE00070000FC000F0000FC000E0001FC000E0001F8000E0001F8001E0003F8001C00
|
|
1036 |
03F0001C0003F0001C0003F0003C0007F000380007E000380007E000700007E000700007
|
|
1037 |
E000700007E000E00007E000E00007E001C00007E003C00003E003800003F007000001F0
|
|
1038 |
0E000000F83C0000007FF80000000FC00000212679A426>118 D<00F000000003FC0001
|
|
1039 |
C0071E0003E00E1F0007E01C1F0007E03C1F0007E0381F000FE0383F000FC0703F000FC0
|
|
1040 |
703F000FC0707F001FC0F07E001F80E07E001F80E0FE001F8000FC003F8000FC003F0001
|
|
1041 |
FC003F0001F8003F0001F8007F0003F8007E0003F0007E0003F0007E0003F000FE0007F0
|
|
1042 |
00FC0007E000FC0007E000FC0007E001FC0007E001F80007E001F80007E001F80007E003
|
|
1043 |
F80007E003F00007E007F00003E00FF00003F01FF00001F87FE000007FF7E000001FC7E0
|
|
1044 |
0000000FE00000000FC00000000FC00000001FC0003F001F80007F003F80007F003F0000
|
|
1045 |
7F007E00007F007C00007E00FC00007001F800007003E000003807C000003C1F8000000F
|
|
1046 |
FE00000003F0000000233679A428>121 D E
|
|
1047 |
%EndDVIPSBitmapFont
|
|
1048 |
%DVIPSBitmapFont: Fq cmsy7 7 4
|
|
1049 |
/Fq 4 51 df<FFFFFFFFFEFFFFFFFFFEFFFFFFFFFE27037A8F34>0
|
|
1050 |
D<000001FFC000000000001FFFFC0000000000FFFFFF8000000001FF007FC000000007F0
|
|
1051 |
0007F00000001F800000FC0000003F0000007E0000007C0000001F000000F00000000780
|
|
1052 |
0001E000000003C00003C000000001E000078000000000F00007000000000070000F0000
|
|
1053 |
00000078001E00000000003C001C00000000001C003C00000000001E003800000000000E
|
|
1054 |
007800000000000F0070000000000007007000000000000700F000000000000780E00000
|
|
1055 |
0000000380E000000000000380E000000000000380E000000000000380E0000000000003
|
|
1056 |
80E000000000000380E000000000000380E000000000000380E000000000000380F00000
|
|
1057 |
0000000780700000000000070070000000000007007800000000000F003800000000000E
|
|
1058 |
003C00000000001E001C00000000001C001E00000000003C000F00000000007800070000
|
|
1059 |
0000007000078000000000F00003C000000001E00001E000000003C00000F00000000780
|
|
1060 |
00007C0000001F0000003F0000007E0000001F800000FC00000007F00007F000000001FF
|
|
1061 |
007FC000000000FFFFFF80000000001FFFFC000000000001FFC000000039357CA842>13
|
|
1062 |
D<00E001F003F803F803F807F007F007F007E007E00FE00FC00FC00FC01F801F801F001F
|
|
1063 |
003F003E003E003E007C007C007C007800F800F800F00010000D1E7D9F13>48
|
|
1064 |
D<0001FFFF000FFFFF003FFFFF00FF000001F8000003E00000078000000F0000001E0000
|
|
1065 |
001C0000003C00000038000000780000007000000070000000F0000000E0000000E00000
|
|
1066 |
00FFFFFFFFFFFFFFFFFFFFFFFFE0000000E0000000F00000007000000070000000780000
|
|
1067 |
00380000003C0000001C0000001E0000000F0000000780000003E0000001F8000000FF00
|
|
1068 |
00003FFFFF000FFFFF0001FFFF20277AA12D>50 D E
|
|
1069 |
%EndDVIPSBitmapFont
|
|
1070 |
/Fr 173[39 3[42 52 36 2[19 3[36 15[29 4[29 8[19 39[{
|
|
1071 |
.167 SlantFont TeXBase1Encoding ReEncodeFont}9 58.1154
|
|
1072 |
/Times-Roman rf /Fs 134[29 1[42 29 29 16 23 19 29 29
|
|
1073 |
29 29 45 16 29 1[16 29 29 19 26 29 26 29 26 12[36 32
|
|
1074 |
2[32 2[52 7[36 1[39 1[42 7[29 29 29 1[29 1[29 29 29 29
|
|
1075 |
16 15 19 15 7[29 33[32 2[{TeXBase1Encoding ReEncodeFont}44
|
|
1076 |
58.1154 /Times-Roman rf
|
|
1077 |
%DVIPSBitmapFont: Ft cmmi7 7 3
|
|
1078 |
/Ft 3 121 df<003FFFE00FFFC0003FFFE00FFFC00001FF0001FC000000FE0001F00000
|
|
1079 |
00FE0001C00000007F0003800000007F0007000000003F000E000000003F801C00000000
|
|
1080 |
1F8038000000001FC070000000001FC0E0000000000FE1C0000000000FE3800000000007
|
|
1081 |
F7000000000007FE000000000003FC000000000003F8000000000001FC000000000001FC
|
|
1082 |
000000000001FE000000000003FE0000000000077F00000000000E7F00000000001C3F00
|
|
1083 |
00000000183F8000000000301F8000000000601FC000000000C01FC000000001800FE000
|
|
1084 |
000003000FE0000000060007F00000000C0007F0000000380003F8000000700003F80000
|
|
1085 |
00F00001FC000001E00001FC00000FF00003FE0000FFFC001FFFE000FFFC001FFFE00032
|
|
1086 |
287DA736>88 D<07801FC0000FE07FF00018F0E0F80030F1807C0030FB007C0060FE003C
|
|
1087 |
0060FC003C0060F8003C00C1F8007C00C1F0007C0001F0007C0001F0007C0003E000F800
|
|
1088 |
03E000F80003E000F80003E001F00007C001F00007C001F06007C003E06007C003E0600F
|
|
1089 |
8007C0C00F8007C0C00F8007C1800F8003C3001F0003C7001F0001FE000E0000F800231B
|
|
1090 |
7D9929>110 D<007C03C001FF0FF007079C300E03B0780C03F0F81803E1F83003E1F830
|
|
1091 |
03E1F06007C0E06007C0000007C0000007C000000F8000000F8000000F8000000F800000
|
|
1092 |
1F0000001F0030381F00307C1F0060FC3E0060FC3E00C0F87E00C0F06F038070C707003F
|
|
1093 |
83FE001F01F8001D1B7D9926>120 D E
|
|
1094 |
%EndDVIPSBitmapFont
|
|
1095 |
%DVIPSBitmapFont: Fu cmr7 7 3
|
|
1096 |
/Fu 3 52 df<00380000780001F8001FF800FEF800E0F80000F80000F80000F80000F800
|
|
1097 |
00F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F800
|
|
1098 |
00F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F80000F800
|
|
1099 |
00F80001FC00FFFFF8FFFFF815267BA521>49 D<00FF000003FFE0000E03F0001800F800
|
|
1100 |
30007C0060007E0078003F00FC003F00FE001F80FE001F80FE001F80FE001F807C001F80
|
|
1101 |
00001F8000001F0000003F0000003E0000007E0000007C000000F8000001F0000003E000
|
|
1102 |
0003C00000078000000E0000001C0000003800000070018000E001800180018003000300
|
|
1103 |
060003000C0003001FFFFF003FFFFF007FFFFE00FFFFFE00FFFFFE0019267DA521>I<00
|
|
1104 |
FF000003FFE0000F01F8001C007C0030007E003C003E007E003F007E003F007E003F007E
|
|
1105 |
003F003C003F0000003E0000007E0000007C000000F8000001F0000007E00001FF800001
|
|
1106 |
FF00000001E0000000F00000007C0000003E0000003F0000001F0000001F8000001F8038
|
|
1107 |
001F807C001F80FE001F80FE001F80FE001F00FC003F0078003E0070007C003800F8001F
|
|
1108 |
01F00007FFC00000FF000019277DA521>I E
|
|
1109 |
%EndDVIPSBitmapFont
|
|
1110 |
%DVIPSBitmapFont: Fv cmsy10 10 19
|
|
1111 |
/Fv 19 107 df<7FFFFFFFFFFF80FFFFFFFFFFFFC0FFFFFFFFFFFFC07FFFFFFFFFFF8032
|
|
1112 |
04799641>0 D<1C007F00FF80FF80FF80FF80FF807F001C000909799917>I<001FF00000
|
|
1113 |
FFFE0001FFFF0007FFFFC00FFFFFE01FFFFFF03FFFFFF83FFFFFF87FFFFFFC7FFFFFFC7F
|
|
1114 |
FFFFFCFFFFFFFEFFFFFFFEFFFFFFFEFFFFFFFEFFFFFFFEFFFFFFFEFFFFFFFEFFFFFFFEFF
|
|
1115 |
FFFFFE7FFFFFFC7FFFFFFC7FFFFFFC3FFFFFF83FFFFFF81FFFFFF00FFFFFE007FFFFC001
|
|
1116 |
FFFF0000FFFE00001FF0001F1F7BA42A>15 D<7FFFFFFFFFFFF8FFFFFFFFFFFFFCFFFFFF
|
|
1117 |
FFFFFFFC7FFFFFFFFFFFF800000000000000000000000000000000000000000000000000
|
|
1118 |
000000000000000000000000000000000000000000000000000000000000000000000000
|
|
1119 |
000000000000000000000000000000000000000000000000000000000000000000000000
|
|
1120 |
007FFFFFFFFFFFF8FFFFFFFFFFFFFCFFFFFFFFFFFFFC7FFFFFFFFFFFF800000000000000
|
|
1121 |
000000000000000000000000000000000000000000000000000000000000000000000000
|
|
1122 |
000000000000000000000000000000000000000000000000000000000000000000000000
|
|
1123 |
000000000000000000000000000000000000007FFFFFFFFFFFF8FFFFFFFFFFFFFCFFFFFF
|
|
1124 |
FFFFFFFC7FFFFFFFFFFFF836287BA841>17 D<00000FFFFFFF800000FFFFFFFFC00003FF
|
|
1125 |
FFFFFFC0000FFFFFFFFF80001FF800000000007F800000000000FE000000000001F80000
|
|
1126 |
00000003F0000000000007E000000000000FC000000000000F8000000000001F00000000
|
|
1127 |
00001F0000000000003E0000000000003E0000000000007C0000000000007C0000000000
|
|
1128 |
0078000000000000F8000000000000F8000000000000F0000000000000F0000000000000
|
|
1129 |
F0000000000000F0000000000000F0000000000000F0000000000000F0000000000000F0
|
|
1130 |
000000000000F8000000000000F8000000000000780000000000007C0000000000007C00
|
|
1131 |
00000000003E0000000000003E0000000000001F0000000000001F0000000000000F8000
|
|
1132 |
000000000FC0000000000007E0000000000003F0000000000001F8000000000000FE0000
|
|
1133 |
000000007F8000000000001FF800000000000FFFFFFFFF800003FFFFFFFFC00000FFFFFF
|
|
1134 |
FFC000000FFFFFFF80000000000000000000000000000000000000000000000000000000
|
|
1135 |
000000000000000000000000000000000000000000000000000000000000000000000000
|
|
1136 |
00000000000000000000000000000000000000000000000000000000000000000000001F
|
|
1137 |
FFFFFFFFFF803FFFFFFFFFFFC03FFFFFFFFFFFC01FFFFFFFFFFF80324479B441>I<003F
|
|
1138 |
800000000800FFF00000001C03FFF80000001C07FFFE0000001C0FFFFF0000001C1FFFFF
|
|
1139 |
C000001C1FC07FE000003C3F000FF00000383C0007FC000078780001FE000078780000FF
|
|
1140 |
8000F07000003FC003F0F000001FF80FE0E000000FFFFFE0E0000003FFFFC0E0000001FF
|
|
1141 |
FF80E00000007FFF00E00000003FFC004000000007F00036137B9D41>24
|
|
1142 |
D<0000000000001E00000000000000001E00000000000000001E00000000000000001E00
|
|
1143 |
000000000000001F00000000000000000F00000000000000000F00000000000000000F80
|
|
1144 |
0000000000000007800000000000000007C00000000000000003E00000000000000003E0
|
|
1145 |
0000000000000001F00000000000000000F80000000000000000FC00000000000000007E
|
|
1146 |
00000000000000003F00000000000000001F80000000000000000FC00000000000000007
|
|
1147 |
F07FFFFFFFFFFFFFFFFCFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFFFFFF
|
|
1148 |
FC0000000000000007F0000000000000000FC0000000000000001F80000000000000003F
|
|
1149 |
00000000000000007E0000000000000000FC0000000000000000F80000000000000001F0
|
|
1150 |
0000000000000003E00000000000000003E00000000000000007C0000000000000000780
|
|
1151 |
000000000000000F80000000000000000F00000000000000000F00000000000000001F00
|
|
1152 |
000000000000001E00000000000000001E00000000000000001E00000000000000001E00
|
|
1153 |
00482C7BAA53>33 D<00000000003C00000000000000003C00000000000000003E000000
|
|
1154 |
00000000001E00000000000000001F00000000000000000F00000000000000000F800000
|
|
1155 |
000000000007C00000000000000003C00000000000000003E00000000000000001F00000
|
|
1156 |
000000000000F800000000000000007C00007FFFFFFFFFFFFE0000FFFFFFFFFFFFFF0000
|
|
1157 |
FFFFFFFFFFFFFF80007FFFFFFFFFFFFFC00000000000000003F00000000000000001F800
|
|
1158 |
00000000000000FE00000000000000003F80000000000000001FE00000000000000007F8
|
|
1159 |
0000000000000001FF0000000000000001FF0000000000000007F8000000000000001FE0
|
|
1160 |
000000000000003F8000000000000000FE0000000000000001F80000000000000003F000
|
|
1161 |
7FFFFFFFFFFFFFC000FFFFFFFFFFFFFF8000FFFFFFFFFFFFFF00007FFFFFFFFFFFFE0000
|
|
1162 |
0000000000007C0000000000000000F80000000000000001F00000000000000003E00000
|
|
1163 |
000000000003C00000000000000007C0000000000000000F80000000000000000F000000
|
|
1164 |
00000000001F00000000000000001E00000000000000003E00000000000000003C000000
|
|
1165 |
00000000003C00000048307BAC53>41 D<000003C000003C000000000007C000003E0000
|
|
1166 |
000000078000001E0000000000078000001E00000000000F8000001F00000000000F0000
|
|
1167 |
000F00000000001F0000000F80000000003E00000007C0000000003C00000003C0000000
|
|
1168 |
007C00000003E000000000F800000001F000000000F000000000F000000001F000000000
|
|
1169 |
F800000003FFFFFFFFFFFC00000007FFFFFFFFFFFE0000000FFFFFFFFFFFFF0000001FFF
|
|
1170 |
FFFFFFFFFF8000003E000000000007C00000FC000000000003F00001F8000000000001F8
|
|
1171 |
0003F0000000000000FC000FE00000000000007F003F800000000000001FC0FF00000000
|
|
1172 |
0000000FF0FF000000000000000FF03F800000000000001FC00FE00000000000007F0003
|
|
1173 |
F0000000000000FC0001F8000000000001F80000FC000000000003F000003E0000000000
|
|
1174 |
07C000001FFFFFFFFFFFFF8000000FFFFFFFFFFFFF00000007FFFFFFFFFFFE00000003FF
|
|
1175 |
FFFFFFFFFC00000001F000000000F800000000F000000000F000000000F800000001F000
|
|
1176 |
0000007C00000003E0000000003C00000003C0000000003E00000007C0000000001F0000
|
|
1177 |
000F80000000000F0000000F00000000000F8000001F0000000000078000001E00000000
|
|
1178 |
00078000001E000000000007C000003E000000000003C000003C0000004C307DAC53>44
|
|
1179 |
D<00001FFFFE0000FFFFFF0003FFFFFF000FFFFFFE001FF00000007F80000000FE000000
|
|
1180 |
01F800000003F000000007E00000000FC00000000F800000001F000000001F000000003E
|
|
1181 |
000000003E000000007C000000007C000000007800000000F800000000F800000000F000
|
|
1182 |
000000F000000000FFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF000000000F00000
|
|
1183 |
0000F800000000F80000000078000000007C000000007C000000003E000000003E000000
|
|
1184 |
001F000000001F000000000F800000000FC000000007E000000003F000000001F8000000
|
|
1185 |
00FE000000007F800000001FF00000000FFFFFFE0003FFFFFF0000FFFFFF00001FFFFE28
|
|
1186 |
3279AD37>50 D<0000000001800000000003C00000000007C00000000007C0000000000F
|
|
1187 |
80000000000F80000000001F00000000001F00000000003E00000000003E00000000007C
|
|
1188 |
00000000007C0000000000F80000000000F80000000001F00000000001F00000000003E0
|
|
1189 |
0000000003E00000000007C0000000000FC0000000000F80000000001F00000000001F00
|
|
1190 |
000000003E00000000003E00000000007C00000000007C0000000000F80000000000F800
|
|
1191 |
00000001F00000000001F00000000003E00000000003E00000000007C00000000007C000
|
|
1192 |
0000000F80000000000F80000000001F00000000001F00000000003E00000000003E0000
|
|
1193 |
0000007C00000000007C0000000000F80000000000F80000000001F00000000001F00000
|
|
1194 |
000003E00000000003E00000000007C00000000007C0000000000F80000000000F800000
|
|
1195 |
00001F00000000001F00000000003E00000000003E00000000007C0000000000FC000000
|
|
1196 |
0000F80000000001F00000000001F00000000003E00000000003E00000000007C0000000
|
|
1197 |
0007C0000000000F80000000000F80000000001F00000000001F00000000003E00000000
|
|
1198 |
003E00000000007C00000000007C0000000000F80000000000F80000000000F000000000
|
|
1199 |
006000000000002A4E75BB00>54 D<600000000018F0000000003CF8000000007CF80000
|
|
1200 |
00007C7800000000787C00000000F87C00000000F83C00000000F03E00000001F03E0000
|
|
1201 |
0001F01F00000003E01F00000003E00F00000003C00F80000007C00F80000007C0078000
|
|
1202 |
00078007C000000F8007C000000F8003E000001F0003E000001F0001FFFFFFFE0001FFFF
|
|
1203 |
FFFE0001FFFFFFFE0000FFFFFFFC0000F800007C0000F800007C00007C0000F800007C00
|
|
1204 |
00F800003C0000F000003E0001F000003E0001F000001E0001E000001F0003E000001F00
|
|
1205 |
03E000000F8007C000000F8007C0000007800780000007C00F80000007C00F80000003C0
|
|
1206 |
0F00000003E01F00000003E01F00000001F03E00000001F03E00000000F03C00000000F8
|
|
1207 |
7C00000000F87C000000007878000000007CF8000000007CF8000000003FF0000000003F
|
|
1208 |
F0000000001FE0000000001FE0000000001FE0000000000FC0000000000FC0000000000F
|
|
1209 |
C000000000078000000000030000002E3C80B92F>56 D<600000000018F0000000003CF0
|
|
1210 |
000000003CF0000000003CF0000000003CF0000000003CF0000000003CF0000000003CF0
|
|
1211 |
000000003CF0000000003CF0000000003CF0000000003CF0000000003CF0000000003CF0
|
|
1212 |
000000003CF0000000003CF0000000003CF0000000003CF0000000003CF0000000003CF0
|
|
1213 |
000000003CF0000000003CF0000000003CF0000000003CF0000000003CF0000000003CF0
|
|
1214 |
000000003CF0000000003CF0000000003CF0000000003CF0000000003CF0000000003CF0
|
|
1215 |
000000003CF0000000003CF0000000003CF0000000003CF0000000003CF8000000007CF8
|
|
1216 |
000000007C7C00000000F87C00000000F83E00000001F03F00000003F01F80000007E00F
|
|
1217 |
C000000FC007F000003F8003FE0001FF0000FFC00FFC00007FFFFFF800001FFFFFE00000
|
|
1218 |
03FFFF000000007FF800002E347CB137>91 D<00000300000000000780000000000FC000
|
|
1219 |
0000000FC0000000001FE0000000001FE0000000001FE0000000003FF0000000003FF000
|
|
1220 |
0000007CF8000000007CF800000000F87C00000000F87C00000000F03C00000001F03E00
|
|
1221 |
000001F03E00000003E01F00000003E01F00000007C00F80000007C00F8000000F8007C0
|
|
1222 |
00000F8007C000000F0003C000001F0003E000001F0003E000003E0001F000003E0001F0
|
|
1223 |
00007C0000F800007C0000F80000780000780000F800007C0000F800007C0001F000003E
|
|
1224 |
0001F000003E0003E000001F0003E000001F0007C000000F8007C000000F800780000007
|
|
1225 |
800F80000007C00F80000007C01F00000003E01F00000003E03E00000001F03E00000001
|
|
1226 |
F03C00000000F07C00000000F87C00000000F8F8000000007CF8000000007CF000000000
|
|
1227 |
3C6000000000182E347CB137>94 D<600000000018F0000000003CF8000000007CF80000
|
|
1228 |
00007C7C00000000F87C00000000F83C00000000F03E00000001F03E00000001F01F0000
|
|
1229 |
0003E01F00000003E00F80000007C00F80000007C007800000078007C000000F8007C000
|
|
1230 |
000F8003E000001F0003E000001F0001F000003E0001F000003E0000F800007C0000F800
|
|
1231 |
007C00007800007800007C0000F800007C0000F800003E0001F000003E0001F000001F00
|
|
1232 |
03E000001F0003E000000F0003C000000F8007C000000F8007C0000007C00F80000007C0
|
|
1233 |
0F80000003E01F00000003E01F00000001F03E00000001F03E00000000F03C00000000F8
|
|
1234 |
7C00000000F87C000000007CF8000000007CF8000000003FF0000000003FF0000000001F
|
|
1235 |
E0000000001FE0000000001FE0000000000FC0000000000FC00000000007800000000003
|
|
1236 |
0000002E347CB137>I<6000000000F000000000F000000000F000000000F000000000F0
|
|
1237 |
00000000F000000000F000000000F000000000F000000000F000000000F000000000F000
|
|
1238 |
000000F000000000F000000000F000000000F000000000F000000000F000000000F00000
|
|
1239 |
0000F000000000F000000000F000000000F000000000F000000000F000000000F0000000
|
|
1240 |
00FFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF000000000F000000000F000000000
|
|
1241 |
F000000000F000000000F000000000F000000000F000000000F000000000F000000000F0
|
|
1242 |
00000000F000000000F000000000F000000000F000000000F000000000F000000000F000
|
|
1243 |
000000F000000000F000000000F000000000F000000000F000000000F000000000F00000
|
|
1244 |
0000F0000000006000000000283A7BB933>I<000001F800000FF800003F800000FC0000
|
|
1245 |
01F8000003F0000007E0000007E000000FE000000FC000000FC000000FC000000FC00000
|
|
1246 |
0FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC00000
|
|
1247 |
0FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC00000
|
|
1248 |
0FC000000FC000000FC000001FC000001F8000003F8000007F000000FE000003F800007F
|
|
1249 |
E00000FF0000007FE0000003F8000000FE0000007F0000003F8000001F8000001FC00000
|
|
1250 |
0FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC00000
|
|
1251 |
0FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC00000
|
|
1252 |
0FC000000FC000000FC000000FC000000FC000000FC000000FC000000FE0000007E00000
|
|
1253 |
07E0000003F0000001F8000000FC0000003F8000000FF8000001F81D537ABD2A>102
|
|
1254 |
D<FC000000FFC0000007F0000001FC0000007E0000003F0000003F8000001F8000001FC0
|
|
1255 |
00000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC0
|
|
1256 |
00000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC0
|
|
1257 |
00000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FE0000007E0
|
|
1258 |
000007F0000003F8000001FC0000007E0000001FF0000007F800001FF000007E000001FC
|
|
1259 |
000003F8000007F0000007E000000FE000000FC000000FC000000FC000000FC000000FC0
|
|
1260 |
00000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC0
|
|
1261 |
00000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC000000FC0
|
|
1262 |
00000FC000000FC000001FC000001F8000003F8000003F0000007E000001FC000007F000
|
|
1263 |
00FFC00000FC0000001D537ABD2A>I<60F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0
|
|
1264 |
F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0
|
|
1265 |
F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F060045377BD17>106
|
|
1266 |
D E
|
|
1267 |
%EndDVIPSBitmapFont
|
|
1268 |
/Fw 134[33 1[48 33 33 18 26 22 1[33 33 33 52 18 33 1[18
|
|
1269 |
33 33 22 29 33 29 1[29 3[22 1[22 1[48 2[48 48 41 37 44
|
|
1270 |
2[48 48 59 41 48 1[22 48 48 37 41 2[44 48 10[33 1[33
|
|
1271 |
2[33 2[17 1[17 2[22 22 40[{TeXBase1Encoding ReEncodeFont}48
|
|
1272 |
66.4176 /Times-Roman rf /Fx 134[37 37 55 37 42 23 32
|
|
1273 |
32 42 42 42 42 60 23 37 1[23 42 42 23 37 42 37 42 42
|
|
1274 |
9[69 2[46 42 2[51 2[69 46 2[28 1[60 51 1[60 2[51 6[28
|
|
1275 |
11[21 28 21 2[28 28 37[42 2[{TeXBase1Encoding ReEncodeFont}42
|
|
1276 |
83.022 /Times-Italic rf /Fy 134[37 1[55 1[46 23 32 32
|
|
1277 |
1[42 42 46 65 23 42 23 23 1[42 1[37 42 37 42 42 12[51
|
|
1278 |
46 7[55 3[60 2[60 55 1[55 65[{TeXBase1Encoding ReEncodeFont}27
|
|
1279 |
83.022 /Times-BoldItalic rf
|
|
1280 |
%DVIPSBitmapFont: Fz cmmi10 10 31
|
|
1281 |
/Fz 31 123 df<00003FC000000000FFF800000007E07C0000000F801F0000003F001F80
|
|
1282 |
0C007E000F800C00FC0007C01C01F80007E01803F00007E01807E00003E0380FE00003F0
|
|
1283 |
300FC00003F0301FC00003F0703F800003F0603F800003F0E07F800003F0C07F000003F1
|
|
1284 |
C07F000003F1807F000003F380FF000003F300FE000003F700FE000003FE00FE000003FC
|
|
1285 |
00FE000003FC00FC000003F800FC000003F000FC000003F000FC000003F000FC000003F0
|
|
1286 |
007E000007F0007E00000FF0003E00001DF8183F000079F8181F0000E1F8380F8007C0F8
|
|
1287 |
3007E03F007CF001FFF8003FC0003FC0000F802E267DA435>11 D<00000007F000000000
|
|
1288 |
1FFE00000000780F80000000E007C0000001C003E00000038001E00000070001F000000E
|
|
1289 |
0001F000001C0000F00000380000F80000300000F80000700001F80000600001F80000E0
|
|
1290 |
0001F00000C00001F00001C00003F00001800003F00001800003E00003800007E0000300
|
|
1291 |
0007C0000300000F80000700001F00000600003E00000603FE7C00000E07FFF800000C0E
|
|
1292 |
03E000000C0FFFF000000C03FC7800001C00007C00001800003E00001800003E00001800
|
|
1293 |
001F00003800001F00003000001F00003000001F00003000001F80007000001F80006000
|
|
1294 |
001F80006000001F80006000001F8000E000003F8000C000003F0000C000003F0000C000
|
|
1295 |
003F0001C000007F0001C000007E00018000007E0001800000FE0003800000FC0003C000
|
|
1296 |
01F80003C00001F80003C00003F00007C00007E00006E0000FC0000660001F8000067000
|
|
1297 |
3E00000E3800FC00000C1E03F000000C07FFC000000C01FE0000001C0000000000180000
|
|
1298 |
000000180000000000180000000000380000000000300000000000300000000000300000
|
|
1299 |
000000700000000000600000000000600000000000600000000000E00000000000C00000
|
|
1300 |
000000C000000000002D4B7EBA2F>I<003F00000000003FC00000000007F00000000003
|
|
1301 |
F80000000003FC0000000001FC0000000001FC0000000000FE0000000000FE0000000000
|
|
1302 |
FE00000000007F00000000007F00000000007F00000000003F80000000003F8000000000
|
|
1303 |
3F80000000001FC0000000001FC0000000001FC0000000000FE0000000000FE000000000
|
|
1304 |
0FE00000000007F00000000007F00000000007F00000000003F80000000003F800000000
|
|
1305 |
03F80000000001FC0000000001FC0000000000FE0000000000FE0000000001FE00000000
|
|
1306 |
03FF0000000007FF000000000F7F000000001E3F800000003C3F80000000783F80000000
|
|
1307 |
F01FC0000001F01FC0000003E01FC0000007C00FE000000F800FE000001F000FE000003F
|
|
1308 |
0007F000007E0007F00000FC0007F00001F80003F80003F00003F80007E00003F8000FE0
|
|
1309 |
0001FC001FC00001FC003F800001FC007F000000FE00FE000000FE00FE0000007F00FC00
|
|
1310 |
00007F80700000001F80293B7CB930>21 D<003FFFFFFFE000FFFFFFFFF001FFFFFFFFF0
|
|
1311 |
07FFFFFFFFF007FFFFFFFFE00F80700600001E00600E00003C00600C00003800E00C0000
|
|
1312 |
7000C00C0000E000C01C0000C001C01C00000001C01C00000001801C0000000380380000
|
|
1313 |
000380380000000780380000000700380000000700380000000F00380000000F00780000
|
|
1314 |
001E007C0000001E007C0000001E007C0000003E007C0000003C007C0000007C007C0000
|
|
1315 |
007C007E000000FC007E000000F8007E000001F8007E000001F8007F000003F8007F0000
|
|
1316 |
03F0003F000003F0003F000003F0003F000001C0001C00002C257EA32F>25
|
|
1317 |
D<00007FFFFFC00003FFFFFFE0000FFFFFFFE0001FFFFFFFE0007FFFFFFFC000FF81FE00
|
|
1318 |
0001FC007E000003F8003F000007F0003F000007E0001F00000FC0001F80001F80001F80
|
|
1319 |
001F80001F80003F00001F80003F00001F80007E00001F80007E00001F80007E00003F80
|
|
1320 |
00FE00003F0000FC00003F0000FC00003F0000FC00007F0000FC00007E0000F800007E00
|
|
1321 |
00F80000FC0000F80000FC0000F80001F80000F80001F80000F80003F000007C0007E000
|
|
1322 |
007C0007C000003C000F8000003E003F0000001F007C0000000F81F800000003FFE00000
|
|
1323 |
00007F000000002B257DA32F>27 D<003FFFFFFE00FFFFFFFF01FFFFFFFF03FFFFFFFF07
|
|
1324 |
FFFFFFFE0F801C00001E001C00003C001C000038003800007000380000E000380000C000
|
|
1325 |
780000000078000000007000000000F000000000F000000000F000000000F000000001E0
|
|
1326 |
00000001E000000001E000000003E000000003E000000003E000000007C000000007C000
|
|
1327 |
000007C00000000FC00000000FC00000000F800000001F800000001F800000001F800000
|
|
1328 |
003F800000003F800000003F000000001E00000028257EA324>I<1C007F00FF80FF80FF
|
|
1329 |
80FF80FF807F001C000909798817>58 D<1C007F00FF80FF80FFC0FFC0FFC07FC01CC000
|
|
1330 |
C000C000C000C001C00180018003800300070006000E001C003800700060000A19798817
|
|
1331 |
>I<0003FFFFFFFFFFE00007FFFFFFFFFFE00007FFFFFFFFFFE0000007F800003FE00000
|
|
1332 |
07F000000FE0000007F0000003C000000FF0000003C000000FF0000001C000000FE00000
|
|
1333 |
01C000000FE0000001C000001FE0000001C000001FE0000001C000001FC0000001C00000
|
|
1334 |
1FC00000018000003FC00000018000003FC00000018000003F800000018000003F800060
|
|
1335 |
018000007F8000E0018000007F8000E0000000007F0000C0000000007F0000C000000000
|
|
1336 |
FF0001C000000000FF0001C000000000FE00038000000000FE00078000000001FE001F80
|
|
1337 |
00000001FFFFFF8000000001FFFFFF0000000001FFFFFF0000000003FC001F0000000003
|
|
1338 |
FC000F0000000003F8000E0000000003F8000E0000000007F8000E0000000007F8000E00
|
|
1339 |
00000007F0000C0000000007F0000C000000000FF0001C000000000FF0001C000000000F
|
|
1340 |
E00000000000000FE00000000000001FE00000000000001FE00000000000001FC0000000
|
|
1341 |
0000001FC00000000000003FC00000000000003FC00000000000003F800000000000003F
|
|
1342 |
800000000000007F800000000000007F800000000000007F00000000000000FF80000000
|
|
1343 |
0000FFFFFFC000000000FFFFFFC000000000FFFFFFC0000000003B397DB835>70
|
|
1344 |
D<0003FFFFFF00000007FFFFFF00000007FFFFFE0000000007FC000000000007F8000000
|
|
1345 |
000007F000000000000FF000000000000FF000000000000FE000000000000FE000000000
|
|
1346 |
001FE000000000001FE000000000001FC000000000001FC000000000003FC00000000000
|
|
1347 |
3FC000000000003F8000000000003F8000000000007F8000000000007F8000000000007F
|
|
1348 |
0000000000007F000000000000FF000000000000FF000000000000FE000000000000FE00
|
|
1349 |
0000000001FE000000000001FE000000000001FC000000000001FC000000000003FC0000
|
|
1350 |
00000003FC000000000003F8000000000003F8000000000007F8000000000007F8000000
|
|
1351 |
400007F0000000C00007F0000000C0000FF0000001C0000FF000000180000FE000000380
|
|
1352 |
000FE000000380001FE000000300001FE000000700001FC000000600001FC000000E0000
|
|
1353 |
3FC000001E00003FC000001C00003F8000003C00003F8000007C00007F800000F800007F
|
|
1354 |
800003F800007F00000FF80000FF00007FF000FFFFFFFFFFF000FFFFFFFFFFF000FFFFFF
|
|
1355 |
FFFFE00032397DB839>76 D<0003FFF8000000003FFF800007FFF8000000007FFF800007
|
|
1356 |
FFFC000000007FFF80000007FC00000000FF8000000006FC00000001BF0000000006FC00
|
|
1357 |
000001BF000000000EFC000000037F000000000EFC000000037E000000000CFC00000006
|
|
1358 |
7E000000000CFC0000000C7E000000001C7E0000000CFE000000001C7E00000018FC0000
|
|
1359 |
0000187E00000030FC00000000187E00000030FC00000000387E00000061FC0000000038
|
|
1360 |
7E00000061F800000000307E000000C1F800000000307E00000181F800000000703F0000
|
|
1361 |
0183F800000000703F00000303F000000000603F00000603F000000000603F00000603F0
|
|
1362 |
00000000E03F00000C07F000000000E03F00000C07E000000000C03F00001807E0000000
|
|
1363 |
00C03F00003007E000000001C01F8000300FE000000001C01F8000600FC000000001801F
|
|
1364 |
8000C00FC000000001801F8000C00FC000000003801F8001801FC000000003801F800300
|
|
1365 |
1F8000000003001F8003001F8000000003000FC006001F8000000007000FC006003F8000
|
|
1366 |
000007000FC00C003F0000000006000FC018003F0000000006000FC018003F000000000E
|
|
1367 |
000FC030007F000000000E000FC060007E000000000C000FC060007E000000000C0007E0
|
|
1368 |
C0007E000000001C0007E0C000FE000000001C0007E18000FC00000000180007E30000FC
|
|
1369 |
00000000180007E30000FC00000000380007E60001FC00000000380007EC0001F8000000
|
|
1370 |
00300007EC0001F800000000300003F80001F800000000700003F80003F8000000007000
|
|
1371 |
03F00003F000000000F00003E00003F000000007FC0003E00007F8000000FFFFE003C007
|
|
1372 |
FFFFF00000FFFFE0038007FFFFF00000FFFFE0018007FFFFF0000051397CB851>I<0003
|
|
1373 |
FFF800001FFFF80007FFFC00003FFFF80007FFFC00003FFFF8000007FC000001FF000000
|
|
1374 |
07FE0000007C00000006FE000000780000000EFF000000700000000E7F00000070000000
|
|
1375 |
0C7F800000600000000C7F800000600000001C3F800000E00000001C3FC00000C0000000
|
|
1376 |
181FC00000C0000000181FE00000C0000000381FE00001C0000000380FF0000180000000
|
|
1377 |
300FF00001800000003007F00001800000007007F80003800000007003F8000300000000
|
|
1378 |
6003FC0003000000006003FC000300000000E001FC000700000000E001FE000600000000
|
|
1379 |
C000FE000600000000C000FF000600000001C0007F000E00000001C0007F800C00000001
|
|
1380 |
80007F800C0000000180003F800C0000000380003FC01C0000000380001FC01800000003
|
|
1381 |
00001FE0180000000300000FE0180000000700000FF0380000000700000FF03000000006
|
|
1382 |
000007F03000000006000007F8300000000E000003F8700000000E000003FC600000000C
|
|
1383 |
000003FC600000000C000001FE600000001C000001FEE00000001C000000FEC000000018
|
|
1384 |
000000FFC0000000180000007FC0000000380000007FC0000000380000007F8000000030
|
|
1385 |
0000003F80000000300000003F80000000700000001F80000000700000001F00000000F0
|
|
1386 |
0000000F00000007FC0000000F000000FFFFE000000F000000FFFFE0000006000000FFFF
|
|
1387 |
E000000600000045397DB843>I<0003FFFFFFFF00000007FFFFFFFFE0000007FFFFFFFF
|
|
1388 |
F800000007F80007FC00000007F00000FE00000007F000007F0000000FF000003F800000
|
|
1389 |
0FF000001FC000000FE000001FC000000FE000001FC000001FE000001FE000001FE00000
|
|
1390 |
1FE000001FC000001FE000001FC000001FE000003FC000001FE000003FC000003FC00000
|
|
1391 |
3F8000003FC000003F8000003FC000007F8000007F8000007F8000007F8000007F000000
|
|
1392 |
7F0000007F000000FE000000FF000001FC000000FF000001F8000000FE000007F0000000
|
|
1393 |
FE00000FE0000001FE00003FC0000001FE0001FF00000001FFFFFFFC00000001FFFFFFE0
|
|
1394 |
00000003FC00000000000003FC00000000000003F800000000000003F800000000000007
|
|
1395 |
F800000000000007F800000000000007F000000000000007F00000000000000FF0000000
|
|
1396 |
0000000FF00000000000000FE00000000000000FE00000000000001FE00000000000001F
|
|
1397 |
E00000000000001FC00000000000001FC00000000000003FC00000000000003FC0000000
|
|
1398 |
0000003F800000000000003F800000000000007F800000000000007F800000000000007F
|
|
1399 |
00000000000000FF800000000000FFFFFF0000000000FFFFFF0000000000FFFFFF000000
|
|
1400 |
00003B397DB835>80 D<00000001FF00000000001FFFF000000000FE01FC00000003F000
|
|
1401 |
7E00000007C0001F8000001F80000FC000003E000007E00000FC000003F00001F8000003
|
|
1402 |
F00003F0000001F80007E0000001F8000FC0000000FC001F80000000FC003F80000000FE
|
|
1403 |
007F00000000FE00FE00000000FE00FE000000007F01FC000000007F03FC000000007F03
|
|
1404 |
F8000000007F07F8000000007F07F0000000007F0FF0000000007F0FE000000000FF1FE0
|
|
1405 |
00000000FF1FE000000000FF3FC000000000FF3FC000000000FF3FC000000000FF7F8000
|
|
1406 |
000001FE7F8000000001FE7F8000000001FE7F8000000001FEFF0000000003FCFF000000
|
|
1407 |
0003FCFF0000000003FCFF0000000007F8FF0000000007F8FF0000000007F0FF00000000
|
|
1408 |
0FF0FF000000000FE0FF000000001FE0FF000000001FC0FF000000003F807F000000003F
|
|
1409 |
807F000000007F007F00000000FE007F0007C000FC003F001FF001F8003F80383803F800
|
|
1410 |
1F80701C07F0001F80E00C0FE0000FC0C00C1F800007E1C00E3F000007E1800E7E000003
|
|
1411 |
F18007F8000001F98007F00000007FC00FC00000003FE07F0003000007FFFE0003000000
|
|
1412 |
FF8F0007000000000F0006000000000F000E000000000F001E000000000F803C00000000
|
|
1413 |
0F807C000000000FC1F8000000000FFFF8000000000FFFF0000000000FFFF0000000000F
|
|
1414 |
FFE0000000000FFFC00000000007FF800000000003FE000000000000F80000384B7CBA42
|
|
1415 |
>I<0003FFFFFFF800000007FFFFFFFF80000007FFFFFFFFE000000007F8001FF8000000
|
|
1416 |
07F00003FC00000007F00000FE0000000FF000007F0000000FF000007F0000000FE00000
|
|
1417 |
3F8000000FE000003F8000001FE000003FC000001FE000003FC000001FC000003FC00000
|
|
1418 |
1FC000003FC000003FC000003FC000003FC000007F8000003F8000007F8000003F800000
|
|
1419 |
7F8000007F800000FF0000007F800000FE0000007F000001FC0000007F000003F8000000
|
|
1420 |
FF000007F0000000FF00000FE0000000FE00001F80000000FE00007F00000001FE0007F8
|
|
1421 |
00000001FFFFFFE000000001FFFFFF0000000001FC000FC000000003FC0003F000000003
|
|
1422 |
FC0001F800000003F80000FC00000003F80000FE00000007F80000FE00000007F800007E
|
|
1423 |
00000007F000007E00000007F000007F0000000FF00000FF0000000FF00000FE0000000F
|
|
1424 |
E00000FE0000000FE00000FE0000001FE00001FE0000001FE00001FE0000001FC00001FE
|
|
1425 |
0000001FC00001FE0000003FC00001FE0000003FC00003FE0000003F800003FC0060003F
|
|
1426 |
800003FC0060007F800003FC00E0007F800003FC00C0007F000003FC01C000FF800001FC
|
|
1427 |
0180FFFFFF0001FC0380FFFFFF0000FE0700FFFFFF00007E0E0000000000001FFC000000
|
|
1428 |
00000007F0003B3B7DB83F>I<7FFFFC00003FFFC0FFFFFC00007FFFC0FFFFFC00007FFF
|
|
1429 |
C003FF00000007FC0001FE00000003E00001FE00000003C00001FE00000003800000FE00
|
|
1430 |
000003000000FE00000007000000FE00000006000000FE0000000C000000FE0000000C00
|
|
1431 |
0000FE00000018000000FF00000030000000FF000000300000007F000000600000007F00
|
|
1432 |
0000E00000007F000000C00000007F000001800000007F000001800000007F0000030000
|
|
1433 |
00007F800006000000007F800006000000003F80000C000000003F80001C000000003F80
|
|
1434 |
0018000000003F800030000000003F800030000000003F800060000000003FC000C00000
|
|
1435 |
00003FC000C0000000001FC00180000000001FC00380000000001FC00300000000001FC0
|
|
1436 |
0600000000001FC00600000000001FC00C00000000001FE01800000000001FE018000000
|
|
1437 |
00000FE03000000000000FE07000000000000FE06000000000000FE0C000000000000FE0
|
|
1438 |
C000000000000FE18000000000000FE30000000000000FF300000000000007F600000000
|
|
1439 |
000007FE00000000000007FC00000000000007F800000000000007F800000000000007F0
|
|
1440 |
00000000000007E000000000000007E000000000000003C000000000000003C000000000
|
|
1441 |
00000380000000000000030000000000003A3B7CB830>86 D<0001FFFFF8007FFFF00001
|
|
1442 |
FFFFF800FFFFF00001FFFFF800FFFFE0000003FF80000FFC00000003FE00000FE0000000
|
|
1443 |
01FE0000078000000001FE00000F0000000000FF00000E0000000000FF00001C00000000
|
|
1444 |
007F00003800000000007F80007000000000007F8000E000000000003FC001C000000000
|
|
1445 |
003FC0038000000000001FC0030000000000001FE0060000000000001FE00C0000000000
|
|
1446 |
000FF0180000000000000FF03000000000000007F06000000000000007F8C00000000000
|
|
1447 |
0007F9C000000000000003FF8000000000000003FF0000000000000001FE000000000000
|
|
1448 |
0001FE0000000000000001FE0000000000000000FF0000000000000000FF000000000000
|
|
1449 |
0000FF0000000000000001FF80000000000000037F80000000000000063FC00000000000
|
|
1450 |
000E3FC00000000000001C1FE0000000000000381FE0000000000000700FE00000000000
|
|
1451 |
00E00FF0000000000000C00FF00000000000018007F80000000000030007F80000000000
|
|
1452 |
060003F800000000000C0003FC0000000000180003FC0000000000300001FE0000000000
|
|
1453 |
700001FE0000000000E00000FE0000000001C00000FF0000000003800000FF0000000007
|
|
1454 |
0000007F800000000E0000007F800000001E0000003F800000007E0000007FC0000003FF
|
|
1455 |
000000FFE000007FFFE0001FFFFFC000FFFFE0001FFFFFC000FFFFE0001FFFFF80004439
|
|
1456 |
7EB845>88 D<00007E00000003FF8000000FC1C380001F00EFC0007E007FC000FC003FC0
|
|
1457 |
01F8003FC003F0001F8007F0001F8007E0001F800FE0003F801FC0003F001FC0003F003F
|
|
1458 |
80003F003F80007F007F80007E007F00007E007F00007E007F0000FE00FF0000FC00FE00
|
|
1459 |
00FC00FE0000FC00FE0001FC00FE0001F800FC0001F80CFC0001F80CFC0003F80CFC0003
|
|
1460 |
F01CFC0003F018FC0007F0187C0007F0387E000FF0303E001FF0303E007BF0701F00E1F0
|
|
1461 |
E00F83C0F9C003FF007F8000FC001F0026267DA42C>97 D<003F00001FFF00001FFF0000
|
|
1462 |
1FFF0000007F0000007E0000007E0000007E000000FE000000FC000000FC000000FC0000
|
|
1463 |
01FC000001F8000001F8000001F8000003F8000003F0000003F0000003F0000007F00000
|
|
1464 |
07E0FC0007E3FF0007E707C00FFE03E00FF801F00FF001F80FE000F81FC000F81FC000FC
|
|
1465 |
1F8000FC1F8000FC3F8000FC3F0000FC3F0000FC3F0001FC7F0001FC7E0001FC7E0001FC
|
|
1466 |
7E0003FCFE0003FCFC0003F8FC0003F8FC0007F8FC0007F0F80007F0F8000FE0F8000FE0
|
|
1467 |
F8000FC0F8001F80F8003F8078003F007C007E007C00FC003C01F8001E03F0000F07C000
|
|
1468 |
07FF000001FC00001E3B7CB924>I<00003FC00001FFF00007E03C000F800E003F000700
|
|
1469 |
7E001F00FC007F01F800FF03F000FF07E000FF0FE000FF0FC000FE1FC000383F8000003F
|
|
1470 |
8000007F8000007F0000007F0000007F000000FF000000FE000000FE000000FE000000FE
|
|
1471 |
000000FC000000FC000000FC000000FC000003FC0000077E0000067E00000E3E00003C3F
|
|
1472 |
0000701F0000E00F8007C007C03F0001FFF800003FC00020267DA424>I<000000003F00
|
|
1473 |
00001FFF0000001FFF0000001FFF000000007F000000007E000000007E00000000FE0000
|
|
1474 |
0000FE00000000FC00000000FC00000001FC00000001FC00000001F800000001F8000000
|
|
1475 |
03F800000003F800000003F000000003F000000007F000000007F000007E07E00003FF87
|
|
1476 |
E0000FC1CFE0001F00EFE0007E007FC000FC003FC001F8003FC003F0001FC007F0001F80
|
|
1477 |
07E0001F800FE0003F801FC0003F801FC0003F003F80003F003F80007F007F80007F007F
|
|
1478 |
00007E007F00007E007F0000FE00FF0000FE00FE0000FC00FE0000FC00FE0001FC00FE00
|
|
1479 |
01FC00FC0001F80CFC0001F80CFC0003F80CFC0003F81CFC0003F018FC0007F0187C0007
|
|
1480 |
F0387E000FF0303E001FF0303E007BF0701F00E1F0E00F83C0F9C003FF007F8000FC001F
|
|
1481 |
00283B7DB92B>I<0000E00003F80003F80007F80007F80007F80007F00001C000000000
|
|
1482 |
000000000000000000000000000000000000000000000000000000000000F80003FE0007
|
|
1483 |
0F000E0F801C0F80180F80380F80300F80701F80601F80603F80E03F00C03F00C07F0000
|
|
1484 |
7E00007E0000FE0000FC0001FC0001FC0001F80003F80003F00003F00007F01807E01807
|
|
1485 |
E0380FE0300FC0300FC0700F80600F80E00F80C00F81C00F838007870003FE0000F80015
|
|
1486 |
397EB71D>105 D<000FC003FFC007FFC007FFC0001FC0001F80001F80003F80003F8000
|
|
1487 |
3F00003F00007F00007F00007E00007E0000FE0000FE0000FC0000FC0001FC0001FC0001
|
|
1488 |
F80001F80003F80003F80003F00003F00007F00007F00007E00007E0000FE0000FE0000F
|
|
1489 |
C0000FC0001FC0001FC0001F80001F80003F80003F80003F00003F00007F00007F00007E
|
|
1490 |
03007E0300FE0700FE0600FC0600FC0600FC0E00FC0C00FC1C00FC18007C38003C70001F
|
|
1491 |
E000078000123B7DB919>108 D<03E0007F0000FE000007F801FFE003FFC0000E3C0781
|
|
1492 |
F00F03E0001C3E1E00F83C01F000383F3800FC7001F800303F7000FCE001F800303FE000
|
|
1493 |
7DC000F800703FC0007F8000F800603F80007F0000F800603F80007F0000F800E03F0000
|
|
1494 |
FE0001F800C07F0000FE0001F800C07E0000FC0001F800C07E0000FC0001F800007E0001
|
|
1495 |
FC0003F80000FE0001FC0003F00000FC0001F80003F00000FC0001F80003F00000FC0003
|
|
1496 |
F80007F00001FC0003F80007E00001F80003F00007E00001F80003F0000FE00001F80007
|
|
1497 |
F0000FC00003F80007F0000FC00003F00007E0001FC06003F00007E0001F806003F0000F
|
|
1498 |
E0003F80E007F0000FE0003F00C007E0000FC0003F00C007E0000FC0003F01C007E0001F
|
|
1499 |
C0003E01800FE0001FC0003E03800FC0001F80003E03000FC0001F80003E07000FC0003F
|
|
1500 |
80003E0E001FC0003F80001E1C001F80003F00000FF8000700000E000003E00043267EA4
|
|
1501 |
49>I<03E0007F000007F801FFE0000E3C0781F0001C3E1E00F800383F3800FC00303F70
|
|
1502 |
00FC00303FE0007C00703FC0007C00603F80007C00603F80007C00E03F0000FC00C07F00
|
|
1503 |
00FC00C07E0000FC00C07E0000FC00007E0001FC0000FE0001F80000FC0001F80000FC00
|
|
1504 |
01F80000FC0003F80001FC0003F00001F80003F00001F80007F00001F80007E00003F800
|
|
1505 |
07E00003F0000FE03003F0000FC03003F0001FC07007F0001F806007E0001F806007E000
|
|
1506 |
1F80E007E0001F00C00FE0001F01C00FC0001F01800FC0001F03800FC0001F07001FC000
|
|
1507 |
0F0E001F800007FC0007000001F0002C267EA432>I<0000FF000003FFC0000F80F0003E
|
|
1508 |
00380078001C0078003C00F000FC01F001FC01E001FC01E001FC01E001FC03F000F003F8
|
|
1509 |
000003FC000001FFE00001FFFC0001FFFF0000FFFF80007FFFC0001FFFE00003FFE00000
|
|
1510 |
3FF0000007F0000003F01E0001F07F0001F07F0001F0FF0001E0FF0001E0FF0001E0FE00
|
|
1511 |
03C0F80003C0E000078070000F0038003E001E00F80007FFE00001FF00001E267CA427>
|
|
1512 |
115 D<0001C0000003E0000007E0000007E0000007E0000007E000000FE000000FC00000
|
|
1513 |
0FC000000FC000001FC000001F8000001F8000001F8000003F8000003F00007FFFFF807F
|
|
1514 |
FFFF80FFFFFF80007E0000007E0000007E000000FE000000FC000000FC000000FC000001
|
|
1515 |
FC000001F8000001F8000001F8000003F8000003F0000003F0000003F0000007F0000007
|
|
1516 |
E0000007E0000007E000000FE000000FC006000FC006000FC00E001FC00C001F801C001F
|
|
1517 |
8018001F8038001F8070001F8060001F80E0000F81C0000787800003FE000000F8000019
|
|
1518 |
357EB31E>I<00F80003C003FE0007E0070F000FE00E0F800FF01C0F800FF0180F800FF0
|
|
1519 |
380F8007F0300F8003F0701F8001F0601F8001F0601F8000F0E03F8000E0C03F0000E0C0
|
|
1520 |
7F0000E0007E0000E0007E0000C000FE0000C000FC0000C000FC0001C001FC00018001F8
|
|
1521 |
00018001F800038001F800030003F800030003F000070003F000060003F0000E0003F000
|
|
1522 |
0C0003F0001C0003F000180003F000380003F000700001F000E00001F801C00000FC0380
|
|
1523 |
00007E0F0000001FFE00000007F0000024267EA428>118 D<0007E001F000001FF807FC
|
|
1524 |
0000783E0E0F0000E01F1C1F0001C01F383F8003800FF07F8003000FE0FF8007000FE0FF
|
|
1525 |
800E000FC0FF000C000FC07E000C001FC03C001C001F80000018001F80000018001F8000
|
|
1526 |
0000003F80000000003F80000000003F00000000003F00000000007F00000000007F0000
|
|
1527 |
0000007E00000000007E0000000000FE0000000000FE0000000000FC000C000000FC000C
|
|
1528 |
000001FC001C001E01FC0018003F01F80018007F81F80038007F83F8007000FF83F80060
|
|
1529 |
00FF07F800E000FE0E7C01C0007C1C7C03800078383E0F00001FF00FFC000007C003F000
|
|
1530 |
0029267EA42F>120 D<00F800000003FE000070070F0000F80E0F8001F81C0F8001F818
|
|
1531 |
0F8001F8380F8003F8300F8003F0701F8003F0601F8003F0603F8007F0E03F0007E0C03F
|
|
1532 |
0007E0C07F0007E0007E000FE0007E000FC000FE000FC000FC000FC000FC001FC001FC00
|
|
1533 |
1F8001F8001F8001F8001F8001F8003F8003F8003F0003F0003F0003F0003F0003F0007F
|
|
1534 |
0003F0007E0003F0007E0003F0007E0003F000FE0003F000FC0003F001FC0001F003FC00
|
|
1535 |
00F807FC00007C1FF800003FF9F800000FE1F800000003F800000003F000000003F0000E
|
|
1536 |
0007F0003F8007E0007F800FC0007F800FC0007F801F80007F801F00007F003E00007C00
|
|
1537 |
7C00007000F800003801F000001E07C000000FFF00000001FC00000025367EA429>I<00
|
|
1538 |
01E00060000FF800E0001FFC00C0003FFE01C0007FFF038000FFFF070000F81FFF0001E0
|
|
1539 |
03FE0001C0001C0001800038000180007000000000E000000001C0000000038000000007
|
|
1540 |
000000000E000000001C000000003800000000F000000001E00000000380000000070000
|
|
1541 |
00000E000000001C0000000038000300007000030000E000070001C00006000380000E00
|
|
1542 |
0700001C000FFC007C001FFF81F8001E0FFFF8003807FFF0007003FFE0006003FFC000E0
|
|
1543 |
01FF0000C0007C000023267DA427>I E
|
|
1544 |
%EndDVIPSBitmapFont
|
|
1545 |
/FA 138[55 33 39 44 2[50 55 83 28 55 1[28 1[50 33 44
|
|
1546 |
55 44 55 50 9[100 4[72 3[72 1[66 2[39 5[72 1[72 11[50
|
|
1547 |
50 50 50 50 2[25 46[{TeXBase1Encoding ReEncodeFont}30
|
|
1548 |
99.6264 /Times-Bold rf
|
|
1549 |
%DVIPSBitmapFont: FB cmss10 10 21
|
|
1550 |
/FB 21 118 df<FFFFFCFFFFFCFFFFFCFFFFFCFFFFFC16057F941C>45
|
|
1551 |
D<FEFEFEFEFEFEFE0707788617>I<000001FF000000001FFFE00000007FFFF8000001FF
|
|
1552 |
FFFC000007FFFFFE00000FFE03FF00001FF0007F80003FC0003FC0007F80001FC000FF00
|
|
1553 |
001FE001FC00000FE003FC001FCFF007F8007FF7F007F001FFFFF00FE003FFFFF81FE007
|
|
1554 |
FFFFF81FC00FF07FF81FC01FE03FF83F803FC01FF83F803F800FF87F007F0007FC7F007F
|
|
1555 |
0007FC7F00FE0003FC7F00FE0003FCFE00FE0003FCFE01FC0001FCFE01FC0001FCFE01FC
|
|
1556 |
0001FCFE01FC0001FCFE01FC0001FCFE01FC0001FCFE01FC0001FCFE01FC0001FCFE01FC
|
|
1557 |
0001FCFE01FC0001FCFE00FE0003F87F00FE0003F87F00FE0003F87F007F0007F07F007F
|
|
1558 |
0007F03F803F800FE03F803FC01FE01FC01FE03FC01FC00FF07F801FE007FFFF000FE003
|
|
1559 |
FFFE0007F001FFFC0007F8007FF00003FC001FC00001FC0000000000FF00000000007F80
|
|
1560 |
000000003FC00000FC001FF00007F8000FFE007FF00007FFFFFFC00001FFFFFF8000007F
|
|
1561 |
FFFE0000001FFFF000000001FF80002E3C7CBA37>64 D<FFC000000007FFFFC000000007
|
|
1562 |
FFFFC000000007FFFFE00000000FFFFFE00000000FFFFFF00000001FFFFEF00000001F7F
|
|
1563 |
FEF00000001F7FFEF80000003F7FFE780000003E7FFE780000003E7FFE7C0000007E7FFE
|
|
1564 |
7C0000007E7FFE3E000000FC7FFE3E000000FC7FFE3E000000FC7FFE3F000001FC7FFE1F
|
|
1565 |
000001F87FFE1F000001F87FFE1F800003F87FFE0F800003F07FFE0FC00007F07FFE0FC0
|
|
1566 |
0007F07FFE07C00007E07FFE07E0000FE07FFE07E0000FE07FFE03E0000FC07FFE03F000
|
|
1567 |
1FC07FFE03F0001FC07FFE01F0001F807FFE01F8003F807FFE01F8003F807FFE00F8003F
|
|
1568 |
007FFE00FC007F007FFE007C007E007FFE007E00FE007FFE007E00FE007FFE003E00FC00
|
|
1569 |
7FFE003F01FC007FFE003F01FC007FFE001F01F8007FFE001F83F8007FFE001F83F8007F
|
|
1570 |
FE000F83F0007FFE000FC7F0007FFE0007C7E0007FFE0007C7E0007FFE0007C7E0007FFE
|
|
1571 |
0003EFC0007FFE0003EFC0007FFE0003FFC0007FFE0001FF80007FFE0001FF80007FFE00
|
|
1572 |
00FF00007FFE0000FF00007FFE0000FF00007FFE00000000007FFE00000000007F383A78
|
|
1573 |
B949>77 D<FFE000001FC0FFE000001FC0FFF000001FC0FFF000001FC0FFF800001FC0FF
|
|
1574 |
F800001FC0FEFC00001FC0FEFC00001FC0FE7E00001FC0FE7E00001FC0FE7F00001FC0FE
|
|
1575 |
3F00001FC0FE3F80001FC0FE1F80001FC0FE1F80001FC0FE0FC0001FC0FE0FC0001FC0FE
|
|
1576 |
0FE0001FC0FE07E0001FC0FE07F0001FC0FE03F0001FC0FE03F8001FC0FE01F8001FC0FE
|
|
1577 |
01FC001FC0FE00FC001FC0FE00FE001FC0FE00FE001FC0FE007F001FC0FE007F001FC0FE
|
|
1578 |
003F801FC0FE003F801FC0FE001FC01FC0FE001FC01FC0FE000FC01FC0FE000FE01FC0FE
|
|
1579 |
0007E01FC0FE0007F01FC0FE0003F01FC0FE0003F81FC0FE0001F81FC0FE0001FC1FC0FE
|
|
1580 |
0000FC1FC0FE0000FC1FC0FE00007E1FC0FE00007E1FC0FE00007F1FC0FE00003F1FC0FE
|
|
1581 |
00003F9FC0FE00001F9FC0FE00001F9FC0FE00000FDFC0FE00000FDFC0FE000007FFC0FE
|
|
1582 |
000007FFC0FE000003FFC0FE000003FFC0FE000001FFC0FE000001FFC02A3A78B93B>I<
|
|
1583 |
001FF00000FFFC0003FFFF000FFFFF801FFFFFC01FE01FE01F000FF01C0007F0180003F8
|
|
1584 |
100003F8000003F8000001FC000001FC000001FC000001FC000001FC000001FC000001FC
|
|
1585 |
00003FFC000FFFFC00FFFFFC03FFFFFC0FFFFFFC1FFE01FC3FE001FC7F8001FC7F0001FC
|
|
1586 |
FE0001FCFE0001FCFE0001FCFE0001FCFE0003FCFF0003FC7F800FFC7FE03FFC3FFFFFFC
|
|
1587 |
1FFFFFFC0FFFF9FC07FFE1FC01FE00001E287DA628>97 D<FE00000000FE00000000FE00
|
|
1588 |
000000FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000FE0000
|
|
1589 |
0000FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000FE000000
|
|
1590 |
00FE00000000FE00000000FE00000000FE01FC0000FE0FFF0000FE3FFFC000FEFFFFE000
|
|
1591 |
FFFFFFF000FFF03FF800FFC007F800FF8003FC00FF0001FC00FE0000FE00FE0000FE00FE
|
|
1592 |
00007F00FE00007F00FE00007F00FE00003F80FE00003F80FE00003F80FE00003F80FE00
|
|
1593 |
003F80FE00003F80FE00003F80FE00003F80FE00003F80FE00003F80FE00007F00FE0000
|
|
1594 |
7F00FE00007F00FE0000FF00FE0000FE00FE0001FE00FF0001FC00FF8003FC00FFC00FF8
|
|
1595 |
00FFF03FF000FFFFFFE000FEFFFFC000FE7FFF8000FE1FFE00000007F80000213B7AB92B
|
|
1596 |
>I<0003FE00001FFFC0007FFFE000FFFFF801FFFFFC03FC03FC07F8007C0FE000381FC0
|
|
1597 |
00081FC000003F8000003F8000007F0000007F0000007F0000007E000000FE000000FE00
|
|
1598 |
0000FE000000FE000000FE000000FE000000FE000000FE000000FE0000007F0000007F00
|
|
1599 |
00007F0000003F8000003F8000003FC000021FC000060FE0001E07F0007E07FC03FE03FF
|
|
1600 |
FFFE00FFFFFC007FFFF0001FFFC00007FC001F287DA625>I<0000003F800000003F8000
|
|
1601 |
00003F800000003F800000003F800000003F800000003F800000003F800000003F800000
|
|
1602 |
003F800000003F800000003F800000003F800000003F800000003F800000003F80000000
|
|
1603 |
3F800000003F800000003F800000003F80000FE03F80003FFC3F8000FFFF3F8001FFFFBF
|
|
1604 |
8003FFFFFF8007FE07FF800FF801FF801FE000FF801FC0007F803FC0003F803F80003F80
|
|
1605 |
7F80003F807F00003F807F00003F807F00003F80FE00003F80FE00003F80FE00003F80FE
|
|
1606 |
00003F80FE00003F80FE00003F80FE00003F80FE00003F80FE00003F80FE00003F807F00
|
|
1607 |
003F807F00003F807F00003F803F80003F803F80007F801FC0007F801FE000FF800FF003
|
|
1608 |
FF8007FE07FF8003FFFFBF8001FFFF3F8000FFFE3F80007FF83F80000FE00000213B7DB9
|
|
1609 |
2B>I<0007F800001FFE00007FFF8001FFFFC003FFFFE007FC0FF00FF003F80FE001F81F
|
|
1610 |
C000FC1F80007C3F80007E3F00003E7F00003E7E00003E7E00001FFE00001FFFFFFFFFFF
|
|
1611 |
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC000000FC000000FE000000FE0000007E0000007E
|
|
1612 |
0000007F0000003F0000003F8000001FC000001FE000020FF0000E07F8003E03FE01FE01
|
|
1613 |
FFFFFE00FFFFFC007FFFF0001FFFC00003FE0020287EA625>I<FE000000FE000000FE00
|
|
1614 |
0000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE00
|
|
1615 |
0000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE01
|
|
1616 |
FC00FE0FFF80FE1FFFC0FE7FFFE0FEFFFFF0FFF81FF8FFE007F8FFC003F8FF8003FCFF80
|
|
1617 |
01FCFF0001FCFF0001FCFF0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE00
|
|
1618 |
01FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE00
|
|
1619 |
01FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE00
|
|
1620 |
01FCFE0001FC1E3A7AB92B>104 D<FFFFFFFFFFFFFFFF0000000000000000000000007F
|
|
1621 |
7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F7F
|
|
1622 |
08397BB814>I<FE00000000FE00000000FE00000000FE00000000FE00000000FE000000
|
|
1623 |
00FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000
|
|
1624 |
FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000FE
|
|
1625 |
00000000FE0003FE00FE0007FC00FE000FF800FE001FF000FE003FE000FE007FC000FE00
|
|
1626 |
FF8000FE01FF0000FE03FE0000FE03FC0000FE07F80000FE0FF00000FE1FE00000FE3FC0
|
|
1627 |
0000FE7F800000FEFFC00000FFFFE00000FFFFE00000FFFFF00000FFF7F80000FFE3F800
|
|
1628 |
00FFC1FC0000FF80FE0000FF00FF0000FE007F0000FE003F8000FE003FC000FE001FC000
|
|
1629 |
FE000FE000FE000FF000FE0007F000FE0003F800FE0001FC00FE0001FE00FE0000FE00FE
|
|
1630 |
00007F00FE00007F80213A7AB929>107 D<FEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFE
|
|
1631 |
FEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFEFE
|
|
1632 |
FEFEFEFE073A7AB914>I<0001FC0003F800FE0FFF801FFF00FE1FFFC03FFF80FE7FFFE0
|
|
1633 |
FFFFC0FEFFFFF1FFFFE0FFF81FFBF03FF0FFE007FBC00FF0FFC003FF8007F0FF8003FF00
|
|
1634 |
07F8FF8001FF0003F8FF0001FE0003F8FF0001FE0003F8FF0001FE0003F8FE0001FC0003
|
|
1635 |
F8FE0001FC0003F8FE0001FC0003F8FE0001FC0003F8FE0001FC0003F8FE0001FC0003F8
|
|
1636 |
FE0001FC0003F8FE0001FC0003F8FE0001FC0003F8FE0001FC0003F8FE0001FC0003F8FE
|
|
1637 |
0001FC0003F8FE0001FC0003F8FE0001FC0003F8FE0001FC0003F8FE0001FC0003F8FE00
|
|
1638 |
01FC0003F8FE0001FC0003F8FE0001FC0003F8FE0001FC0003F8FE0001FC0003F8FE0001
|
|
1639 |
FC0003F8FE0001FC0003F8FE0001FC0003F8FE0001FC0003F835267AA542>I<0001FC00
|
|
1640 |
FE0FFF80FE1FFFC0FE7FFFE0FEFFFFF0FFF81FF8FFE007F8FFC003F8FF8003FCFF8001FC
|
|
1641 |
FF0001FCFF0001FCFF0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FC
|
|
1642 |
FE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FC
|
|
1643 |
FE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FC
|
|
1644 |
FE0001FC1E267AA52B>I<0003FE0000000FFF8000003FFFE00000FFFFF80001FFFFFC00
|
|
1645 |
03FE03FE0007F800FF000FF0007F800FE0003F801FC0001FC03F80000FE03F80000FE03F
|
|
1646 |
000007E07F000007F07F000007F07E000003F0FE000003F8FE000003F8FE000003F8FE00
|
|
1647 |
0003F8FE000003F8FE000003F8FE000003F8FE000003F8FE000003F87F000007F07F0000
|
|
1648 |
07F07F000007F03F80000FE03F80000FE01FC0001FC01FE0003FC00FF0007F8007F800FF
|
|
1649 |
0003FE03FE0001FFFFFC0000FFFFF800007FFFF000001FFFC0000003FE000025287EA62A
|
|
1650 |
>I<0000F0FC07F0FC0FF0FC3FF0FC7FF0FCFFF0FDFF00FDFC00FFF000FFE000FFC000FF
|
|
1651 |
C000FF8000FF0000FF0000FF0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE
|
|
1652 |
0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE
|
|
1653 |
0000FE0000FE000014267AA51C>114 D<007FE00001FFFC0007FFFF800FFFFFC01FFFFF
|
|
1654 |
C03FC03FC03F0007803F0001807E0000007E0000007E0000007E0000007F0000007F0000
|
|
1655 |
003F8000003FF000003FFF80001FFFF0000FFFFC0007FFFE0003FFFF0000FFFF80001FFF
|
|
1656 |
800000FFC000003FC000000FE000000FE0000007E0000007E0000007E0400007E0600007
|
|
1657 |
E078000FC0FE001FC0FFC07F80FFFFFF807FFFFF001FFFFE0003FFF800007FC0001B287E
|
|
1658 |
A620>I<01FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC0000
|
|
1659 |
01FC000001FC0000FFFFFF00FFFFFF00FFFFFF00FFFFFF00FFFFFF0001FC000001FC0000
|
|
1660 |
01FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC0000
|
|
1661 |
01FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC0000
|
|
1662 |
01FC000001FC000001FC000001FC000001FC000001FE008001FE018000FF07C000FFFFC0
|
|
1663 |
00FFFFC0007FFF00003FFC00001FE0001A307FAE1E>I<FE0001FCFE0001FCFE0001FCFE
|
|
1664 |
0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE
|
|
1665 |
0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE
|
|
1666 |
0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0001FCFE0003FCFE0003FCFE
|
|
1667 |
0007FCFF001FFC7F807FFC7FFFFFFC3FFFF9FC3FFFF1FC0FFFC1FC03FC00001E267AA42B
|
|
1668 |
>I E
|
|
1669 |
%EndDVIPSBitmapFont
|
|
1670 |
/FC 75[28 11[28 16[83 42 1[37 37 24[37 42 42 60 42 42
|
|
1671 |
23 32 28 42 42 42 42 65 23 42 23 23 42 42 28 37 42 37
|
|
1672 |
42 37 3[28 1[28 3[78 60 60 51 46 55 1[46 60 60 74 51
|
|
1673 |
60 32 28 60 1[46 51 60 55 55 60 5[23 23 42 42 42 42 42
|
|
1674 |
42 42 42 42 42 23 21 28 21 2[28 28 28 36[46 2[{
|
|
1675 |
TeXBase1Encoding ReEncodeFont}75 83.022 /Times-Roman
|
|
1676 |
rf /FD 139[28 39 33 2[50 50 1[28 2[28 50 2[44 1[44 50
|
|
1677 |
44 11[72 6[72 89 9[66 67[{TeXBase1Encoding ReEncodeFont}16
|
|
1678 |
99.6264 /Times-Roman rf /FE 135[60 3[40 47 53 3[66 8[53
|
|
1679 |
66 53 66 60 27[80 3[86 65[{TeXBase1Encoding ReEncodeFont}12
|
|
1680 |
119.552 /Times-Bold rf /FF 137[72 80 48 56 64 2[72 80
|
|
1681 |
120 40 2[40 80 72 48 64 80 64 80 72 10[104 1[96 1[104
|
|
1682 |
8[56 2[88 2[104 96 104 65[{TeXBase1Encoding ReEncodeFont}26
|
|
1683 |
143.462 /Times-Bold rf end
|
|
1684 |
%%EndProlog
|
|
1685 |
%%BeginSetup
|
|
1686 |
%%Feature: *Resolution 600dpi
|
|
1687 |
TeXDict begin
|
|
1688 |
%%PaperSize: A4
|
|
1689 |
end
|
|
1690 |
%%EndSetup
|
|
1691 |
%%Page: 1 1
|
|
1692 |
TeXDict begin 1 0 bop 0 TeXcolorgray Black 0 TeXcolorgray
|
|
1693 |
0 TeXcolorgray 0 TeXcolorgray -135 157 a FF(A)36 b(F)l(ormal)e(T)-11
|
|
1694 |
b(r)m(eatment)34 b(of)i(the)f(Bar)m(endr)m(egt)f(V)-13
|
|
1695 |
b(ariable)33 b(Con)-6 b(v)o(ention)33 b(in)j(Rule)1615
|
|
1696 |
340 y(Inductions)1462 539 y FE(Extended)31 b(Abstract)626
|
|
1697 |
788 y FD(Christian)25 b(Urban)266 929 y FC(Ludwig-Maximilians-Uni)n(v)o
|
|
1698 |
(ersity)15 b(Munich)310 1045 y FB(urban@mathematik.uni-muenchen.de)2611
|
|
1699 |
788 y FD(Michael)24 b(Norrish)2530 929 y FC(Canberra)19
|
|
1700 |
b(Research)h(Lab)m(.,)2395 1029 y(National)f(ICT)i(Australia)f(\(NICT)
|
|
1701 |
-8 b(A\))2419 1145 y FB(Michael.No)n(rrish@nicta.com.au)p
|
|
1702 |
Black 0 TeXcolorgray 1 TeXcolorgray 0 TeXcolorgray 1
|
|
1703 |
TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray
|
|
1704 |
1 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray
|
|
1705 |
0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray
|
|
1706 |
0.25 TeXcolorgray 0 TeXcolorgray 0.5 TeXcolorgray 0 TeXcolorgray
|
|
1707 |
-150 1612 a FA(Abstract)-150 1745 y FC(Barendre)o(gt')j(s)28
|
|
1708 |
b(v)n(ariable)f(con)m(v)o(ention)f(simpli\002es)k(man)o(y)e(informal)
|
|
1709 |
-150 1845 y(proofs)33 b(in)h(the)g Fz(\025)p FC(-calculus)g(by)f(allo)n
|
|
1710 |
(wing)g(the)h(consideration)e(of)-150 1944 y(only)26
|
|
1711 |
b(those)g(bound)e(v)n(ariables)i(that)g(ha)n(v)o(e)g(been)f(suitably)h
|
|
1712 |
(chosen.)-150 2044 y(Barendre)o(gt)c(does)j(not)e(gi)n(v)o(e)h(a)h
|
|
1713 |
(formal)e(justi\002cation)h(for)g(the)g(v)n(ari-)-150
|
|
1714 |
2143 y(able)15 b(con)m(v)o(ention,)d(which)j(mak)o(es)g(it)i(hard)d(to)
|
|
1715 |
i(formalise)e(such)h(infor)n(-)-150 2243 y(mal)j(proofs.)d(In)j(this)g
|
|
1716 |
(paper)e(we)i(sho)n(w)f(ho)n(w)g(a)h(form)e(of)i(the)f(v)n(ariable)-150
|
|
1717 |
2343 y(con)m(v)o(ention)f(can)j(be)g(b)n(uilt)g(into)g(the)g(reasoning)
|
|
1718 |
f(principles)g(for)g(rule)-150 2442 y(inductions.)d(W)-7
|
|
1719 |
b(e)18 b(gi)n(v)o(e)e(tw)o(o)h(e)o(xamples)e(e)o(xplaining)g(our)h
|
|
1720 |
(technique.)-150 2606 y Fy(Categories)29 b(and)f(Subject)h(Descriptors)
|
|
1721 |
83 b FC(F)-7 b(.4.1)29 b([)p Fx(Mathematical)-150 2706
|
|
1722 |
y(Lo)o(gic)p FC(]:)36 b(Lambda-calculus)d(and)j(related)f(systems;)63
|
|
1723 |
b(I.2.3)34 b([)p Fx(De-)-150 2806 y(duction)19 b(and)g(Theor)m(em)h(Pr)
|
|
1724 |
l(o)o(ving)p FC(]:)f(Deduction)-150 2970 y Fy(General)h(T)-8
|
|
1725 |
b(erms)84 b FC(Theory)-5 b(,)17 b(V)-9 b(eri\002cation)-150
|
|
1726 |
3134 y Fy(K)n(eyw)o(ords)83 b FC(Lambda-calculus,)48
|
|
1727 |
b(nominal)i(logic,)h(POPLmark)-150 3234 y(challenge)-150
|
|
1728 |
3455 y FA(1.)99 b(Intr)n(oduction)-150 3588 y FC(In)23
|
|
1729 |
b(informal)f(proofs)g(about)g(languages)g(that)i(feature)e(bound)g(v)n
|
|
1730 |
(ari-)-150 3688 y(ables,)16 b(one)g(often)f(assumes)h(\(e)o(xplicitly)f
|
|
1731 |
(or)h(implicitly\))f(rather)g(con-)-150 3787 y(v)o(enient)k(con)m(v)o
|
|
1732 |
(entions)f(about)h(those)h(bound)f(v)n(ariables.)g(F)o(or)h(e)o(xam-)
|
|
1733 |
-150 3887 y(ple,)g(in)g(Barendre)o(gt')-5 b(s)19 b(seminal)h(book)f([2)
|
|
1734 |
o(])h(about)g(the)g Fz(\025)p FC(-calculus:)p 0 TeXcolorgray
|
|
1735 |
0 TeXcolorgray -40 4067 a(2)t(.)t(1)t(.)t(1)t(2)t(.)35
|
|
1736 |
b(C)t Fw(O)t(N)t(V)t(E)t(N)t(T)t(I)t(O)t(N)r FC(.)f(T)-6
|
|
1737 |
b(erms)32 b(that)h(are)g Fz(\013)p FC(-congruent)-42
|
|
1738 |
4166 y(are)15 b(identi\002ed.)f(So)i(no)n(w)e(we)i(write)f
|
|
1739 |
Fz(\025x:x)25 b Fv(\021)d Fz(\025y)s(:y)s FC(,)16 b(etcetera.)-40
|
|
1740 |
4338 y(2)t(.)t(1)t(.)t(1)t(3)t(.)42 b(V)-6 b Fw(A)t(R)t(I)t(A)t(B)t(L)t
|
|
1741 |
(E)43 b FC(C)t Fw(O)t(N)t(V)t(E)t(N)t(T)t(I)t(O)t(N)r
|
|
1742 |
FC(.)d(If)f Fz(M)1388 4350 y Fu(1)1424 4338 y Fz(;)14
|
|
1743 |
b(:)g(:)g(:)g(;)g(M)1690 4350 y Ft(n)-42 4438 y FC(occur)28
|
|
1744 |
b(in)i(a)g(certain)f(mathematical)f(conte)o(xt)g(\(e.g.)h(de\002ni-)-42
|
|
1745 |
4537 y(tion,)h(proof\),)e(then)i(in)g(these)h(terms)f(all)h(bound)e(v)n
|
|
1746 |
(ariables)-42 4637 y(are)20 b(chosen)f(to)i(be)f(dif)n(ferent)e(from)i
|
|
1747 |
(the)g(free)f(v)n(ariables.)p 0 TeXcolorgray -150 5002
|
|
1748 |
a Fs(Permission)g(to)h(mak)o(e)f(digital)h(or)f(hard)h(copies)e(of)i
|
|
1749 |
(all)f(or)g(part)h(of)f(this)g(w)o(ork)h(for)g(personal)f(or)-150
|
|
1750 |
5068 y(classroom)d(use)f(is)h(granted)h(without)f(fee)g(pro)o(vided)h
|
|
1751 |
(that)g(copies)e(are)h(not)h(made)f(or)g(distrib)o(uted)-150
|
|
1752 |
5135 y(for)e(pro\002t)g(or)g(commercial)g(adv)o(antage)e(and)h(that)h
|
|
1753 |
(copies)f(bear)g(this)g(notice)h(and)f(the)g(full)h(citation)-150
|
|
1754 |
5201 y(on)i(the)g(\002rst)g(page.)f(T)-5 b(o)16 b(cop)o(y)h(otherwise,)
|
|
1755 |
e(to)h(republish,)g(to)g(post)g(on)g(serv)o(ers)g(or)g(to)g(redistrib)o
|
|
1756 |
(ute)-150 5268 y(to)f(lists,)e(requires)i(prior)h(speci\002c)e
|
|
1757 |
(permission)g(and/or)h(a)g(fee.)-150 5351 y Fr(MERLIN'05)64
|
|
1758 |
b Fs(September)15 b(30,)f(2005,)h(T)-5 b(allinn,)14 b(Estonia.)-150
|
|
1759 |
5417 y(Cop)o(yright)120 5415 y(c)100 5417 y Fq(\015)g
|
|
1760 |
Fs(2005)h(A)n(CM)f(1-59593-072-8/05/0009.)9 b(.)g(.)g($5.00.)p
|
|
1761 |
0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 2141 1610
|
|
1762 |
a FC(Both)23 b(con)m(v)o(entions)d(gi)n(v)o(e)i(rise)h(to)g(v)o(ery)f
|
|
1763 |
(slick)h(informal)e(proofs:)2042 1709 y(the)30 b(\002rst)h(con)m(v)o
|
|
1764 |
(ention)d(assumes)i(that)h(the)f(\223data)g(structure\224)f(o)o(v)o(er)
|
|
1765 |
2042 1809 y(which)j(the)g(proofs)g(are)g(done)g(is)h(not)g(that)f(of)h
|
|
1766 |
(syntax-trees,)e(b)n(ut)2042 1909 y(of)38 b Fz(\013)p
|
|
1767 |
FC(-equi)n(v)n(alent)f(lambda-terms)f(\(or)i Fz(\013)p
|
|
1768 |
FC(-equi)n(v)n(alence)e(classes\).)2042 2008 y(Ho)n(we)n(v)o(er)m(,)16
|
|
1769 |
b(the)i(claim)g(to)g(be)g(using)g Fz(\013)p FC(-equi)n(v)n(alence)e
|
|
1770 |
(classes,)j(rather)2042 2108 y(than)g(syntax-trees,)g(is)i(often)f
|
|
1771 |
(blurred)e(by)i(statements)g(lik)o(e)h([2)o(]:)p 0 TeXcolorgray
|
|
1772 |
0 TeXcolorgray 2152 2257 a(2)t(.)t(1)t(.)t(1)t(4)t(.)d(M)t
|
|
1773 |
Fw(O)t(R)t(A)t(L)r FC(.)e(Using)f(con)m(v)o(entions)d(2.1.12)h(and)i
|
|
1774 |
(2.1.13)2150 2357 y(one)k(can)h(w)o(ork)g(with)g Fz(\025)p
|
|
1775 |
FC(-terms)h(in)f(the)g(nai)n(v)o(e)f(w)o(ay)-5 b(.)2141
|
|
1776 |
2505 y(One)18 b(adv)n(antage)d(of)i(using)g Fz(\013)p
|
|
1777 |
FC(-equi)n(v)n(alence)f(classes)i(is)h(that)e(cap-)2042
|
|
1778 |
2605 y(ture)23 b(a)n(v)n(oiding)g(substitution)g(can)h(be)g(de\002ned)f
|
|
1779 |
(as)h(a)h(total)f(function)2042 2705 y(satisfying)19
|
|
1780 |
b(the)i(follo)n(wing)d(four)h(properties)g([6)o(,)i(13)o(]:)p
|
|
1781 |
0 TeXcolorgray 0 TeXcolorgray 2042 2927 a Fv(\017)47
|
|
1782 |
b Fp(var)9 b Fo(\()p Fz(a)p Fo(\)[)p Fz(a)24 b Fo(:=)e
|
|
1783 |
Fz(N)9 b Fo(])23 b(=)g Fz(N)2042 3051 y Fv(\017)47 b
|
|
1784 |
Fp(var)9 b Fo(\()p Fz(b)p Fo(\)[)p Fz(a)23 b Fo(:=)g
|
|
1785 |
Fz(N)9 b Fo(])23 b(=)g Fp(var)9 b Fo(\()p Fz(b)p Fo(\))104
|
|
1786 |
b FC(pro)o(vided)18 b Fz(b)k Fv(6)p Fo(=)h Fz(a)2042
|
|
1787 |
3174 y Fv(\017)47 b Fp(app)6 b Fo(\()p Fz(M)2376 3186
|
|
1788 |
y Fu(1)2413 3174 y Fz(;)14 b(M)2531 3186 y Fu(2)2568
|
|
1789 |
3174 y Fo(\)[)p Fz(a)23 b Fo(:=)g Fz(N)9 b Fo(])23 b(=)f
|
|
1790 |
Fp(app)7 b Fo(\()p Fz(M)3256 3186 y Fu(1)3293 3174 y
|
|
1791 |
Fo([)p Fz(a)23 b Fo(:=)g Fz(N)9 b Fo(])p Fz(;)14 b(M)3711
|
|
1792 |
3186 y Fu(2)3747 3174 y Fo([)p Fz(a)23 b Fo(:=)g Fz(N)9
|
|
1793 |
b Fo(]\))2042 3297 y Fv(\017)47 b Fp(lam)6 b Fo(\()p
|
|
1794 |
Fz(b;)14 b(M)9 b Fo(\)[)p Fz(a)23 b Fo(:=)g Fz(N)9 b
|
|
1795 |
Fo(])23 b(=)f Fp(lam)7 b Fo(\()p Fz(b;)14 b(M)9 b Fo([)p
|
|
1796 |
Fz(a)23 b Fo(:=)f Fz(N)9 b Fo(]\))2957 3397 y FC(pro)o(vided)18
|
|
1797 |
b Fz(b)23 b Fv(6)p Fo(=)f Fz(a)f FC(and)f Fz(b)i Fv(62)i
|
|
1798 |
Fz(F)12 b(V)18 b Fo(\()p Fz(N)9 b Fo(\))2042 3537 y FC(The)33
|
|
1799 |
b(second)g(con)m(v)o(ention)e(assumes)j(that)g(binders)e(ha)n(v)o(e)h
|
|
1800 |
(al)o(w)o(ays)2042 3636 y(been)d(so)g(chosen)g(that)h(the)o(y)e(do)h
|
|
1801 |
(not)h(clash)f(with)h(free)f(v)n(ariables.)2042 3736
|
|
1802 |
y(This)g(a)n(v)n(oids)f(ha)n(ving)g(to)h(rename)e(bound)g(v)n
|
|
1803 |
(ariables.)h(When)g(per)n(-)2042 3836 y(forming)34 b(a)j(structural)e
|
|
1804 |
(induction,)g(renaming)f(bound)h(v)n(ariables)2042 3935
|
|
1805 |
y(can)h(be)h(handled)e(by)h(switching)g(to)h(inductions)e(on)h(term)g
|
|
1806 |
(size,)2042 4035 y(as)25 b(done)f(by)h(Homeier)f([7)o(].)g(When)h
|
|
1807 |
(performing)d(rule)j(inductions,)2042 4134 y(proofs)20
|
|
1808 |
b(typically)h(need)h(to)g(be)g(entirely)f(recast,)h(perhaps)e(by)i(pro)
|
|
1809 |
o(v-)2042 4234 y(ing)17 b(properties)g(in)m(v)n(olving)f(iterated)h
|
|
1810 |
(substitutions.)g(In)h(either)g(case,)2042 4334 y(and)25
|
|
1811 |
b(particularly)g(the)h(latter)m(,)g(the)g(mechanisation)e(can)i(hardly)
|
|
1812 |
f(be)2042 4433 y(seen)20 b(as)h(f)o(aithful)e(to)i(the)f(original)f
|
|
1813 |
(presentation.)2141 4533 y(A)i(typical)f(informal)f(proof)g(making)g
|
|
1814 |
(use)i(of)f(both)g(con)m(v)o(entions)2042 4633 y(is)h(presented)e(in)h
|
|
1815 |
(Figure)g(1.)2141 4732 y(In)34 b(this)g(proof,)e(the)i(equational)e
|
|
1816 |
(reasoning)g(in)i(the)f(v)n(ariable-)2042 4832 y(case)23
|
|
1817 |
b(\(1.1.\2261.3.\))d(relies)j(on)g(the)g(f)o(act)g(that)g(substitution)
|
|
1818 |
g(is)h(a)f(func-)2042 4932 y(tion.)g(In)h(the)g(lambda-case,)f(the)h
|
|
1819 |
(reasoning)e(further)h(relies)h(on)g(the)2042 5031 y(v)n(ariable)f(con)
|
|
1820 |
m(v)o(ention.)e(This)k(gi)n(v)o(es)f(the)h(assumption)e(that)i
|
|
1821 |
Fz(z)j FC(satis-)2042 5131 y(\002es)20 b(freshness)f(constraints)f
|
|
1822 |
(which)h(allo)n(w)g(the)h(substitutions)e(to)i(be)2042
|
|
1823 |
5230 y(pushed)k(under)g(the)h(binder)-5 b(.)24 b(Then)h(one)g(can)g
|
|
1824 |
(apply)f(the)i(induction)2042 5330 y(hypothesis,)e(and)h(\002nally)g
|
|
1825 |
(pull)h(the)f(substitutions)h(back)f(out)g(from)2042
|
|
1826 |
5430 y(under)16 b(the)h(binder)-5 b(.)16 b(In)h(the)g(absence)f(of)h
|
|
1827 |
(the)g(v)n(ariable)f(con)m(v)o(ention,)e Fz(z)p 0 TeXcolorgray
|
|
1828 |
0 TeXcolorgray eop end
|
|
1829 |
%%Page: 2 2
|
|
1830 |
TeXDict begin 2 1 bop 0 TeXcolorgray 0 TeXcolorgray 0
|
|
1831 |
TeXcolorgray 0 TeXcolorgray -150 3 1993 4 v -150 2419
|
|
1832 |
4 2416 v -120 86 a FC(2)t(.)t(1)t(.)t(1)t(6)t(.)42 b(S)t
|
|
1833 |
Fw(U)t(B)t(S)t(T)t(I)t(T)t(U)t(T)t(I)t(O)t(N)i FC(L)t
|
|
1834 |
Fw(E)t(M)t(M)t(A)r FC(.)c(If)f Fz(x)58 b Fv(6\021)g Fz(y)42
|
|
1835 |
b FC(and)c Fz(x)59 b Fv(62)-122 186 y Fz(F)12 b(V)19
|
|
1836 |
b Fo(\()p Fz(L)p Fo(\))p FC(,)i(then)-33 368 y Fz(M)9
|
|
1837 |
b Fo([)p Fz(x)23 b Fo(:=)f Fz(N)9 b Fo(][)p Fz(y)26 b
|
|
1838 |
Fo(:=)d Fz(L)p Fo(])f Fv(\021)h Fz(M)9 b Fo([)p Fz(y)25
|
|
1839 |
b Fo(:=)e Fz(L)p Fo(][)p Fz(x)g Fo(:=)g Fz(N)9 b Fo([)p
|
|
1840 |
Fz(y)26 b Fo(:=)c Fz(L)p Fo(]])p Fz(:)-120 551 y FC(P)t
|
|
1841 |
Fw(R)q(O)t(O)t(F)n FC(.)i(By)d(induction)d(on)i(the)g(structure)f(of)h
|
|
1842 |
Fz(M)9 b FC(.)-122 675 y Fn(Case)21 b(1:)f Fz(M)29 b
|
|
1843 |
FC(is)21 b(a)g(v)n(ariable.)-72 802 y(Case)g(1.1.)h Fz(M)32
|
|
1844 |
b Fv(\021)23 b Fz(x)p FC(.)e(Then)e(both)g(sides)i(equal)258
|
|
1845 |
902 y Fz(N)9 b Fo([)p Fz(y)26 b Fo(:=)d Fz(L)p Fo(])d
|
|
1846 |
FC(since)g Fz(x)k Fv(6\021)e Fz(y)s FC(.)-72 1049 y(Case)f(1.2.)h
|
|
1847 |
Fz(M)32 b Fv(\021)23 b Fz(y)s FC(.)d(Then)f(both)h(sides)g(equal)g
|
|
1848 |
Fz(L)p FC(,)g(for)258 1148 y Fz(x)k Fv(62)f Fz(F)12 b(V)19
|
|
1849 |
b Fo(\()p Fz(L)p Fo(\))i FC(implies)f Fz(L)p Fo([)p Fz(x)j
|
|
1850 |
Fo(:=)g Fz(:)14 b(:)g(:)p Fo(])23 b Fv(\021)g Fz(L)p
|
|
1851 |
FC(.)-72 1295 y(Case)e(1.3.)h Fz(M)32 b Fv(\021)23 b
|
|
1852 |
Fz(z)j Fv(6\021)d Fz(x;)14 b(y)s FC(.)20 b(Then)f(both)h(sides)h(equal)
|
|
1853 |
e Fz(z)t FC(.)-122 1433 y Fn(Case)i(2:)g Fz(M)33 b Fv(\021)25
|
|
1854 |
b Fz(\025z)t(:M)560 1445 y Fu(1)596 1433 y FC(.)c(By)h(the)f(v)n
|
|
1855 |
(ariable)f(con)m(v)o(ention)e(we)j(may)-122 1533 y(assume)27
|
|
1856 |
b(that)h Fz(z)39 b Fv(6\021)c Fz(x;)14 b(y)31 b FC(and)26
|
|
1857 |
b Fz(z)31 b FC(is)d(not)f(free)g(in)g Fz(N)t(;)14 b(L)p
|
|
1858 |
FC(.)27 b(Then)f(by)-122 1632 y(induction)19 b(hypothesis)p
|
|
1859 |
0 TeXcolorgray 0 TeXcolorgray 312 1770 a Fo(\()p Fz(\025z)t(:M)539
|
|
1860 |
1782 y Fu(1)576 1770 y Fo(\)[)p Fz(x)24 b Fo(:=)f Fz(N)9
|
|
1861 |
b Fo(][)p Fz(y)25 b Fo(:=)e Fz(L)p Fo(])200 1893 y Fv(\021)47
|
|
1862 |
b Fz(\025z)t(:)p Fo(\()p Fz(M)539 1905 y Fu(1)576 1893
|
|
1863 |
y Fo([)p Fz(x)24 b Fo(:=)e Fz(N)9 b Fo(][)p Fz(y)26 b
|
|
1864 |
Fo(:=)d Fz(L)p Fo(]\))200 2016 y Fv(\021)47 b Fz(\025z)t(:)p
|
|
1865 |
Fo(\()p Fz(M)539 2028 y Fu(1)576 2016 y Fo([)p Fz(y)26
|
|
1866 |
b Fo(:=)c Fz(L)p Fo(][)p Fz(x)i Fo(:=)e Fz(N)9 b Fo([)p
|
|
1867 |
Fz(y)26 b Fo(:=)d Fz(L)p Fo(]]\))200 2139 y Fv(\021)47
|
|
1868 |
b Fo(\()p Fz(\025z)t(:M)539 2151 y Fu(1)576 2139 y Fo(\)[)p
|
|
1869 |
Fz(y)26 b Fo(:=)d Fz(L)p Fo(][)p Fz(x)g Fo(:=)g Fz(N)9
|
|
1870 |
b Fo([)p Fz(y)25 b Fo(:=)e Fz(L)p Fo(]])p FC(.)-122 2276
|
|
1871 |
y Fn(Case)28 b(3:)f Fz(M)46 b Fv(\021)36 b Fz(M)483 2288
|
|
1872 |
y Fu(1)520 2276 y Fz(M)601 2288 y Fu(2)666 2276 y FC(The)28
|
|
1873 |
b(statement)f(follo)n(ws)g(again)g(from)-122 2376 y(the)20
|
|
1874 |
b(induction)f(hypothesis.)p 1839 2419 V -150 2422 1993
|
|
1875 |
4 v -150 2458 1993 3 v -99 2549 a Fn(Figur)o(e)g(1.)41
|
|
1876 |
b FC(Barendre)o(gt')-5 b(s)19 b(proof)g(of)h(the)g(Substitution)f
|
|
1877 |
(Lemma)p 0 TeXcolorgray -150 3027 a(might)g(not)g(be)g(distinct)h(from)
|
|
1878 |
e(the)i(free)f(v)n(ariables)g(in)g(the)h(induction)-150
|
|
1879 |
3126 y(\()p Fv(f)p Fz(x;)14 b(y)s Fv(g)21 b([)i Fz(F)12
|
|
1880 |
b(V)19 b Fo(\()p Fz(N)t(;)14 b(L)p Fo(\))p FC(\),)25
|
|
1881 |
b(and)g(one)g(has)h(to)f(rename)g Fz(z)k FC(a)o(w)o(ay)c(from)-150
|
|
1882 |
3226 y(that)20 b(set)h(in)g(order)e(to)h(mo)o(v)o(e)f(the)h
|
|
1883 |
(substitutions)f(around.)-50 3326 y(The)29 b(approaches)f(reported)g
|
|
1884 |
(in)i([6)o(,)g(14)o(,)g(7,)g(10)o(])g(sho)n(w)g(ho)n(w)f(to)-150
|
|
1885 |
3425 y(deal)24 b(with)g(the)g(\002rst)h(con)m(v)o(ention)c(in)j(a)g
|
|
1886 |
(formal)f(setting,)h(and)f(do)h(so)-150 3525 y(without)f(ha)n(ving)f
|
|
1887 |
(to)i(resort)f(to)h(a)g(nameless)f(de-Bruijn)g(or)g(HO)m(AS-)-150
|
|
1888 |
3624 y(representation)29 b(for)i Fz(\013)p FC(-equated)g
|
|
1889 |
Fz(\025)p FC(-terms.)g(The)o(y)g(construct)f(data)-150
|
|
1890 |
3724 y(structures)e(which)h(allo)n(w)f(one)h(to)g(write)g
|
|
1891 |
Fp(var)9 b Fo(\()p Fz(a)p Fo(\))p FC(,)30 b Fp(app)6
|
|
1892 |
b Fo(\()p Fz(M)1618 3736 y Fu(1)1656 3724 y Fz(;)14 b(M)1774
|
|
1893 |
3736 y Fu(2)1810 3724 y Fo(\))-150 3824 y FC(and)25 b
|
|
1894 |
Fp(lam)7 b Fo(\()p Fz(a;)14 b(M)9 b Fo(\))25 b FC(to)h(denote)e
|
|
1895 |
Fz(\013)p FC(-equated)g(v)n(ariables,)g(applications)-150
|
|
1896 |
3923 y(and)c(abstractions.)f(Furthermore,)e(one)j(has)g(the)h(equation)
|
|
1897 |
429 4228 y Fp(lam)7 b Fo(\()p Fz(a;)14 b(M)9 b Fo(\))23
|
|
1898 |
b(=)g Fp(lam)7 b Fo(\()p Fz(b;)14 b(N)9 b Fo(\))482 b
|
|
1899 |
FC(\(1\))-150 4533 y(whene)n(v)o(er)13 b(the)i(corresponding)d
|
|
1900 |
(syntax-trees)i(\223)p Fz(\025a:M)9 b FC(\224)16 b(and)e(\223)p
|
|
1901 |
Fz(\025b:N)9 b FC(\224)-150 4633 y(are)20 b Fz(\013)p
|
|
1902 |
FC(-equi)n(v)n(alent.)-50 4732 y(One)i(problem)f(when)h(w)o(orking)f
|
|
1903 |
(with)i(name-carrying)c Fz(\013)p FC(-equi-)-150 4832
|
|
1904 |
y(v)n(alence)25 b(classes)h(is)h(that)e(con)m(v)o(enient)e(structural)h
|
|
1905 |
(induction)g(prin-)-150 4932 y(ciples)h(do)e(not)h(come)g(for)g
|
|
1906 |
(\223free\224,)f(b)n(ut)h(need)g(to)g(be)g(deri)n(v)o(ed.)e(Such)-150
|
|
1907 |
5031 y(con)m(v)o(enient)g(structural)i(induction)f(principles)g(are)i
|
|
1908 |
(deri)n(v)o(ed)e(in)i([5)o(,)-150 5131 y(14)o(,)e(13)o(].)g(These)f
|
|
1909 |
(induction)f(principles)g(are)i(stated)g(in)g(such)f(a)h(w)o(ay)-150
|
|
1910 |
5230 y(that)c(the)o(y)g(come)f(v)o(ery)g(close)h(to)h(the)f(con)m(v)o
|
|
1911 |
(enience)d(of)i(the)i(informal)-150 5330 y(reasoning)14
|
|
1912 |
b(using)h(Barendre)o(gt')-5 b(s)15 b(v)n(ariable)g(con)m(v)o(ention.)d
|
|
1913 |
(The)j(struc-)-150 5430 y(tural)23 b(induction)e(principle)h(of)g
|
|
1914 |
(Urban)g(and)h(T)-7 b(asson,)22 b(for)h(e)o(xample,)p
|
|
1915 |
0 TeXcolorgray 0 TeXcolorgray 2042 70 a(is:)2120 40 y
|
|
1916 |
Fs(1)2105 218 y Fv(8)p Fz(x)14 b(z)t(:)44 b(P)35 b Fo(\()p
|
|
1917 |
Fp(var)10 b Fo(\()p Fz(z)t Fo(\)\))23 b Fz(x)2105 341
|
|
1918 |
y Fv(8)p Fz(x)14 b(M)21 b(N)t(:)2188 440 y Fo(\()p Fv(8)p
|
|
1919 |
Fz(y)s(:)h(P)35 b(M)c(y)s Fo(\))42 b Fv(^)g Fo(\()p Fv(8)p
|
|
1920 |
Fz(y)s(:)22 b(P)35 b(N)d(y)s Fo(\))46 b Fv(\))23 b Fz(P)35
|
|
1921 |
b Fo(\()p Fp(app)7 b Fo(\()p Fz(M)t(;)14 b(N)9 b Fo(\)\))23
|
|
1922 |
b Fz(x)2105 564 y Fv(8)p Fz(x)14 b(z)i(M)t(:)2188 663
|
|
1923 |
y(z)26 b Fo(#)d Fz(x)42 b Fv(^)g Fo(\()p Fv(8)p Fz(y)s(:)22
|
|
1924 |
b(P)35 b(M)d(y)s Fo(\))46 b Fv(\))g Fz(P)35 b Fo(\()p
|
|
1925 |
Fp(lam)7 b Fo(\()p Fz(z)t(;)14 b(M)9 b Fo(\)\))23 b Fz(x)p
|
|
1926 |
2105 713 1867 4 v 2914 786 a(P)35 b(M)d(x)3938 886 y
|
|
1927 |
FC(\(2\))2042 986 y(where)19 b Fz(P)32 b FC(stands)20
|
|
1928 |
b(for)f(the)g(property)f(to)i(be)f(pro)o(v)o(ed;)f Fz(M)28
|
|
1929 |
b FC(is)21 b(the)f(v)n(ari-)2042 1085 y(able)31 b(o)o(v)o(er)f(which)h
|
|
1930 |
(the)g(induction)f(is)i(done,)e(and)h(the)h(v)n(ariable)e
|
|
1931 |
Fz(x)2042 1185 y FC(for)18 b(the)h Fx(conte)n(xt)f FC(of)h(the)g
|
|
1932 |
(induction.)d(By)k(\223the)e(conte)o(xt)g(of)g(an)h(induc-)2042
|
|
1933 |
1285 y(tion\224,)d(we)i(mean)e(all)i(free)f(v)n(ariables)f(of)h(the)g
|
|
1934 |
(induction)f(hypothesis,)2042 1384 y(e)o(xcept)g(the)g(v)n(ariable)g(o)
|
|
1935 |
o(v)o(er)f(which)i(the)g(induction)e(is)i(performed.)d(In)2042
|
|
1936 |
1484 y(case)26 b(of)f(the)h(substitution)f(lemma,)g(the)h(induction)d
|
|
1937 |
(hypothesis)h Fz(P)2042 1583 y FC(is)2170 1756 y Fz(M)9
|
|
1938 |
b Fo([)p Fz(x)23 b Fo(:=)g Fz(N)9 b Fo(][)p Fz(y)25 b
|
|
1939 |
Fo(:=)e Fz(L)p Fo(])g Fv(\021)f Fz(M)9 b Fo([)p Fz(y)26
|
|
1940 |
b Fo(:=)c Fz(L)p Fo(][)p Fz(x)i Fo(:=)e Fz(N)9 b Fo([)p
|
|
1941 |
Fz(y)26 b Fo(:=)d Fz(L)p Fo(]])2042 1929 y FC(with)d
|
|
1942 |
Fz(M)29 b FC(being)19 b(the)g(v)n(ariable)g(o)o(v)o(er)f(which)i(the)f
|
|
1943 |
(induction)f(is)j(done.)2042 2028 y(So)j(in)h(this)g(case,)g(the)f
|
|
1944 |
(conte)o(xt)f Fz(x)j FC(w)o(ould)e(need)f(to)i(be)g(instantiated)2042
|
|
1945 |
2128 y(with)e(the)f(tuple)g Fo(\()p Fz(x;)14 b(y)s(;)g(N)t(;)g(L)p
|
|
1946 |
Fo(\))p FC(.)23 b(Then,)f(when)g(one)g(comes)g(to)h(pro)o(v)o(e)2042
|
|
1947 |
2227 y(the)d(lambda-case,)e(one)i(can)g(assume)g(in)h(\(2\))e(that)h
|
|
1948 |
(the)h(binder)e Fz(z)24 b FC(in)2551 2400 y Fz(P)35 b
|
|
1949 |
Fo(\()p Fp(lam)7 b Fo(\()p Fz(z)t(;)14 b(M)9 b Fo(\)\))23
|
|
1950 |
b(\()p Fz(x;)14 b(y)s(;)g(M)t(;)g(N)9 b Fo(\))2042 2573
|
|
1951 |
y FC(is)29 b(fresh)e(w)-5 b(.r)g(.t.)27 b Fo(\()p Fz(x;)14
|
|
1952 |
b(y)s(;)g(N)t(;)g(L)p Fo(\))p FC(\227meaning)27 b(roughly)e(that)j
|
|
1953 |
Fz(z)k FC(cannot)2042 2672 y(be)f(equal)h(to)g Fz(x)g
|
|
1954 |
FC(and)g Fz(y)s FC(,)f(and)h(that)f Fz(z)36 b FC(cannot)31
|
|
1955 |
b(be)g(a)i(free)e(v)n(ariable)2042 2772 y(in)24 b Fz(N)34
|
|
1956 |
b FC(and)24 b Fz(L)p FC(.)g(In)g(ef)n(fect,)g(one)g(can)g(formalise)g
|
|
1957 |
(Barendre)o(gt')-5 b(s)22 b(slick)2042 2871 y(informal)c(proof)h
|
|
1958 |
(without)h(dif)n(\002culties.)2141 2971 y(In)31 b(this)h(paper)e(we)h
|
|
1959 |
(sho)n(w)g(that)g(similar)h(induction)d(principles)2042
|
|
1960 |
3071 y(can)20 b(be)g(gi)n(v)o(en)f(for)h(rule)f(inductions,)g(pro)o
|
|
1961 |
(vided)f(a)i(certain)g(property)2042 3170 y(holds)32
|
|
1962 |
b(for)h(the)g(relations)f(o)o(v)o(er)g(which)h(the)g(rule)f(inductions)
|
|
1963 |
g(are)2042 3270 y(performed.)23 b(W)-7 b(e)27 b(illustrate)f(our)g
|
|
1964 |
(technique)e(with)j(tw)o(o)f(e)o(xamples:)2042 3370 y(one)k(is)i(the)f
|
|
1965 |
(proof)f(of)g(the)h(substituti)n(vity)g(property)d(of)j(the)g
|
|
1966 |
@beginspecial @setspecial
|
|
1967 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
1968 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
1969 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
1970 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
1971 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
1972 |
0 setlinecap stroke grestore end
|
|
1973 |
|
|
1974 |
@endspecial 3933 3381 a Fm(1)2042
|
|
1975 |
3469 y FC(relation)23 b(\(this)g(is)i(one)e(part)g(of)g(the)h(simple)f
|
|
1976 |
(Church-Rosser)f(proof)2042 3569 y(due)15 b(to)g(T)-7
|
|
1977 |
b(ait)17 b(and)e(Martin-L)7 b(\250)-35 b(of)13 b(for)i
|
|
1978 |
Fz(\014)t FC(-reduction)f([2)o(]\),)h(and)g(the)h(other)2042
|
|
1979 |
3668 y(is)21 b(the)f(usual)g(proof)f(of)h(the)g(weak)o(ening)e(lemma)i
|
|
1980 |
(for)g(simple)g(types.)2141 3768 y(The)38 b(proof)f(by)g(T)-7
|
|
1981 |
b(ait)39 b(and)e(Martin-L)7 b(\250)-35 b(of)37 b(does)g(not)h(sho)n(w)g
|
|
1982 |
(the)2042 3868 y(Church-Rosser)28 b(property)f(directly)i(for)g
|
|
1983 |
Fz(\014)t FC(-reduction,)f(b)n(ut)h(for)g(a)2042 3967
|
|
1984 |
y(more)19 b(general)g(reduction)g(relation)g(de\002ned)g(as:)p
|
|
1985 |
2300 4150 346 4 v 2300 4224 a Fz(M)9 b @beginspecial
|
|
1986 |
@setspecial
|
|
1987 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
1988 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
1989 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
1990 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
1991 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
1992 |
0 setlinecap stroke grestore end
|
|
1993 |
|
|
1994 |
@endspecial 2454 4235 a Fm(1)2555 4224 y
|
|
1995 |
Fz(M)3121 4125 y(M)g @beginspecial @setspecial
|
|
1996 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
1997 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
1998 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
1999 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2000 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2001 |
0 setlinecap stroke grestore end
|
|
2002 |
|
|
2003 |
@endspecial
|
|
2004 |
3275 4136 a Fm(1)3377 4125 y Fz(M)3467 4095 y Fq(0)p
|
|
2005 |
2834 4145 943 4 v 2834 4224 a Fp(lam)e Fo(\()p Fz(x;)14
|
|
2006 |
b(M)9 b Fo(\))p @beginspecial @setspecial
|
|
2007 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2008 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2009 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2010 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2011 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2012 |
0 setlinecap stroke grestore end
|
|
2013 |
|
|
2014 |
@endspecial
|
|
2015 |
3275 4235 a Fm(1)3377 4224 y Fp(lam)d Fo(\()p Fz(x;)14
|
|
2016 |
b(M)3720 4194 y Fq(0)3744 4224 y Fo(\))2642 4363 y Fz(M)9
|
|
2017 |
b @beginspecial @setspecial
|
|
2018 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2019 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2020 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2021 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2022 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2023 |
0 setlinecap stroke grestore end
|
|
2024 |
|
|
2025 |
@endspecial 2796 4374 a
|
|
2026 |
Fm(1)2897 4363 y Fz(M)2987 4333 y Fq(0)3093 4363 y Fz(N)g
|
|
2027 |
@beginspecial @setspecial
|
|
2028 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2029 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2030 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2031 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2032 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2033 |
0 setlinecap stroke grestore end
|
|
2034 |
|
|
2035 |
@endspecial 3233 4374 a Fm(1)3335
|
|
2036 |
4363 y Fz(N)3411 4333 y Fq(0)p 2535 4383 1007 4 v 2535
|
|
2037 |
4462 a Fp(app)d Fo(\()p Fz(M)t(;)14 b(N)9 b Fo(\))p @beginspecial
|
|
2038 |
@setspecial
|
|
2039 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2040 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2041 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2042 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2043 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2044 |
0 setlinecap stroke grestore end
|
|
2045 |
|
|
2046 |
@endspecial 2994 4473 a Fm(1)3095 4462 y
|
|
2047 |
Fp(app)e Fo(\()p Fz(M)3350 4432 y Fq(0)3373 4462 y Fz(;)14
|
|
2048 |
b(N)3486 4432 y Fq(0)3509 4462 y Fo(\))2642 4602 y Fz(M)9
|
|
2049 |
b @beginspecial @setspecial
|
|
2050 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2051 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2052 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2053 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2054 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2055 |
0 setlinecap stroke grestore end
|
|
2056 |
|
|
2057 |
@endspecial 2796 4613 a
|
|
2058 |
Fm(1)2897 4602 y Fz(M)2987 4572 y Fq(0)3093 4602 y Fz(N)g
|
|
2059 |
@beginspecial @setspecial
|
|
2060 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2061 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2062 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2063 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2064 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2065 |
0 setlinecap stroke grestore end
|
|
2066 |
|
|
2067 |
@endspecial 3233 4613 a Fm(1)3335
|
|
2068 |
4602 y Fz(N)3411 4572 y Fq(0)p 2392 4622 1292 4 v 2392
|
|
2069 |
4701 a Fp(app)e Fo(\()p Fp(lam)g Fo(\()p Fz(x;)14 b(M)9
|
|
2070 |
b Fo(\))p Fz(;)14 b(N)9 b Fo(\))p @beginspecial @setspecial
|
|
2071 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2072 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2073 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2074 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2075 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2076 |
0 setlinecap stroke grestore end
|
|
2077 |
|
|
2078 |
|
|
2079 |
@endspecial 3143 4712 a Fm(1)3245 4701 y Fz(M)3335 4671
|
|
2080 |
y Fq(0)3357 4701 y Fo([)p Fz(x)24 b Fo(:=)f Fz(N)3638
|
|
2081 |
4671 y Fq(0)3661 4701 y Fo(])3938 4417 y FC(\(3\))2042
|
|
2082 |
4864 y(A)d(central)g(lemma)g(in)g(this)h(Church-Rosser)e(proof)f(is)j
|
|
2083 |
(then:)2044 5010 y(S)t Fw(U)t(B)t(S)t(T)t(I)t(T)t(U)t(T)t(I)t(V)t(I)t
|
|
2084 |
(T)t(Y)38 b(O)t(F)e @beginspecial @setspecial
|
|
2085 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2086 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2087 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2088 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2089 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2090 |
0 setlinecap stroke grestore end
|
|
2091 |
|
|
2092 |
@endspecial
|
|
2093 |
2872 5021 a Fm(1)2974 5010 y FC(.)d(If)g Fz(M)9 b @beginspecial
|
|
2094 |
@setspecial
|
|
2095 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2096 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2097 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2098 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2099 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2100 |
0 setlinecap stroke grestore end
|
|
2101 |
|
|
2102 |
@endspecial 3271 5021 a Fm(1)3373 5010 y
|
|
2103 |
Fz(M)3463 4980 y Fq(0)3519 5010 y FC(and)33 b Fz(N)9
|
|
2104 |
b @beginspecial @setspecial
|
|
2105 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2106 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2107 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2108 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2109 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2110 |
0 setlinecap stroke grestore end
|
|
2111 |
|
|
2112 |
@endspecial 3813 5021 a
|
|
2113 |
Fm(1)3915 5010 y Fz(N)3991 4980 y Fq(0)4014 5010 y FC(,)2042
|
|
2114 |
5109 y(then)19 b Fz(M)9 b Fo([)p Fz(x)24 b Fo(:=)e Fz(N)9
|
|
2115 |
b Fo(])p @beginspecial @setspecial
|
|
2116 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2117 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2118 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2119 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2120 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2121 |
0 setlinecap stroke grestore end
|
|
2122 |
|
|
2123 |
@endspecial 2663
|
|
2124 |
5120 a Fm(1)2764 5109 y Fz(M)2854 5079 y Fq(0)2877 5109
|
|
2125 |
y Fo([)p Fz(x)24 b Fo(:=)e Fz(N)3157 5079 y Fq(0)3180
|
|
2126 |
5109 y Fo(])p FC(.)p 0 TeXcolorgray 2042 5197 997 3 v
|
|
2127 |
2042 5248 a Fk(1)2079 5272 y Fw(This)k(is)h(a)f(slightly)j
|
|
2128 |
(strengthened)h(v)o(ersion)d(of)g(the)g(induction)i(principle)g(gi)n(v)
|
|
2129 |
o(en)2042 5351 y(in)18 b([14)q(],)f(which)i(in)f(the)h(light)g(of)f
|
|
2130 |
(this)h(w)o(ork)f(seems)g(more)g(useful)h(than)g(the)g(original)2042
|
|
2131 |
5430 y(v)o(ersion.)p 0 TeXcolorgray 0 TeXcolorgray 0
|
|
2132 |
TeXcolorgray eop end
|
|
2133 |
%%Page: 3 3
|
|
2134 |
TeXDict begin 3 2 bop 0 TeXcolorgray 0 TeXcolorgray 0
|
|
2135 |
TeXcolorgray -50 66 a FC(This)23 b(proof)e(proceeds)h(in)h([2)o(])g(by)
|
|
2136 |
g(an)g(induction)e(o)o(v)o(er)g(the)i(de\002-)-150 166
|
|
2137 |
y(nition)g(of)h Fz(M)9 b @beginspecial @setspecial
|
|
2138 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2139 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2140 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2141 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2142 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2143 |
0 setlinecap stroke grestore end
|
|
2144 |
|
|
2145 |
@endspecial
|
|
2146 |
316 177 a Fm(1)418 166 y Fz(M)508 136 y Fq(0)531 166
|
|
2147 |
y FC(.)24 b(Though)e(Barendre)o(gt)g(does)i(not)g(ackno)n(w-)-150
|
|
2148 |
266 y(ledge)15 b(the)h(f)o(act)h(e)o(xplicitly)e(\(as)h(he)g(did)g(in)g
|
|
2149 |
(the)g(substitution)f(lemma\),)-150 365 y(there)k(are)g(tw)o(o)g
|
|
2150 |
(places)g(in)h(this)f(proof)f(where)g(the)i(v)n(ariable)e(con)m(v)o
|
|
2151 |
(en-)-150 465 y(tion)25 b(is)h(used.)f(In)f(the)h(case)h(of)f(the)g
|
|
2152 |
(second)f(rule)h(of)g @beginspecial @setspecial
|
|
2153 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2154 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2155 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2156 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2157 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2158 |
0 setlinecap stroke grestore end
|
|
2159 |
|
|
2160 |
@endspecial
|
|
2161 |
1467 476 a Fm(1)1569 465 y FC(,)g(for)g(e)o(x-)-150 565
|
|
2162 |
y(ample,)20 b(Barendre)o(gt)g(writes)h(\(slightly)g(changed)e(to)i
|
|
2163 |
(conform)e(with)-150 664 y(our)g(syntax\):)-48 764 y(C)t
|
|
2164 |
Fw(A)t(S)t(E)28 b FC(2)r(.)c Fz(M)9 b @beginspecial @setspecial
|
|
2165 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2166 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2167 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2168 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2169 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2170 |
0 setlinecap stroke grestore end
|
|
2171 |
|
|
2172 |
|
|
2173 |
@endspecial 416 775 a Fm(1)517 764 y Fz(M)607 734 y
|
|
2174 |
Fq(0)654 764 y FC(is)25 b Fp(lam)7 b Fo(\()p Fz(y)s(;)14
|
|
2175 |
b(P)e Fo(\))p @beginspecial @setspecial
|
|
2176 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2177 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2178 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2179 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2180 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2181 |
0 setlinecap stroke grestore end
|
|
2182 |
|
|
2183 |
@endspecial
|
|
2184 |
1146 775 a Fm(1)1248 764 y Fp(lam)7 b Fo(\()p Fz(y)s(;)14
|
|
2185 |
b(P)1564 734 y Fq(0)1587 764 y Fo(\))24 b FC(and)f(is)-150
|
|
2186 |
863 y(a)d(direct)f(consequence)e(of)i(of)g Fz(P)12 b
|
|
2187 |
@beginspecial @setspecial
|
|
2188 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2189 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2190 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2191 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2192 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2193 |
0 setlinecap stroke grestore end
|
|
2194 |
|
|
2195 |
@endspecial 867 874 a Fm(1)969
|
|
2196 |
863 y Fz(P)1034 833 y Fq(0)1057 863 y FC(.)19 b(By)h(induction)e
|
|
2197 |
(hypothe-)-150 963 y(sis)j(one)f(has)361 1150 y Fz(P)12
|
|
2198 |
b Fo([)p Fz(x)23 b Fo(:=)g Fz(N)9 b Fo(])p @beginspecial
|
|
2199 |
@setspecial
|
|
2200 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2201 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2202 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2203 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2204 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2205 |
0 setlinecap stroke grestore end
|
|
2206 |
|
|
2207 |
@endspecial 793 1161 a Fm(1)895 1150 y Fz(P)j
|
|
2208 |
Fo([)p Fz(x)23 b Fo(:=)g Fz(N)1240 1116 y Fq(0)1263 1150
|
|
2209 |
y Fo(])g Fz(:)-150 1337 y FC(But)e(then)66 1524 y Fp(lam)7
|
|
2210 |
b Fo(\()p Fz(y)s(;)14 b(P)e Fo([)p Fz(x)23 b Fo(:=)g
|
|
2211 |
Fz(N)9 b Fo(]\))p @beginspecial @setspecial
|
|
2212 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2213 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2214 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2215 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2216 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2217 |
0 setlinecap stroke grestore end
|
|
2218 |
|
|
2219 |
@endspecial
|
|
2220 |
781 1535 a Fm(1)883 1524 y Fp(lam)e Fo(\()p Fz(y)s(;)14
|
|
2221 |
b(P)1199 1490 y Fq(0)1222 1524 y Fo([)p Fz(x)23 b Fo(:=)g
|
|
2222 |
Fz(N)1502 1490 y Fq(0)1525 1524 y Fo(]\))h Fz(;)-150
|
|
2223 |
1711 y FC(i.e.)c Fz(M)9 b Fo([)p Fz(x)23 b Fo(:=)g Fz(N)9
|
|
2224 |
b Fo(])p @beginspecial @setspecial
|
|
2225 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2226 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2227 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2228 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2229 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2230 |
0 setlinecap stroke grestore end
|
|
2231 |
|
|
2232 |
@endspecial 429 1722
|
|
2233 |
a Fm(1)531 1711 y Fz(M)621 1681 y Fq(0)644 1711 y Fo([)p
|
|
2234 |
Fz(x)23 b Fo(:=)g Fz(N)924 1681 y Fq(0)947 1711 y Fo(])p
|
|
2235 |
FC(.)-50 1810 y(The)c(last)j(step)e(in)g(this)h(case)g(only)e(w)o(orks)
|
|
2236 |
h(if)g(one)g(kno)n(ws)g(that)-9 1990 y Fp(lam)7 b Fo(\()p
|
|
2237 |
Fz(y)s(;)14 b(P)e Fo([)p Fz(x)24 b Fo(:=)e Fz(N)9 b Fo(]\))71
|
|
2238 |
b(=)23 b Fp(lam)7 b Fo(\()p Fz(y)s(;)14 b(P)e Fo(\)[)p
|
|
2239 |
Fz(x)23 b Fo(:=)g Fz(N)9 b Fo(])129 b FC(and)-9 2113
|
|
2240 |
y Fp(lam)7 b Fo(\()p Fz(y)s(;)14 b(P)307 2083 y Fq(0)330
|
|
2241 |
2113 y Fo([)p Fz(x)24 b Fo(:=)f Fz(N)611 2083 y Fq(0)634
|
|
2242 |
2113 y Fo(]\))h(=)f Fp(lam)7 b Fo(\()p Fz(y)s(;)14 b(P)1117
|
|
2243 |
2083 y Fq(0)1140 2113 y Fo(\)[)p Fz(x)23 b Fo(:=)g Fz(N)1452
|
|
2244 |
2083 y Fq(0)1475 2113 y Fo(])-150 2291 y FC(which)31
|
|
2245 |
b(only)g(holds)f(for)h Fz(y)k FC(being)30 b(not)i(equal)e(to)i
|
|
2246 |
Fz(x)g FC(and)f(not)h(free)-150 2390 y(in)37 b Fz(N)47
|
|
2247 |
b FC(and)36 b Fz(N)299 2360 y Fq(0)322 2390 y FC(.)h(If)g
|
|
2248 |
Fz(y)k FC(did)36 b(not)h(satisfy)g(these)h(constraints,)e(one)-150
|
|
2249 |
2490 y(w)o(ould)28 b(ha)n(v)o(e)h(to)g(rename)f(\002rst.)h(The)g
|
|
2250 |
(contrib)n(ution)e(of)i(this)g(paper)-150 2590 y(is)e(the)g(technique)d
|
|
2251 |
(allo)n(wing)i(the)g(deri)n(v)n(ation)e(of)i(a)h(rule)f(induction)-150
|
|
2252 |
2689 y(principle)j(for)g @beginspecial @setspecial
|
|
2253 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2254 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2255 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2256 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2257 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2258 |
0 setlinecap stroke grestore end
|
|
2259 |
|
|
2260 |
@endspecial
|
|
2261 |
367 2700 a Fm(1)500 2689 y FC(in)h(which)f(the)h(abo)o(v)o(e)e(case)j
|
|
2262 |
(can)f(be)f(pro)o(v)o(ed)-150 2789 y(under)j(the)i(assumption)f(that)h
|
|
2263 |
Fz(y)51 b Fv(6)p Fo(=)d Fz(x)35 b FC(and)e Fz(y)52 b
|
|
2264 |
Fv(62)c Fz(F)12 b(V)19 b Fo(\()p Fz(N)t(;)14 b(N)1766
|
|
2265 |
2759 y Fq(0)1789 2789 y Fo(\))p FC(.)-150 2889 y(This)34
|
|
2266 |
b(additional)e(assumption)h(allo)n(ws)h(one)f(to)h(reason)f(just)i(lik)
|
|
2267 |
o(e)-150 2988 y(Barendre)o(gt)18 b(in)j(a)f(rigorous,)f(mechanised)f
|
|
2268 |
(setting.)-50 3088 y(Our)32 b(technique)f(w)o(orks)h(for)g(relations)g
|
|
2269 |
(that)h(are)g(inducti)n(v)o(ely-)-150 3187 y(de\002ned)22
|
|
2270 |
b(by)g(a)h(set)h(of)e(rules.)h(Such)f(relations)g(come)g(with)h(a)g
|
|
2271 |
(notion)-150 3287 y(of)28 b(rule)g(induction,)e(which)h(can)h(be)g
|
|
2272 |
(used)g(to)g(pro)o(v)o(e)e(theorems)h(of)-150 3387 y(the)20
|
|
2273 |
b(form)225 3574 y Fz(R)q Fo(\()p Fz(M)402 3586 y Fu(1)439
|
|
2274 |
3574 y Fz(;)14 b(:)g(:)g(:)f(;)h(M)704 3586 y Ft(n)749
|
|
2275 |
3574 y Fo(\))23 b Fv(\))g Fz(P)12 b Fo(\()p Fz(M)1088
|
|
2276 |
3586 y Fu(1)1125 3574 y Fz(;)i(:)g(:)g(:)g(;)g(M)1391
|
|
2277 |
3586 y Ft(n)1435 3574 y Fo(\))-150 3761 y FC(with)k Fz(R)g
|
|
2278 |
FC(the)g(original)e(inducti)n(v)o(e)f(relation)i(on)g
|
|
2279 |
Fz(n)h FC(ar)o(guments,)d(and)i Fz(P)-150 3860 y FC(another)22
|
|
2280 |
b(relation,)g(which)h(is)h(sho)n(wn)e(to)i(be)f(a)g(superset)g(of)g
|
|
2281 |
Fz(R)q FC(.)g(The)-150 3960 y(property)g(we)i(need)g(for)f(deri)n(ving)
|
|
2282 |
g(our)g(rule)h(induction)e(principles)-150 4059 y(with)32
|
|
2283 |
b(a)g(b)n(uilt-in)f(form)g(of)g(the)h(v)n(ariable)e(con)m(v)o(ention)f
|
|
2284 |
(is)j(that)g(the)-150 4159 y(relation)19 b Fz(R)j FC(is)f
|
|
2285 |
Fx(equivariant)e FC([3)o(,)h(12)o(],)g(that)66 4346 y
|
|
2286 |
Fv(8)p Fz(\031)s(:)i(R)q Fo(\()p Fz(M)385 4358 y Fu(1)422
|
|
2287 |
4346 y Fz(;)14 b(:)g(:)g(:)g(;)g(M)688 4358 y Ft(n)732
|
|
2288 |
4346 y Fo(\))24 b Fv(\))f Fz(R)q Fo(\()p Fz(\031)1040
|
|
2289 |
4355 y Fj(\001)1078 4346 y Fz(M)1159 4358 y Fu(1)1196
|
|
2290 |
4346 y Fz(;)14 b(:)g(:)g(:)f(;)h(\031)1430 4355 y Fj(\001)1469
|
|
2291 |
4346 y Fz(M)1550 4358 y Ft(n)1595 4346 y Fo(\))-150 4533
|
|
2292 |
y FC(Equi)n(v)n(ariance)41 b(therefore)g(is)j(the)g(property)d(that)i
|
|
2293 |
(a)h(relation)e(is)-150 4633 y(preserv)o(ed)e(under)g(an)o(y)i
|
|
2294 |
(permutation)d Fz(\031)s FC(,)k(where)e(permutations)-150
|
|
2295 |
4732 y(are)36 b(\002nite)g(bijecti)n(v)o(e)f(mappings)f(from)h(atoms)h
|
|
2296 |
(to)g(atoms.)g(Beta-)-150 4832 y(reduction,)25 b(typing)h(and)h
|
|
2297 |
@beginspecial @setspecial
|
|
2298 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
2299 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
2300 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
2301 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
2302 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
2303 |
0 setlinecap stroke grestore end
|
|
2304 |
|
|
2305 |
@endspecial 665 4843 a Fm(1)794
|
|
2306 |
4832 y FC(are)h(instances)f(of)g(equi)n(v)n(ariant)e(re-)-150
|
|
2307 |
4932 y(lations.)35 b(So)h(too)f(are)h(the)g(reduction)d(and)i(typing)g
|
|
2308 |
(relations)g(for)-150 5031 y(systems)24 b(such)f(as)h(the)f
|
|
2309 |
(polymorphic)d Fz(\025)p FC(-calculus.)i(In)h(f)o(act,)g(equi)n(v-)-150
|
|
2310 |
5131 y(ariance)36 b(is)h(v)o(ery)e(common.)f(Its)j(absence)f(w)o(ould)g
|
|
2311 |
(imply)f(that)i(a)-150 5230 y(particular)26 b(relation)h(didn')o(t)f
|
|
2312 |
(beha)n(v)o(e)g(uniformly)f(o)o(v)o(er)h(choices)h(of)-150
|
|
2313 |
5330 y(the)20 b(names)g(\(atoms\))f(used)h(as)h(v)n(ariables.)-50
|
|
2314 |
5430 y(Our)e(technique)g(applies)h(to)g(all)h(equi)n(v)n(ariant)d
|
|
2315 |
(relations.)p 0 TeXcolorgray 0 TeXcolorgray 2141 66 a(This)31
|
|
2316 |
b(paper)e(is)i(or)o(ganised)d(as)j(follo)n(ws:)f(Sec.)g(2)h(gi)n(v)o
|
|
2317 |
(es)e(a)i(v)o(ery)2042 166 y(brief)36 b(o)o(v)o(ervie)n(w)f(about)g
|
|
2318 |
(the)i(nominal)f(logic)g(w)o(ork.)g(Proofs)g(are)2042
|
|
2319 |
266 y(omitted,)17 b(b)n(ut)h(can)f(be)h(found)e(in)i([3)o(,)g(12)o(,)h
|
|
2320 |
(14)o(].)e(Sec.)h(3)g(illustrates)h(our)2042 365 y(technique)h(by)h
|
|
2321 |
(deri)n(ving)g(impro)o(v)o(ed)e(principles)i(of)g(rule)h(induction)2042
|
|
2322 |
465 y(for)39 b(tw)o(o)h(standard)e(relations)h(from)g(the)h
|
|
2323 |
(literature.)e(The)i(ease-)2042 565 y(of-use)33 b(of)h(the)g(ne)n(w)g
|
|
2324 |
(principles)f(is)i(also)f(demonstrated.)e(Sec.)i(4)2042
|
|
2325 |
664 y(mentions)19 b(some)h(related)g(w)o(ork)f(and)h(Sec.)g(5)g
|
|
2326 |
(concludes.)2042 851 y FA(2.)99 b(Nominal)24 b(Logic)2042
|
|
2327 |
984 y FC(There)16 b(are)i(tw)o(o)f(central)g(notions)g(in)g(nominal)g
|
|
2328 |
(logic:)g(permutations)2042 1083 y(and)25 b(support.)g(As)i(mentioned)d
|
|
2329 |
(in)j(the)f(pre)n(vious)f(section,)h(permu-)2042 1183
|
|
2330 |
y(tations)k(are)h(\002nite)g(bijecti)n(v)o(e)f(mappings)f(from)h(atoms)
|
|
2331 |
g(to)h(atoms,)2042 1283 y(where)17 b(atoms)h(are)g(dra)o(wn)f(from)g(a)
|
|
2332 |
i(countably)d(in\002nite)i(set)g(denoted)2042 1382 y(by)29
|
|
2333 |
b Fi(A)17 b FC(.)36 b(W)-7 b(e)31 b(represent)d(permutations)g(as)j
|
|
2334 |
(\002nite)e(lists)j(whose)d(ele-)2042 1482 y(ments)k(are)g(sw)o
|
|
2335 |
(appings)g(\(i.e.)g(pairs)g(of)g(atoms\).)g(W)-7 b(e)35
|
|
2336 |
b(write)e(such)2042 1581 y(permutations)26 b(as)j Fo(\()p
|
|
2337 |
Fz(a)2678 1593 y Fu(1)2729 1581 y Fz(b)2765 1593 y Fu(1)2802
|
|
2338 |
1581 y Fo(\)\()p Fz(a)2910 1593 y Fu(2)2962 1581 y Fz(b)2998
|
|
2339 |
1593 y Fu(2)3034 1581 y Fo(\))14 b Fv(\001)g(\001)g(\001)g
|
|
2340 |
Fo(\()p Fz(a)3267 1593 y Ft(n)3327 1581 y Fz(b)3363 1593
|
|
2341 |
y Ft(n)3407 1581 y Fo(\))p FC(;)29 b(the)g(empty)e(list)i
|
|
2342 |
Fo([])2042 1681 y FC(stands)23 b(for)g(the)h(identity)e(permutation.)f
|
|
2343 |
(A)j(permutation)d Fz(\031)28 b Fx(acting)2042 1781 y
|
|
2344 |
FC(on)20 b(an)g(atom)f Fz(a)i FC(is)g(de\002ned)e(as:)2665
|
|
2345 |
1932 y Fo([])2711 1941 y Fj(\001)2749 1932 y Fz(a)2876
|
|
2346 |
1885 y Fs(def)2881 1932 y Fo(=)87 b Fz(a)2263 2133 y
|
|
2347 |
Fo(\(\()p Fz(a)2371 2145 y Fu(1)2422 2133 y Fz(a)2466
|
|
2348 |
2145 y Fu(2)2504 2133 y Fo(\))23 b(::)g Fz(\031)s Fo(\))2710
|
|
2349 |
2142 y Fj(\001)2749 2133 y Fz(a)2876 2086 y Fs(def)2881
|
|
2350 |
2133 y Fo(=)3033 1962 y Fh(8)3033 2037 y(<)3033 2187
|
|
2351 |
y(:)3148 2032 y Fz(a)3192 2044 y Fu(2)3364 2032 y FC(if)g
|
|
2352 |
Fz(\031)3488 2041 y Fj(\001)3526 2032 y Fz(a)g Fo(=)g
|
|
2353 |
Fz(a)3725 2044 y Fu(1)3148 2132 y Fz(a)3192 2144 y Fu(1)3364
|
|
2354 |
2132 y FC(if)g Fz(\031)3488 2141 y Fj(\001)3526 2132
|
|
2355 |
y Fz(a)g Fo(=)g Fz(a)3725 2144 y Fu(2)3148 2231 y Fz(\031)3198
|
|
2356 |
2240 y Fj(\001)3237 2231 y Fz(a)83 b FC(otherwise)2042
|
|
2357 |
2379 y(where)30 b Fo(\()p Fz(a)14 b(b)p Fo(\))44 b(::)f
|
|
2358 |
Fz(\031)35 b FC(is)d(the)g(composition)d(of)i(a)g(permutation)e(fol-)
|
|
2359 |
2042 2479 y(lo)n(wed)16 b(by)h(the)g(sw)o(apping)f Fo(\()p
|
|
2360 |
Fz(a)e(b)p Fo(\))p FC(.)j(The)g(composition)e(of)i Fz(\031)k
|
|
2361 |
FC(follo)n(wed)2042 2579 y(by)35 b(another)g(permutation)e
|
|
2362 |
Fz(\031)2934 2548 y Fq(0)2994 2579 y FC(is)k(gi)n(v)o(en)e(by)g
|
|
2363 |
(list-concatenation,)2042 2678 y(written)27 b(as)h Fz(\031)2452
|
|
2364 |
2648 y Fq(0)2475 2678 y Fo(@)p Fz(\031)s FC(,)g(and)f(the)g(in)m(v)o
|
|
2365 |
(erse)f(of)h(a)h(permutation)d(is)j(gi)n(v)o(en)2042
|
|
2366 |
2778 y(by)g(list)i(re)n(v)o(ersal,)d(written)h(as)i Fz(\031)3007
|
|
2367 |
2748 y Fq(\000)p Fu(1)3096 2778 y FC(.)f(Our)f(representation)f(of)h
|
|
2368 |
(per)n(-)2042 2877 y(mutations)e(as)i(lists)h(does)e(not)g(gi)n(v)o(e)g
|
|
2369 |
(unique)f(representati)n(v)o(es:)g(for)2042 2977 y(e)o(xample,)16
|
|
2370 |
b(the)h(permutation)e Fo(\()p Fz(a)f(a)p Fo(\))19 b FC(is)f
|
|
2371 |
(\223equal\224)e(to)i(the)g(identity)e(per)n(-)2042 3077
|
|
2372 |
y(mutation.)2141 3176 y(W)-7 b(e)40 b(equate)f(the)g(representations)e
|
|
2373 |
(of)h(permutations)f(with)i(a)2042 3276 y(relation)19
|
|
2374 |
b Fv(\030)p FC(:)p 0 TeXcolorgray 2042 3414 a Fn(De\002nition)j(1)g
|
|
2375 |
FC(\(Permutation)e(Equality\))p Fn(.)p 0 TeXcolorgray
|
|
2376 |
40 w Fx(T)-6 b(wo)22 b(permutations)f(ar)m(e)2042 3514
|
|
2377 |
y FC(equal)p Fx(,)33 b(written)i Fz(\031)2594 3526 y
|
|
2378 |
Fu(1)2680 3514 y Fv(\030)48 b Fz(\031)2840 3526 y Fu(2)2877
|
|
2379 |
3514 y Fx(,)35 b(pr)l(o)o(vided)e Fz(\031)3305 3526 y
|
|
2380 |
Fu(1)3342 3523 y Fj(\001)3381 3514 y Fz(x)49 b Fo(=)f
|
|
2381 |
Fz(\031)3637 3526 y Fu(2)3674 3523 y Fj(\001)3713 3514
|
|
2382 |
y Fz(x)p Fx(,)34 b(for)h(all)2042 3613 y Fz(x)23 b Fv(2)h
|
|
2383 |
Fi(A)17 b Fx(.)2141 3751 y FC(The)27 b(action)f(of)h(a)g(permutation)e
|
|
2384 |
(can)h(be)h(lifted)g(to)g(other)f(types)2042 3851 y(as)c(long)e(as)i
|
|
2385 |
(the)f(action)f(on)h(the)g(ne)n(w)g(type)f(is)i Fx(sensible)p
|
|
2386 |
FC(.)f(By)h(this)g(we)2042 3950 y(mean)d(that)i(it)g(has)f(to)g
|
|
2387 |
(satisfy)h(the)f(follo)n(wing)f(three)g(properties:)p
|
|
2388 |
0 TeXcolorgray 0 TeXcolorgray 2477 4081 a Fo(\()p Fz(i)p
|
|
2389 |
Fo(\))100 b([])2716 4090 y Fj(\001)2754 4081 y Fz(x)23
|
|
2390 |
b Fo(=)g Fz(x)2448 4204 y Fo(\()p Fz(ii)p Fo(\))100 b(\()p
|
|
2391 |
Fz(\031)2749 4216 y Fu(1)2786 4204 y Fo(@)p Fz(\031)2898
|
|
2392 |
4216 y Fu(2)2936 4204 y Fo(\))2968 4213 y Fj(\001)3006
|
|
2393 |
4204 y Fz(x)24 b Fo(=)e Fz(\031)3211 4216 y Fu(1)3249
|
|
2394 |
4213 y Fj(\001)3287 4204 y Fo(\()p Fz(\031)3366 4216
|
|
2395 |
y Fu(2)3404 4213 y Fj(\001)3442 4204 y Fz(x)p Fo(\))2420
|
|
2396 |
4327 y(\()p Fz(iii)p Fo(\))99 b FC(if)20 b Fz(\031)2788
|
|
2397 |
4339 y Fu(1)2849 4327 y Fv(\030)i Fz(\031)2983 4339 y
|
|
2398 |
Fu(2)3042 4327 y FC(then)d Fz(\031)3252 4339 y Fu(1)3290
|
|
2399 |
4336 y Fj(\001)3328 4327 y Fz(x)24 b Fo(=)e Fz(\031)3533
|
|
2400 |
4339 y Fu(2)3571 4336 y Fj(\001)3609 4327 y Fz(x)2042
|
|
2401 |
4456 y FC(From)g(this)h(we)g(can)g(de\002ne)f(\223permutation)e
|
|
2402 |
(sets\224)k(as)f(those)g(ha)n(ving)2042 4556 y(a)d(sensible)h
|
|
2403 |
(permutation)d(action:)p 0 TeXcolorgray 2042 4694 a Fn(De\002nition)k
|
|
2404 |
(2)h FC(\(PSets\))p Fn(.)p 0 TeXcolorgray 42 w Fx(A)g(set)g
|
|
2405 |
Fz(X)30 b Fx(equipped)20 b(with)j(a)f(permutation)2042
|
|
2406 |
4794 y(action)32 b Fz(\031)2333 4803 y Fj(\001)2372 4794
|
|
2407 |
y Fo(\()p Fv(\000)p Fo(\))i Fx(is)g(said)g(to)f(be)h(a)f(pset,)h(if)g
|
|
2408 |
(for)g(all)g Fz(x)48 b Fv(2)g Fz(X)7 b Fx(,)33 b(the)2042
|
|
2409 |
4893 y(permutation)18 b(action)i(satis\002es)g(the)h(pr)l(operties)f
|
|
2410 |
Fo(\()p Fz(i)p Fo(\))p Fx(-)p Fo(\()p Fz(iii)p Fo(\))p
|
|
2411 |
Fx(.)2141 5031 y FC(The)f(informal)e(notation)g Fz(x)23
|
|
2412 |
b Fv(2)h Fx(pset)18 b FC(will)i(be)e(adopted)f(whene)n(v)o(er)2042
|
|
2413 |
5131 y(it)f(needs)f(to)h(be)g(indicated)e(that)i Fz(x)h
|
|
2414 |
FC(comes)e(from)f(a)i Fx(pset)p FC(.)g(T)-7 b(ypical)15
|
|
2415 |
b(per)n(-)2042 5230 y(mutation)21 b(actions)g(permute)g(all)i(atoms)f
|
|
2416 |
(in)g(a)h(gi)n(v)o(en)d Fx(pset)p FC(-element.)2042 5330
|
|
2417 |
y(F)o(or)c(e)o(xample,)e(lists,)j(tuples)g(and)e(sets)j(can)e(be)g
|
|
2418 |
(seen)g(as)h Fx(pset)p FC(s)g(if)f(their)2042 5430 y(respecti)n(v)o(e)j
|
|
2419 |
(permutation)f(actions)i(are)g(de\002ned)f(point-wise:)p
|
|
2420 |
0 TeXcolorgray 0 TeXcolorgray eop end
|
|
2421 |
%%Page: 4 4
|
|
2422 |
TeXDict begin 4 3 bop 0 TeXcolorgray 0 TeXcolorgray 0
|
|
2423 |
TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 57 95 a FC(lists:)516
|
|
2424 |
b Fz(\031)779 104 y Fj(\001)818 95 y Fo([])911 48 y Fs(def)916
|
|
2425 |
95 y Fo(=)52 b([])541 220 y Fz(\031)591 229 y Fj(\001)630
|
|
2426 |
220 y Fo(\()p Fz(x)23 b Fo(::)h Fz(t)p Fo(\))911 173
|
|
2427 |
y Fs(def)916 220 y Fo(=)52 b(\()p Fz(\031)1115 229 y
|
|
2428 |
Fj(\001)1153 220 y Fz(x)p Fo(\))24 b(::)f(\()p Fz(\031)1407
|
|
2429 |
229 y Fj(\001)1446 220 y Fz(t)p Fo(\))57 345 y FC(tuples:)70
|
|
2430 |
b Fz(\031)399 354 y Fj(\001)437 345 y Fo(\()p Fz(x)516
|
|
2431 |
357 y Fu(1)554 345 y Fz(;)14 b(:)g(:)g(:)g(;)g(x)786
|
|
2432 |
357 y Ft(n)832 345 y Fo(\))911 298 y Fs(def)916 345 y
|
|
2433 |
Fo(=)52 b(\()p Fz(\031)1115 354 y Fj(\001)1153 345 y
|
|
2434 |
Fz(x)1200 357 y Fu(1)1238 345 y Fz(;)14 b(:)g(:)g(:)g(;)g(\031)1473
|
|
2435 |
354 y Fj(\001)1511 345 y Fz(x)1558 357 y Ft(n)1604 345
|
|
2436 |
y Fo(\))57 470 y FC(sets:)496 b Fz(\031)750 479 y Fj(\001)789
|
|
2437 |
470 y Fz(X)911 423 y Fs(def)916 470 y Fo(=)52 b Fv(f)p
|
|
2438 |
Fz(\031)1125 479 y Fj(\001)1163 470 y Fz(x)14 b Fv(j)g
|
|
2439 |
Fz(x)23 b Fv(2)h Fz(X)7 b Fv(g)-150 602 y FC(On)16 b
|
|
2440 |
Fz(\013)p FC(-equated)f Fz(\025)p FC(-terms)h(the)h(permutation)d
|
|
2441 |
(action)h(is)i(de\002ned)e(such)-150 701 y(that)20 b(it)h(satis\002es:)
|
|
2442 |
401 847 y Fz(\031)451 856 y Fj(\001)489 847 y Fp(var)10
|
|
2443 |
b Fo(\()p Fz(a)p Fo(\))48 b(=)f Fp(var)9 b Fo(\()p Fz(\031)1088
|
|
2444 |
856 y Fj(\001)1127 847 y Fz(a)p Fo(\))164 970 y Fz(\031)214
|
|
2445 |
979 y Fj(\001)253 970 y Fp(app)d Fo(\()p Fz(M)498 982
|
|
2446 |
y Fu(1)536 970 y Fz(;)14 b(M)654 982 y Fu(2)690 970 y
|
|
2447 |
Fo(\))48 b(=)f Fp(app)6 b Fo(\()p Fz(\031)1096 979 y
|
|
2448 |
Fj(\001)1135 970 y Fz(M)1216 982 y Fu(1)1253 970 y Fz(;)14
|
|
2449 |
b(\031)1340 979 y Fj(\001)1378 970 y Fz(M)1459 982 y
|
|
2450 |
Fu(2)1496 970 y Fo(\))261 1094 y Fz(\031)311 1103 y Fj(\001)350
|
|
2451 |
1094 y Fp(lam)7 b Fo(\()p Fz(a;)14 b(M)9 b Fo(\))47 b(=)g
|
|
2452 |
Fp(lam)6 b Fo(\()p Fz(\031)1101 1103 y Fj(\001)1140 1094
|
|
2453 |
y Fz(a;)14 b(\031)1271 1103 y Fj(\001)1310 1094 y Fz(M)9
|
|
2454 |
b Fo(\))1746 971 y FC(\(4\))-150 1255 y(W)-7 b(e)21 b(note)f(the)g
|
|
2455 |
(follo)n(wing:)p 0 TeXcolorgray -150 1395 a Fn(Lemma)32
|
|
2456 |
b(1.)p 0 TeXcolorgray 48 w FC(The)f(follo)n(wing)f(sets)j(are)e
|
|
2457 |
Fx(pset)p FC(s:)h Fi(A)17 b FC(,)38 b(the)31 b(set)h(of)f
|
|
2458 |
Fz(\013)p FC(-)-150 1495 y(equated)16 b(lambda-terms,)e(and)j(e)n(v)o
|
|
2459 |
(ery)e(set)j(of)f(lists)h(\(similarly)e(tuples)-150 1595
|
|
2460 |
y(and)k(sets\))h(containing)d(elements)i(from)f Fx(pset)p
|
|
2461 |
FC(s.)-50 1735 y(One)k(interesting)g(consequence)f(of)i(nominal)e
|
|
2462 |
(logic)i([3)o(])g(is)h(that)-150 1834 y(as)j(soon)e(as)h(one)g(\002x)o
|
|
2463 |
(es)g(the)f(notion)g(of)h(permutation)d(action)i(for)h(a)-150
|
|
2464 |
1934 y Fx(pset)p FC(,)17 b(then)f(the)h(notion)e(of)h(support,)f(v)o
|
|
2465 |
(ery)h(roughly)e(speaking)i(its)h(set)-150 2033 y(of)24
|
|
2466 |
b(free)h(atoms,)f(is)h(\002x)o(ed)f(as)i(well.)f(The)f(support)f(and)h
|
|
2467 |
(the)h(deri)n(v)o(ed)-150 2133 y(notion)19 b(of)h(freshness)g(is)h
|
|
2468 |
(de\002ned)e(as)i(follo)n(ws:)p 0 TeXcolorgray -150 2273
|
|
2469 |
a Fn(De\002nition)27 b(3)g FC(\(Support)e(and)h(Freshness\))p
|
|
2470 |
Fn(.)p 0 TeXcolorgray 45 w Fx(Given)g Fz(x)36 b Fv(2)f
|
|
2471 |
Fx(pset,)27 b(its)-150 2373 y FC(support)19 b Fx(is)i(de\002ned)d(as:)
|
|
2472 |
54 2566 y Fg(supp)o Fo(\()p Fz(x)p Fo(\))364 2514 y Ff(def)367
|
|
2473 |
2566 y Fo(=)26 b Fv(f)p Fz(a)c Fv(j)h Fg(infinite)m Fv(f)p
|
|
2474 |
Fz(b)f Fv(j)h Fo(\()p Fz(a)14 b(b)p Fo(\))1265 2575 y
|
|
2475 |
Fj(\001)1304 2566 y Fz(x)23 b Fv(6)p Fo(=)g Fz(x)p Fv(gg)f
|
|
2476 |
Fz(:)-150 2736 y Fx(An)h(atom)h Fz(a)g Fx(is)g(said)g(to)f(be)h
|
|
2477 |
FC(fresh)f Fx(for)h(suc)o(h)f(an)g Fz(x)p Fx(,)h(written)h
|
|
2478 |
Fz(a)k Fo(#)g Fz(x)p Fx(,)-150 2836 y(pr)l(o)o(vided)19
|
|
2479 |
b Fz(a)k Fv(62)h Fg(supp)n Fo(\()p Fz(x)p Fo(\))p Fx(.)-150
|
|
2480 |
2976 y FC(W)m(ith)d(these)g(notions)f(in)h(place)f(we)i(can)e(mak)o(e)h
|
|
2481 |
(the)f(equation)g(in)h(\(1\))-150 3076 y(precise,)f(stating)g(when)f
|
|
2482 |
(tw)o(o)i Fz(\013)p FC(-equated)e(abstractions)g(are)h(equal:)190
|
|
2483 |
3238 y Fp(lam)7 b Fo(\()p Fz(a;)14 b(M)9 b Fo(\))23 b(=)g
|
|
2484 |
Fp(lam)7 b Fo(\()p Fz(b;)14 b(N)9 b Fo(\))22 b Fv(,)356
|
|
2485 |
3350 y Fo(\()p Fz(a)h Fo(=)g Fz(b)18 b Fv(^)h Fz(M)31
|
|
2486 |
b Fo(=)23 b Fz(N)9 b Fo(\))23 b Fv(_)356 3450 y Fo(\()p
|
|
2487 |
Fz(a)g Fv(6)p Fo(=)g Fz(b)18 b Fv(^)h Fz(M)31 b Fo(=)23
|
|
2488 |
b(\()p Fz(a)14 b(b)p Fo(\))1029 3459 y Fj(\001)1067 3450
|
|
2489 |
y Fz(N)27 b Fv(^)19 b Fz(a)k Fo(#)g Fz(N)9 b Fo(\))1746
|
|
2490 |
3345 y FC(\(5\))-150 3611 y(In)22 b(what)g(follo)n(ws)g(we)g(will)h
|
|
2491 |
(often)e(mak)o(e)h(use)g(the)g(follo)n(wing)f(prop-)-150
|
|
2492 |
3711 y(erties)g(of)e Fx(pset)p FC(s:)p 0 TeXcolorgray
|
|
2493 |
-150 3851 a Fn(Lemma)i(2.)p 0 TeXcolorgray 41 w FC(F)o(or)e(all)i
|
|
2494 |
Fz(x)j Fv(2)f Fx(pset)p FC(,)57 3942 y Fo(\()p Fz(i)p
|
|
2495 |
Fo(\))99 b Fz(a)23 b Fo(#)h Fz(x)d FC(implies)f Fz(\031)792
|
|
2496 |
3951 y Fj(\001)831 3942 y Fz(a)j Fo(#)g Fz(\031)1040
|
|
2497 |
3951 y Fj(\001)1078 3942 y Fz(x)28 4042 y Fo(\()p Fz(ii)p
|
|
2498 |
Fo(\))99 b FC(if)21 b Fz(a)i Fo(#)g Fz(x)e FC(and)f Fz(b)j
|
|
2499 |
Fo(#)g Fz(x)p FC(,)e(then)f Fo(\()p Fz(a)14 b(b)p Fo(\))1251
|
|
2500 |
4051 y Fj(\001)1289 4042 y Fz(x)23 b Fo(=)g Fz(x)-1 4141
|
|
2501 |
y Fo(\()p Fz(iii)p Fo(\))99 b Fz(a)23 b Fo(#)h(\()p Fz(x;)14
|
|
2502 |
b(y)s Fo(\))21 b FC(if)f(and)g(only)f(if)i Fz(a)i Fo(#)g
|
|
2503 |
Fz(x)e FC(and)f Fz(a)j Fo(#)g Fz(y)-50 4272 y FC(A)f(further)f
|
|
2504 |
(restriction)g(on)h Fx(pset)p FC(s)h(\002lters)g(out)f(all)h
|
|
2505 |
Fx(pset)o FC(s)g(contain-)-150 4372 y(ing)d(elements)g(with)g
|
|
2506 |
(in\002nite)g(support:)p 0 TeXcolorgray -150 4512 a Fn(De\002nition)g
|
|
2507 |
(4)f FC(\(Finitely)h(Supported)d(PSets\))p Fn(.)p 0 TeXcolorgray
|
|
2508 |
41 w Fx(A)i(pset)h Fz(X)27 b Fx(is)20 b(said)g(to)-150
|
|
2509 |
4611 y(be)g(an)g(fs-pset)g(if)h(e)o(very)g(element)f(in)g
|
|
2510 |
Fz(X)27 b Fx(has)20 b(\002nite)g(support.)-50 4751 y
|
|
2511 |
FC(W)-7 b(e)21 b(note)f(the)g(follo)n(wing:)p 0 TeXcolorgray
|
|
2512 |
-150 4891 a Fn(Lemma)25 b(3.)p 0 TeXcolorgray 43 w Fx(The)f(following)g
|
|
2513 |
(sets)h(ar)m(e)f(fs-psets:)h Fi(A)17 b Fx(,)30 b(the)24
|
|
2514 |
b(set)h(of)f Fz(\013)p Fx(-)-150 4991 y(equated)d Fz(\025)p
|
|
2515 |
Fx(-terms,)j(and)d(e)o(very)i(set)h(of)e(lists)i(\(similarly)f(tuples)g
|
|
2516 |
(and)-150 5090 y(\002nite)d(sets\))h(containing)d(elements)i(fr)l(om)h
|
|
2517 |
(fs-psets.)-50 5230 y FC(Since)28 b(the)h(set)g(of)f(atoms)g
|
|
2518 |
Fi(A)52 b FC(is)30 b(in\002nite,)e(the)g(most)h(important)-150
|
|
2519 |
5330 y(property)21 b(of)i Fx(fs-pset)o FC(s)h(is)g(that)f(for)g(each)f
|
|
2520 |
(element)h(one)f(can)h(choose)-150 5430 y(a)e(fresh)e(atom.)p
|
|
2521 |
0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 2042 66
|
|
2522 |
a Fn(Lemma)24 b(4.)p 0 TeXcolorgray 43 w Fx(F)-9 b(or)24
|
|
2523 |
b(all)g Fz(x)30 b Fv(2)g Fx(fs-pset)o(,)24 b(ther)m(e)g(e)n(xists)h(an)
|
|
2524 |
e(atom)g Fz(a)h Fx(suc)o(h)2042 166 y(that)c Fz(a)j Fo(#)g
|
|
2525 |
Fz(x)p Fx(.)2141 323 y FC(Unwinding)34 b(the)h(de\002nitions)f(for)h
|
|
2526 |
(permutation)e(actions)h(and)2042 423 y(support)15 b(one)i(can)f(often)
|
|
2527 |
g(easily)i(calculate)e(the)h(support)f(for)g Fx(fs-pset)p
|
|
2528 |
FC(-)2042 523 y(elements:)p 0 TeXcolorgray 0 TeXcolorgray
|
|
2529 |
2042 754 a(atoms:)216 b Fg(supp)o Fo(\()p Fz(a)p Fo(\))23
|
|
2530 |
b(=)g Fv(f)p Fz(a)p Fv(g)2042 877 y FC(tuples:)216 b
|
|
2531 |
Fg(supp)o Fo(\()p Fz(x)2734 889 y Fu(1)2772 877 y Fz(;)14
|
|
2532 |
b(:)g(:)g(:)f(;)h(x)3003 889 y Ft(n)3049 877 y Fo(\))23
|
|
2533 |
b(=)g Fg(supp)n Fo(\()p Fz(x)3445 889 y Fu(1)3483 877
|
|
2534 |
y Fo(\))c Fv([)g Fz(:)14 b(:)g(:)k Fv([)h Fg(supp)n Fo(\()p
|
|
2535 |
Fz(x)4050 889 y Ft(n)4096 877 y Fo(\))2042 1000 y FC(lists:)282
|
|
2536 |
b Fg(supp)o Fo(\([]\))24 b(=)e Fi(?)2480 1100 y Fg(supp)o
|
|
2537 |
Fo(\()p Fz(x)i Fo(::)f Fz(xs)p Fo(\))h(=)e Fg(supp)n
|
|
2538 |
Fo(\()p Fz(x)p Fo(\))e Fv([)f Fg(supp)n Fo(\()p Fz(xs)p
|
|
2539 |
Fo(\))2042 1223 y FC(\002nite)h(sets:)100 b Fg(supp)o
|
|
2540 |
Fo(\()p Fz(X)7 b Fo(\))23 b(=)2905 1161 y Fh(S)2975 1248
|
|
2541 |
y Ft(x)p Fq(2)p Ft(X)3134 1223 y Fg(supp)n Fo(\()p Fz(x)p
|
|
2542 |
Fo(\))2042 1346 y Fz(\013)p FC(-equated)c(lambda-terms:)2480
|
|
2543 |
1470 y Fg(supp)o Fo(\()p Fp(var)10 b Fo(\()p Fz(a)p Fo(\)\))23
|
|
2544 |
b(=)g Fv(f)p Fz(a)p Fv(g)2480 1569 y Fg(supp)o Fo(\()p
|
|
2545 |
Fp(app)7 b Fo(\()p Fz(M)t(;)14 b(N)9 b Fo(\)\))23 b(=)g
|
|
2546 |
Fg(supp)n Fo(\()p Fz(M)9 b Fo(\))19 b Fv([)g Fg(supp)n
|
|
2547 |
Fo(\()p Fz(N)9 b Fo(\))2480 1669 y Fg(supp)o Fo(\()p
|
|
2548 |
Fp(lam)e Fo(\()p Fz(a;)14 b(M)9 b Fo(\)\))23 b(=)g Fg(supp)n
|
|
2549 |
Fo(\()p Fz(M)9 b Fo(\))19 b Fv(\000)f(f)p Fz(a)p Fv(g)2141
|
|
2550 |
1817 y FC(The)40 b(last)h(three)f(equations)f(sho)n(w)g(that)i(the)f
|
|
2551 |
(support)e(of)i Fz(\013)p FC(-)2042 1917 y(equated)35
|
|
2552 |
b(lambda-terms)f(coincides)i(with)g(the)h(usual)f(notion)f(of)2042
|
|
2553 |
2017 y(free)23 b(v)n(ariables.)g(In)h(turn,)f Fz(a)29
|
|
2554 |
b Fo(#)h Fz(M)j FC(with)24 b Fz(M)33 b FC(being)23 b(an)h
|
|
2555 |
Fz(\013)p FC(-equated)2042 2116 y(lambda-term)17 b(coincides)i(with)h
|
|
2556 |
Fz(a)g FC(not)g(being)f(free)g(in)h Fz(M)9 b FC(.)20
|
|
2557 |
b(If)f Fz(b)h FC(is)h(an)2042 2216 y(atom,)e(then)h Fz(a)j
|
|
2558 |
Fo(#)g Fz(b)e FC(coincides)e(with)h Fz(a)j Fv(6)p Fo(=)g
|
|
2559 |
Fz(b)p FC(.)2042 2464 y FA(3.)99 b(Rule)25 b(Inductions)2042
|
|
2560 |
2597 y FC(Inductions)40 b(o)o(v)o(er)i(inducti)n(v)o(ely-de\002ned)c
|
|
2561 |
(relations,)k(also)h(called)2042 2696 y(rule)f(inductions,)f(are)i
|
|
2562 |
(important)e(reasoning)g(tools)i(in)g(the)f Fz(\025)p
|
|
2563 |
FC(-)2042 2796 y(calculus)26 b(and)g(programming)d(languages)h([1].)i
|
|
2564 |
(Here)g(we)h(pro)o(vide)2042 2895 y(tw)o(o)18 b(small,)g(b)n(ut)g
|
|
2565 |
(typical,)g(e)o(xamples)f(of)h(such)f(rule)h(inductions,)e(and)2042
|
|
2566 |
2995 y(illustrate)k(our)g(technique)e(on)i(both.)2042
|
|
2567 |
3194 y Fn(3.1)82 b(W)-5 b(eak)o(ening)19 b(f)n(or)h(Simple)h(T)-6
|
|
2568 |
b(ypes)2042 3326 y FC(T)g(erms)26 b(of)g(the)h Fz(\025)p
|
|
2569 |
FC(-calculus)f(can)g(be)h(gi)n(v)o(en)e(types)h(with)h(respect)f(to)
|
|
2570 |
2042 3426 y(conte)o(xts)c(\(for)h(e)o(xample)f(\002nite)h(sets)i(of)e
|
|
2571 |
(name-type)e(pairs\).)i(T)-7 b(ypes)2042 3526 y(are)20
|
|
2572 |
b(of)g(the)g(form)2618 3741 y Fp(ty)30 b Fo(:)106 b Fz(\034)56
|
|
2573 |
b Fo(::=)46 b Fz(X)29 b Fv(j)23 b Fz(\034)33 b Fv(!)23
|
|
2574 |
b Fz(\034)2042 3956 y FC(Conte)o(xts)d(are)g Fx(valid)i
|
|
2575 |
FC(if)e(no)g(v)n(ariable)f(occurs)g(twice:)p 2548 4180
|
|
2576 |
308 4 v 2548 4259 a Fp(valid)11 b Fo(\()p Fi(?)p Fo(\))2939
|
|
2577 |
4139 y Fz(a)23 b Fo(#)g(\000)83 b Fp(valid)10 b Fo(\(\000\))p
|
|
2578 |
2939 4180 589 4 v 2990 4259 a Fp(valid)h Fo(\()p Fz(a)23
|
|
2579 |
b Fo(:)g Fz(\034)5 b(;)14 b Fo(\000\))2042 4465 y FC(The)27
|
|
2580 |
b(relation)f(associating)h(terms)g(and)g(types)g(is)h(straightforw)o
|
|
2581 |
(ard)2042 4564 y(to)20 b(de\002ne:)2198 4747 y Fp(valid)10
|
|
2582 |
b Fo(\(\000\))84 b(\()p Fz(a)23 b Fo(:)g Fz(\034)9 b
|
|
2583 |
Fo(\))24 b Fv(2)f Fo(\000)p 2198 4788 755 4 v 2327 4867
|
|
2584 |
a(\000)g Fv(`)f Fp(var)10 b Fo(\()p Fz(a)p Fo(\))23 b(:)h
|
|
2585 |
Fz(\034)3035 4752 y(a)f Fo(#)g(\000)83 b Fz(a)23 b Fo(:)g
|
|
2586 |
Fz(\034)5 b(;)14 b Fo(\000)23 b Fv(`)g Fz(M)32 b Fo(:)23
|
|
2587 |
b Fz(\033)p 3035 4788 844 4 v 3049 4867 a Fo(\000)g Fv(`)g
|
|
2588 |
Fp(lam)6 b Fo(\()p Fz(a;)14 b(M)9 b Fo(\))23 b(:)h Fz(\034)32
|
|
2589 |
b Fv(!)23 b Fz(\033)2560 5025 y Fo(\000)g Fv(`)g Fz(M)32
|
|
2590 |
b Fo(:)23 b Fz(\034)33 b Fv(!)23 b Fz(\033)86 b Fo(\000)23
|
|
2591 |
b Fv(`)g Fz(N)32 b Fo(:)23 b Fz(\034)p 2560 5045 956
|
|
2592 |
4 v 2706 5124 a Fo(\000)g Fv(`)g Fp(app)7 b Fo(\()p Fz(M)t(;)14
|
|
2593 |
b(N)9 b Fo(\))23 b(:)g Fz(\033)2042 5330 y FC(Making)34
|
|
2594 |
b(such)h(a)h(de\002nition)e(also)i(results)g(in)f(the)h(proof)e(of)h
|
|
2595 |
(the)2042 5430 y(associated)20 b(induction)f(principle,)g(with)i
|
|
2596 |
Fz(P)33 b FC(a)21 b(three-place,)d(curried)p 0 TeXcolorgray
|
|
2597 |
0 TeXcolorgray eop end
|
|
2598 |
%%Page: 5 5
|
|
2599 |
TeXDict begin 5 4 bop 0 TeXcolorgray 0 TeXcolorgray 0
|
|
2600 |
TeXcolorgray -150 66 a FC(predicate:)-49 216 y Fv(8)p
|
|
2601 |
Fo(\000)14 b Fz(a)g(\034)5 b(:)45 b Fp(valid)11 b Fo(\(\000\))18
|
|
2602 |
b Fv(^)h Fo(\()p Fz(a)24 b Fo(:)f Fz(\034)9 b Fo(\))24
|
|
2603 |
b Fv(2)f Fo(\000)g Fv(\))g Fz(P)35 b Fo(\000)23 b(\()p
|
|
2604 |
Fp(var)10 b Fo(\()p Fz(a)p Fo(\)\))24 b Fz(\034)-49 339
|
|
2605 |
y Fv(8)p Fo(\000)14 b Fz(M)22 b(N)g(\034)i(\033)n(:)47
|
|
2606 |
b Fo(\000)23 b Fv(`)g Fz(M)31 b Fo(:)23 b Fz(\034)33
|
|
2607 |
b Fv(!)23 b Fz(\033)f Fv(^)d Fz(P)35 b Fo(\000)23 b Fz(M)31
|
|
2608 |
b Fo(\()p Fz(\034)i Fv(!)23 b Fz(\033)s Fo(\))h Fv(^)431
|
|
2609 |
439 y Fo(\000)f Fv(`)g Fz(N)31 b Fo(:)24 b Fz(\034)k
|
|
2610 |
Fv(^)18 b Fz(P)35 b Fo(\000)23 b Fz(N)32 b(\034)h Fv(\))431
|
|
2611 |
538 y Fz(P)i Fo(\000)23 b(\()p Fp(app)6 b Fo(\()p Fz(M)t(;)14
|
|
2612 |
b(N)9 b Fo(\)\))24 b Fz(\033)-49 662 y Fv(8)p Fo(\000)14
|
|
2613 |
b Fz(a)g(M)21 b(\034)j(\033)n(:)47 b(a)23 b Fo(#)g(\000)18
|
|
2614 |
b Fv(^)h Fo(\()p Fz(a)24 b Fo(:)f Fz(\034)5 b(;)14 b
|
|
2615 |
Fo(\000\))23 b Fv(`)g Fz(M)31 b Fo(:)23 b Fz(\033)k Fv(^)399
|
|
2616 |
761 y Fz(P)35 b Fo(\()p Fz(a)23 b Fo(:)g Fz(\034)5 b(;)14
|
|
2617 |
b Fo(\000\))23 b Fz(M)32 b(\033)27 b Fv(\))399 861 y
|
|
2618 |
Fz(P)35 b Fo(\000)23 b(\()p Fp(lam)7 b Fo(\()p Fz(a;)14
|
|
2619 |
b(M)9 b Fo(\)\))23 b(\()p Fz(\034)33 b Fv(!)23 b Fz(\033)s
|
|
2620 |
Fo(\))p -90 911 1873 4 v 421 985 a(\000)g Fv(`)g Fz(M)32
|
|
2621 |
b Fo(:)23 b Fz(\034)56 b Fv(\))46 b Fz(P)35 b Fo(\000)23
|
|
2622 |
b Fz(M)31 b(\034)1746 1084 y FC(\(6\))-50 1184 y(W)-7
|
|
2623 |
b(e)20 b(wish)f(to)g(pro)o(v)o(e)e(the)i(follo)n(wing)e(property)-5
|
|
2624 |
b(,)16 b(where)i(a)h(conte)o(xt)-150 1284 y Fo(\000)-98
|
|
2625 |
1296 y Fu(2)-39 1284 y FC(is)i(weak)o(er)f(than)h Fo(\000)514
|
|
2626 |
1296 y Fu(1)572 1284 y FC(\(written)g Fo(\000)909 1296
|
|
2627 |
y Fu(1)970 1284 y Fv(\022)j Fo(\000)1111 1296 y Fu(2)1148
|
|
2628 |
1284 y FC(\),)d(if)g(e)n(v)o(ery)e(name-type)-150 1383
|
|
2629 |
y(pair)h(in)g Fo(\000)137 1395 y Fu(1)195 1383 y FC(also)h(appears)e
|
|
2630 |
(in)h Fo(\000)761 1395 y Fu(2)798 1383 y FC(:)p 0 TeXcolorgray
|
|
2631 |
-150 1522 a Fn(Lemma)f(5)f FC(\(W)-7 b(eak)o(ening)16
|
|
2632 |
b(Lemma\))p Fn(.)p 0 TeXcolorgray 36 w Fx(If)i Fo(\000)1078
|
|
2633 |
1534 y Fu(1)1138 1522 y Fv(`)23 b Fz(M)32 b Fo(:)23 b
|
|
2634 |
Fz(\034)28 b Fx(is)19 b(derivable)o(,)-150 1622 y(and)j
|
|
2635 |
Fo(\000)50 1634 y Fu(1)116 1622 y Fv(\022)29 b Fo(\000)262
|
|
2636 |
1634 y Fu(2)322 1622 y Fx(with)24 b Fo(\000)541 1634
|
|
2637 |
y Fu(2)602 1622 y Fx(being)f(valid,)f(then)h Fo(\000)1240
|
|
2638 |
1634 y Fu(2)1306 1622 y Fv(`)28 b Fz(M)38 b Fo(:)28 b
|
|
2639 |
Fz(\034)34 b Fx(is)24 b(also)-150 1721 y(derivable)o(.)-50
|
|
2640 |
1860 y FC(Proofs)e(of)h(this)g(lemma)f(are)h(often)f(claimed)h(to)g(be)
|
|
2641 |
g(straightfor)n(-)-150 1959 y(w)o(ard)18 b(\(e.g.)f([11)n(]\).)h(The)g
|
|
2642 |
(informal)e(proof)h(usually)g(goes)h(as)g(follo)n(ws:)-148
|
|
2643 |
2099 y(I)t Fw(N)t(F)t(O)t(R)t(M)t(A)t(L)25 b FC(P)t Fw(R)q(O)t(O)t(F)i
|
|
2644 |
(O)t(F)e(T)t(H)t(E)g FC(W)t Fw(E)t(A)t(K)t(E)t(N)t(I)t(N)t(G)g
|
|
2645 |
FC(L)t Fw(E)t(M)t(M)t(A)r FC(.)c(By)g(rule)-150 2198
|
|
2646 |
y(induction)d(o)o(v)o(er)h Fo(\000)402 2210 y Fu(1)462
|
|
2647 |
2198 y Fv(`)k Fz(M)32 b Fo(:)23 b Fz(\034)9 b FC(.)-48
|
|
2648 |
2298 y(C)t Fw(A)t(S)t(E)26 b FC(1)t(:)d Fo(\000)315 2310
|
|
2649 |
y Fu(1)378 2298 y Fv(`)h Fz(M)34 b Fo(:)25 b Fz(\034)32
|
|
2650 |
b FC(is)22 b Fo(\000)813 2310 y Fu(1)875 2298 y Fv(`)j
|
|
2651 |
Fp(var)10 b Fo(\()p Fz(a)p Fo(\))25 b(:)g Fz(\034)9 b
|
|
2652 |
FC(.)23 b(By)e(assumption)-150 2398 y(we)j(kno)n(w)f
|
|
2653 |
Fz(v)s(al)r(id)p Fo(\(\000)448 2410 y Fu(2)484 2398 y
|
|
2654 |
Fo(\))p FC(,)h Fo(\()p Fz(a)30 b Fo(:)f Fz(\034)9 b Fo(\))31
|
|
2655 |
b Fv(2)e Fo(\000)963 2410 y Fu(1)1025 2398 y FC(and)23
|
|
2656 |
b Fo(\000)1221 2410 y Fu(1)1287 2398 y Fv(\022)29 b Fo(\000)1433
|
|
2657 |
2410 y Fu(2)1470 2398 y FC(.)24 b(Therefore)-150 2497
|
|
2658 |
y(we)d(can)f(use)g(the)g(typing)f(rules)h(to)h(deri)n(v)o(e)e
|
|
2659 |
Fo(\000)1135 2509 y Fu(2)1195 2497 y Fv(`)k Fp(var)9
|
|
2660 |
b Fo(\()p Fz(a)p Fo(\))24 b(:)f Fz(\034)9 b FC(.)-48
|
|
2661 |
2597 y(C)t Fw(A)t(S)t(E)31 b FC(2)t(:)d Fo(\000)325 2609
|
|
2662 |
y Fu(1)397 2597 y Fv(`)34 b Fz(M)43 b Fo(:)34 b Fz(\034)j
|
|
2663 |
FC(is)27 b Fo(\000)870 2609 y Fu(1)941 2597 y Fv(`)35
|
|
2664 |
b Fp(app)6 b Fo(\()p Fz(M)1272 2609 y Fu(1)1309 2597
|
|
2665 |
y Fz(;)14 b(M)1427 2609 y Fu(2)1464 2597 y Fo(\))34 b(:)h
|
|
2666 |
Fz(\034)9 b FC(.)27 b(Case)-150 2696 y(follo)n(ws)20
|
|
2667 |
b(from)f(the)h(induction)f(hypotheses)f(and)h(the)i(typing)e(rules.)-48
|
|
2668 |
2796 y(C)t Fw(A)t(S)t(E)33 b FC(3)t(:)e Fo(\000)330 2808
|
|
2669 |
y Fu(1)406 2796 y Fv(`)39 b Fz(M)47 b Fo(:)39 b Fz(\034)g
|
|
2670 |
FC(is)30 b Fo(\000)898 2808 y Fu(1)974 2796 y Fv(`)38
|
|
2671 |
b Fp(lam)7 b Fo(\()p Fz(a;)14 b(M)1395 2808 y Fu(1)1432
|
|
2672 |
2796 y Fo(\))39 b(:)g Fz(\034)49 b Fv(!)38 b Fz(\033)s
|
|
2673 |
FC(.)-150 2896 y(Although,)33 b(one)h(has)h(to)g(pro)o(v)o(e)d(this)k
|
|
2674 |
(case)f(for)f(all)h Fz(a)p FC(,)g(using)f(the)-150 2995
|
|
2675 |
y(v)n(ariable)22 b(con)m(v)o(ention)e(we)j(assume)g(that)g
|
|
2676 |
Fz(a)h FC(does)f(not)f(occur)g(in)i Fo(\000)1785 3007
|
|
2677 |
y Fu(2)1822 2995 y FC(.)-150 3095 y(Then)17 b(we)h(kno)n(w)f(by)g(the)h
|
|
2678 |
(induction)e(hypothesis)g(that)i Fo(\()p Fz(a)23 b Fo(:)g
|
|
2679 |
Fz(\034)5 b(;)14 b Fo(\000)1699 3107 y Fu(2)1736 3095
|
|
2680 |
y Fo(\))24 b Fv(`)-150 3195 y Fz(M)-69 3207 y Fu(1)-8
|
|
2681 |
3195 y Fo(:)h Fz(\033)g FC(holds.)c(Hence)f(also)i Fo(\000)776
|
|
2682 |
3207 y Fu(2)837 3195 y Fv(`)j Fp(lam)7 b Fo(\()p Fz(a;)14
|
|
2683 |
b(M)1245 3207 y Fu(1)1282 3195 y Fo(\))25 b(:)f Fz(\034)35
|
|
2684 |
b Fv(!)24 b Fz(\033)h FC(by)c(the)-150 3294 y(typing)e(rules.)p
|
|
2685 |
1725 3294 4 57 v 1729 3241 50 4 v 1729 3294 V 1778 3294
|
|
2686 |
4 57 v 1413 w(\223)90 b(\224)-50 3433 y(Because)23 b(of)g(the)g(ar)o
|
|
2687 |
(guably)e(questionable)h(use)h(of)g(the)g(v)n(ariable)-150
|
|
2688 |
3533 y(con)m(v)o(ention)j(in)j(the)g(third)f(case,)h(this)h(informal)d
|
|
2689 |
(proof)g(is)j(painful)-150 3633 y(to)g(formalise)f(using)g(the)h
|
|
2690 |
(original)e(induction)g(principle)h(\(6\))n(,)i(see)-150
|
|
2691 |
3732 y(for)25 b(e)o(xample)f([4)o(].)i(In)f(particular)m(,)e(the)j
|
|
2692 |
(abstraction)e(case)i(in)g(a)g(for)n(-)-150 3832 y(mal)k(proof)e(will)i
|
|
2693 |
(typically)e(require)h(the)g(abstraction)f(to)i(ha)n(v)o(e)f(its)-150
|
|
2694 |
3932 y(bound)e(v)n(ariable)g(renamed)g(to)i(be)g(suitably)f(fresh.)g
|
|
2695 |
(The)g(proof)f(of)-150 4031 y(the)20 b(lemma)g(also)g(then)g(requires)f
|
|
2696 |
(an)h(equi)n(v)n(ariance)e(result)252 4188 y Fo(\000)23
|
|
2697 |
b Fv(`)g Fz(M)32 b Fo(:)23 b Fz(\034)56 b Fv(\))46 b
|
|
2698 |
Fo(\()p Fz(\031)863 4197 y Fj(\001)902 4188 y Fo(\000\))23
|
|
2699 |
b Fv(`)g Fo(\()p Fz(\031)1165 4197 y Fj(\001)1203 4188
|
|
2700 |
y Fz(M)9 b Fo(\))23 b(:)g Fz(\034)316 b FC(\(7\))-150
|
|
2701 |
4345 y(to)26 b(be)g(sho)n(wn.)283 4315 y Fs(2)341 4345
|
|
2702 |
y FC(This)f(lemma)h(is)g(generally)f(useful,)g(and)g(because)-150
|
|
2703 |
4445 y(of)18 b(the)h(e)o(xistence)f(of)g(in)m(v)o(erses)f(for)h
|
|
2704 |
(permutations)f(can)h(be)h(recast)f(as)252 4602 y Fo(\()p
|
|
2705 |
Fz(\031)334 4611 y Fj(\001)373 4602 y Fo(\000\))23 b
|
|
2706 |
Fv(`)g Fo(\()p Fz(\031)636 4611 y Fj(\001)675 4602 y
|
|
2707 |
Fz(M)9 b Fo(\))23 b(:)g Fz(\034)56 b Fv(,)46 b Fo(\000)23
|
|
2708 |
b Fv(`)g Fz(M)31 b Fo(:)23 b Fz(\034)-150 4759 y FC(or)d(e)n(v)o(en)208
|
|
2709 |
4916 y Fo(\()p Fz(\031)290 4925 y Fj(\001)329 4916 y
|
|
2710 |
Fo(\000\))j Fv(`)g Fz(M)31 b Fo(:)23 b Fz(\034)56 b Fv(,)46
|
|
2711 |
b Fo(\000)23 b Fv(`)g Fo(\()p Fz(\031)1120 4882 y Fq(\000)p
|
|
2712 |
Fu(1)1210 4925 y Fj(\001)1248 4916 y Fz(M)9 b Fo(\))23
|
|
2713 |
b(:)g Fz(\034)-150 5074 y FC(which)d(is)i(a)g(useful)e(theorem)f(to)i
|
|
2714 |
(re)n(write)g(with)g(because)f(it)i(collects)-150 5173
|
|
2715 |
y(all)34 b(of)f(the)h(permutations)e(in)h(a)h(typing)f(judgement)e(and)
|
|
2716 |
i(mo)o(v)o(es)-150 5273 y(them)20 b(so)g(that)h(the)o(y)e(apply)g(only)
|
|
2717 |
h(to)g(the)g(term)g(ar)o(gument.)p 0 TeXcolorgray -150
|
|
2718 |
5355 997 3 v -150 5406 a Fk(2)-113 5430 y Fw(The)d(proof)h(is)f(an)g
|
|
2719 |
(easy)h(induction)h(using)f(\(6\).)p 0 TeXcolorgray 0
|
|
2720 |
TeXcolorgray 0 TeXcolorgray 2141 66 a FC(\(Another)39
|
|
2721 |
b(possibility)h(when)g(formalising)f(results)i(such)f(as)2042
|
|
2722 |
166 y(these)34 b(is)h(to)f(sho)n(w)g(that)g(the)h(relation)e(is)i
|
|
2723 |
(preserv)o(ed)d(under)h(iter)n(-)2042 266 y(ated)f(v)n(ariable-for)n
|
|
2724 |
(-v)n(ariable)c(substitutions.)k(This)h(result)f(applies)2042
|
|
2725 |
365 y(when)f(the)h(body)f(of)g(an)h(abstraction)f(acquires)g(an)h(e)o
|
|
2726 |
(xtra)f(substi-)2042 465 y(tution)g(through)f(renaming.)g(Because)j
|
|
2727 |
(substitutions)e(are)h(harder)2042 565 y(to)e(reason)g(with)g(than)g
|
|
2728 |
(permutations,)e(this)j(approach)d(is)j(usually)2042
|
|
2729 |
664 y(less)d(attracti)n(v)o(e)f(than)g(performing)e(the)i(body')-5
|
|
2730 |
b(s)27 b(renaming)f(with)h(a)2042 764 y(permutation.\))2141
|
|
2731 |
863 y(The)22 b(painful)f(requirement)e(to)j(rename)f(the)h(bound)e(v)n
|
|
2732 |
(ariable)h(in)2042 963 y(the)15 b(rule)g(induction)f(tends)h(to)h
|
|
2733 |
(happen)e(e)n(v)o(ery)g(time)i(a)g(rule)f(induction)2042
|
|
2734 |
1063 y(with)22 b(\(6\))g(is)h(performed)d(\(though)g(not)i(in)h(the)f
|
|
2735 |
(proof)f(of)h(\(7\))n(,)h(pleas-)2042 1162 y(antly\).)17
|
|
2736 |
b(W)-7 b(e)20 b(can)e(a)n(v)n(oid)g(this)h(by)f(pro)o(ving)e(a)i(more)g
|
|
2737 |
(useful)g(induction)2042 1262 y(hypothesis)g(once)i(and)f(for)h(all:)p
|
|
2738 |
0 TeXcolorgray 2042 1401 a Fn(Theor)o(em)15 b(1.)p 0
|
|
2739 |
TeXcolorgray 33 w Fx(F)-9 b(or)16 b(all)g(typing)f(conte)n(xts)g
|
|
2740 |
Fo(\000)p Fx(,)h(all)g Fz(\013)p Fx(-equated)e Fz(\025)p
|
|
2741 |
Fx(-terms)2042 1501 y Fz(M)9 b Fx(,)28 b(all)g Fz(\034)48
|
|
2742 |
b Fv(2)38 b Fp(ty)d Fx(and)28 b(all)g(conte)n(xts)g Fz(x)38
|
|
2743 |
b Fv(2)g Fx(fs-pset,)28 b(the)h(following)2042 1601 y(implication)19
|
|
2744 |
b(holds:)2100 1758 y Fv(8)p Fz(x)14 b Fo(\000)g Fz(a)g(\034)5
|
|
2745 |
b(:)46 b Fp(valid)10 b Fo(\(\000\))19 b Fv(^)g Fo(\()p
|
|
2746 |
Fz(a)k Fo(:)g Fz(\034)9 b Fo(\))24 b Fv(2)f Fo(\000)g
|
|
2747 |
Fv(\))g Fz(P)35 b Fo(\000)23 b(\()p Fp(var)10 b Fo(\()p
|
|
2748 |
Fz(a)p Fo(\)\))24 b Fz(\034)33 b(x)2100 1881 y Fv(8)p
|
|
2749 |
Fz(x)14 b Fo(\000)g Fz(M)22 b(N)h(\034)g(\033)n(:)2183
|
|
2750 |
1981 y Fo(\000)g Fv(`)g Fz(M)32 b Fo(:)23 b Fz(\034)33
|
|
2751 |
b Fv(!)23 b Fz(\033)f Fv(^)c Fo(\()p Fv(8)p Fz(z)t(:)45
|
|
2752 |
b(P)35 b Fo(\000)23 b Fz(M)32 b Fo(\()p Fz(\034)h Fv(!)23
|
|
2753 |
b Fz(\033)s Fo(\))h Fz(z)t Fo(\))e Fv(^)2183 2080 y Fo(\000)h
|
|
2754 |
Fv(`)g Fz(N)32 b Fo(:)23 b Fz(\034)28 b Fv(^)19 b Fo(\()p
|
|
2755 |
Fv(8)p Fz(z)t(:)45 b(P)35 b Fo(\000)23 b Fz(N)32 b(\034)g(z)t
|
|
2756 |
Fo(\))46 b Fv(\))2183 2180 y Fz(P)35 b Fo(\000)23 b(\()p
|
|
2757 |
Fp(app)7 b Fo(\()p Fz(M)t(;)14 b(N)9 b Fo(\)\))24 b Fz(\033)i(x)2100
|
|
2758 |
2303 y Fv(8)p Fz(x)14 b(a)g Fo(\000)g Fz(M)22 b(\034)h(\033)n(:)2183
|
|
2759 |
2403 y(a)g Fo(#)h Fz(x)42 b Fv(^)18 b Fz(a)23 b Fo(#)h(\000)18
|
|
2760 |
b Fv(^)h Fo(\()p Fz(a)k Fo(:)g Fz(\034)5 b(;)14 b Fo(\000\))23
|
|
2761 |
b Fv(`)g Fz(M)32 b Fo(:)23 b Fz(\033)j Fv(^)2183 2502
|
|
2762 |
y Fo(\()p Fv(8)p Fz(z)t(:)c(P)35 b Fo(\()p Fz(a)23 b
|
|
2763 |
Fo(:)h Fz(\034)5 b(;)14 b Fo(\000\))23 b Fz(M)31 b(\033)c(z)t
|
|
2764 |
Fo(\))46 b Fv(\))2183 2602 y Fz(P)35 b Fo(\000)23 b(\()p
|
|
2765 |
Fp(lam)8 b Fo(\()p Fz(a;)14 b(M)9 b Fo(\)\))23 b(\()p
|
|
2766 |
Fz(\034)33 b Fv(!)23 b Fz(\033)s Fo(\))h Fz(x)p 2059
|
|
2767 |
2652 1959 4 v 2578 2726 a Fo(\000)f Fv(`)g Fz(M)31 b
|
|
2768 |
Fo(:)23 b Fz(\034)56 b Fv(\))46 b Fz(P)35 b Fo(\000)23
|
|
2769 |
b Fz(M)32 b(\034)h(x)p 0 TeXcolorgray 2042 2892 a Fx(Pr)l(oof.)p
|
|
2770 |
0 TeXcolorgray 28 w FC(The)d(proof)g(uses)h(the)g(original)e(induction)
|
|
2771 |
g(principle)h(\(6\))o(.)2042 2991 y(W)-7 b(e)21 b(strengthen)e(the)h
|
|
2772 |
(goal)g(by)f(aiming)h(to)g(pro)o(v)o(e)2062 3157 y Fv(8)p
|
|
2773 |
Fz(\031)26 b Fo(\000)14 b Fz(M)22 b(\034)i Fo(\()p Fz(x)f
|
|
2774 |
Fv(2)h Fx(fs-pset)p Fo(\))p Fz(:)46 b Fo(\()23 b Fz(:)14
|
|
2775 |
b(:)g(:)23 b Fo(\))h Fv(\))f Fz(P)35 b Fo(\()p Fz(\031)3417
|
|
2776 |
3166 y Fj(\001)3455 3157 y Fo(\000\))24 b(\()p Fz(\031)3645
|
|
2777 |
3166 y Fj(\001)3683 3157 y Fz(M)9 b Fo(\))23 b Fz(\034)33
|
|
2778 |
b(x)47 b(:)2042 3323 y FC(In)20 b(the)g(v)n(ariable-case)f(we)h(need)g
|
|
2779 |
(to)g(pro)o(v)o(e)2617 3488 y Fz(P)35 b Fo(\()p Fz(\031)2787
|
|
2780 |
3497 y Fj(\001)2826 3488 y Fo(\000\))23 b(\()p Fp(var)10
|
|
2781 |
b Fo(\()p Fz(\031)3172 3497 y Fj(\001)3211 3488 y Fz(a)p
|
|
2782 |
Fo(\)\))23 b Fz(\034)33 b(x)2042 3654 y FC(while)22 b(kno)n(wing)e
|
|
2783 |
(that)i Fp(valid)11 b Fo(\(\000\))23 b FC(and)e Fo(\()p
|
|
2784 |
Fz(a)27 b Fo(:)f Fz(\034)9 b Fo(\))28 b Fv(2)f Fo(\000)22
|
|
2785 |
b FC(hold.)f(V)-9 b(alidity)2042 3754 y(of)37 b(conte)o(xts)f(is)j
|
|
2786 |
(preserv)o(ed)c(under)h(permutations,)f(so)j(we)f(ha)n(v)o(e)2042
|
|
2787 |
3853 y Fp(valid)10 b Fo(\()p Fz(\031)2302 3862 y Fj(\001)2341
|
|
2788 |
3853 y Fo(\000\))p FC(.)18 b(From)f Fo(\()p Fz(a)23 b
|
|
2789 |
Fo(:)h Fz(\034)9 b Fo(\))24 b Fv(2)f Fo(\000)18 b FC(we)g(can)g(infer)f
|
|
2790 |
Fo(\()p Fz(\031)3563 3862 y Fj(\001)3601 3853 y Fz(a)23
|
|
2791 |
b Fo(:)g Fz(\034)9 b Fo(\))25 b Fv(2)e Fz(\031)3944 3862
|
|
2792 |
y Fj(\001)3982 3853 y Fo(\000)2042 3953 y FC(and)c(hence)h(we)g(can)g
|
|
2793 |
(use)h(the)f(assumed)g(implication)2153 4119 y Fv(8)p
|
|
2794 |
Fz(x)14 b Fo(\000)g Fz(a)g(\034)5 b(:)46 b Fp(valid)10
|
|
2795 |
b Fo(\(\000\))19 b Fv(^)g Fo(\()p Fz(a)k Fo(:)g Fz(\034)9
|
|
2796 |
b Fo(\))24 b Fv(2)f Fo(\000)g Fv(\))g Fz(P)35 b Fo(\000)23
|
|
2797 |
b Fp(var)10 b Fo(\()p Fz(a)p Fo(\))23 b Fz(\034)33 b(x)2042
|
|
2798 |
4284 y FC(to)20 b(obtain)f Fz(P)35 b Fo(\()p Fz(\031)2525
|
|
2799 |
4293 y Fj(\001)2564 4284 y Fo(\000\))23 b(\()p Fp(var)10
|
|
2800 |
b Fo(\()p Fz(\031)2910 4293 y Fj(\001)2949 4284 y Fz(a)p
|
|
2801 |
Fo(\)\))23 b Fz(\034)33 b(x)p FC(.)2141 4384 y(The)16
|
|
2802 |
b(application-case)e(is)j(routine.)e(The)h(interesting)f(case)i(is)g
|
|
2803 |
(the)2042 4484 y(lambda-case.)h(In)i(this)h(case)f(we)h(need)f(to)g
|
|
2804 |
(pro)o(v)o(e)2381 4649 y Fz(P)35 b Fo(\()p Fz(\031)2551
|
|
2805 |
4658 y Fj(\001)2590 4649 y Fo(\000\))23 b(\()p Fp(lam)7
|
|
2806 |
b Fo(\()p Fz(\031)2949 4658 y Fj(\001)2988 4649 y Fz(a;)14
|
|
2807 |
b(\031)3119 4658 y Fj(\001)3157 4649 y Fz(M)9 b Fo(\)\))24
|
|
2808 |
b(\()p Fz(\034)33 b Fv(!)23 b Fz(\033)s Fo(\))g Fz(x)2042
|
|
2809 |
4815 y FC(under)c(the)h(assumption)f(that)2398 4973 y
|
|
2810 |
Fo(\()p Fz(i)p Fo(\))83 b Fz(a)23 b Fo(#)g(\000)2369
|
|
2811 |
5073 y(\()p Fz(ii)p Fo(\))83 b Fz(a)23 b Fo(:)g Fz(\034)5
|
|
2812 |
b(;)14 b Fo(\000)23 b Fv(`)g Fz(M)31 b Fo(:)23 b Fz(\033)2340
|
|
2813 |
5172 y Fo(\()p Fz(iii)p Fo(\))83 b Fv(8)p Fz(\031)16
|
|
2814 |
b(x:)24 b(P)34 b Fo(\()p Fz(\031)2947 5181 y Fj(\001)2986
|
|
2815 |
5172 y Fo(\()p Fz(a)23 b Fo(:)h Fz(\034)5 b(;)14 b Fo(\000\)\))23
|
|
2816 |
b(\()p Fz(\031)3431 5181 y Fj(\001)3470 5172 y Fz(M)9
|
|
2817 |
b Fo(\))23 b Fz(\033)j(x)3938 5073 y FC(\(8\))2042 5330
|
|
2818 |
y(Since)j(atoms,)h Fz(\025)p FC(-terms)f(and)g(typing)g(conte)o(xts)f
|
|
2819 |
(are)i(\002nitely)f(sup-)2042 5430 y(ported)22 b(and)h(by)h(assumption)
|
|
2820 |
e(also)i Fz(x)p FC(,)h(there)e(e)o(xists)h(by)g(Lem.)f(4)h(an)p
|
|
2821 |
0 TeXcolorgray 0 TeXcolorgray eop end
|
|
2822 |
%%Page: 6 6
|
|
2823 |
TeXDict begin 6 5 bop 0 TeXcolorgray 0 TeXcolorgray 0
|
|
2824 |
TeXcolorgray -150 66 a FC(atom)29 b Fz(c)g FC(with)h
|
|
2825 |
Fz(c)39 b Fo(#)h(\()p Fz(\031)555 75 y Fj(\001)594 66
|
|
2826 |
y Fz(a;)14 b(\031)725 75 y Fj(\001)763 66 y Fz(M)t(;)g(\031)935
|
|
2827 |
75 y Fj(\001)974 66 y Fo(\000)p Fz(;)g(x)p Fo(\))p FC(.)30
|
|
2828 |
b(Using)f Fo(\()p Fz(iii)p Fo(\))g FC(we)g(can)-150 166
|
|
2829 |
y(infer)1 314 y Fv(8)p Fz(x:)23 b(P)35 b Fo(\(\()p Fz(c)28
|
|
2830 |
b(\031)407 323 y Fj(\001)445 314 y Fz(a)p Fo(\))521 323
|
|
2831 |
y Fj(\001)560 314 y Fz(\031)610 323 y Fj(\001)648 314
|
|
2832 |
y Fo(\()p Fz(a)23 b Fo(:)g Fz(\034)5 b(;)14 b Fo(\000\)\))24
|
|
2833 |
b(\(\()p Fz(c)k(\031)1189 323 y Fj(\001)1228 314 y Fz(a)p
|
|
2834 |
Fo(\))1304 323 y Fj(\001)1342 314 y Fz(\031)1392 323
|
|
2835 |
y Fj(\001)1430 314 y Fz(M)9 b Fo(\))23 b Fz(\034)33 b(x)-150
|
|
2836 |
463 y FC(which)20 b(is)-11 611 y Fv(8)p Fz(x:)j(P)34
|
|
2837 |
b Fo(\()p Fz(c)24 b Fo(:)f Fz(\034)5 b(;)14 b Fo(\()p
|
|
2838 |
Fz(c)28 b(\031)578 620 y Fj(\001)616 611 y Fz(a)p Fo(\))692
|
|
2839 |
620 y Fj(\001)731 611 y Fz(\031)781 620 y Fj(\001)819
|
|
2840 |
611 y Fo(\000\))23 b(\(\()p Fz(c)28 b(\031)1104 620 y
|
|
2841 |
Fj(\001)1143 611 y Fz(a)p Fo(\))1219 620 y Fj(\001)1257
|
|
2842 |
611 y Fz(\031)1307 620 y Fj(\001)1346 611 y Fz(M)9 b
|
|
2843 |
Fo(\))23 b Fz(\034)32 b(x)140 b FC(\(9\))-150 759 y(From)22
|
|
2844 |
b Fo(\()p Fz(i)p Fo(\))h FC(and)f(Lem.)g(2)p Fo(\()p
|
|
2845 |
Fz(i)p Fo(\))h FC(follo)n(ws)f(that)h Fz(\031)1134 768
|
|
2846 |
y Fj(\001)1172 759 y Fz(a)k Fo(#)h Fz(\031)1390 768 y
|
|
2847 |
Fj(\001)1429 759 y Fo(\000)p FC(.)22 b(W)m(ith)h Fz(c)k
|
|
2848 |
Fo(#)-150 859 y Fz(\031)-100 868 y Fj(\001)-62 859 y
|
|
2849 |
Fo(\000)17 b FC(we)f(can)g(infer)f(using)g(Lem.)h(2)p
|
|
2850 |
Fo(\()p Fz(ii)p Fo(\))g FC(that)g Fo(\()p Fz(c)27 b(\031)1277
|
|
2851 |
868 y Fj(\001)1316 859 y Fz(a)p Fo(\))1392 868 y Fj(\001)1430
|
|
2852 |
859 y Fz(\031)1480 868 y Fj(\001)1519 859 y Fo(\000)c(=)f
|
|
2853 |
Fz(\031)1731 868 y Fj(\001)1770 859 y Fo(\000)p FC(,)-150
|
|
2854 |
958 y(and)e(hence)f(simplify)h(\(9\))f(further)g(to)187
|
|
2855 |
1106 y Fv(8)p Fz(x:)j(P)35 b Fo(\()p Fz(c)23 b Fo(:)h
|
|
2856 |
Fz(\034)5 b(;)14 b(\031)680 1115 y Fj(\001)718 1106 y
|
|
2857 |
Fo(\000\))23 b(\(\()p Fz(c)28 b(\031)1003 1115 y Fj(\001)1042
|
|
2858 |
1106 y Fz(a)p Fo(\))1118 1115 y Fj(\001)1156 1106 y Fz(\031)1206
|
|
2859 |
1115 y Fj(\001)1245 1106 y Fz(M)9 b Fo(\))23 b Fz(\034)32
|
|
2860 |
b(x)199 b FC(\(10\))-150 1255 y(By)28 b(equi)n(v)n(ariance)c(of)j(the)g
|
|
2861 |
(typing)f(relation)h(\(7\))n(,)h(we)f(can)g(use)h Fo(\()p
|
|
2862 |
Fz(ii)p Fo(\))-150 1354 y FC(and)20 b(infer)152 1503
|
|
2863 |
y Fo(\()p Fz(c)28 b(\031)298 1512 y Fj(\001)337 1503
|
|
2864 |
y Fz(a)p Fo(\))413 1512 y Fj(\001)451 1503 y Fz(\031)501
|
|
2865 |
1512 y Fj(\001)539 1503 y Fo(\()p Fz(a)c Fo(:)f Fz(\034)5
|
|
2866 |
b(;)14 b Fo(\000\))23 b Fv(`)g Fo(\()p Fz(c)28 b(\031)1090
|
|
2867 |
1512 y Fj(\001)1128 1503 y Fz(a)p Fo(\))1204 1512 y Fj(\001)1243
|
|
2868 |
1503 y Fz(\031)1293 1512 y Fj(\001)1331 1503 y Fz(M)k
|
|
2869 |
Fo(:)23 b Fz(\033)-150 1651 y FC(which)d(is)306 1750
|
|
2870 |
y Fo(\()p Fz(c)j Fo(:)g Fz(\034)5 b(;)14 b(\031)571 1759
|
|
2871 |
y Fj(\001)609 1750 y Fo(\000\))24 b Fv(`)e Fo(\()p Fz(c)28
|
|
2872 |
b(\031)936 1759 y Fj(\001)975 1750 y Fz(a)p Fo(\))1051
|
|
2873 |
1759 y Fj(\001)1089 1750 y Fz(\031)1139 1759 y Fj(\001)1178
|
|
2874 |
1750 y Fz(M)j Fo(:)24 b Fz(\033)320 b FC(\(11\))-150
|
|
2875 |
1879 y(No)n(w)38 b(we)h(can)f(use)g Fz(c)56 b Fo(#)h
|
|
2876 |
Fz(x)p FC(,)39 b(\(10\))n(,)g(\(11\))e(and)g(infer)h(from)f(the)-150
|
|
2877 |
1979 y(assumed)20 b(implication)f(in)h(the)g(lambda-case)f(that)86
|
|
2878 |
2127 y Fz(P)35 b Fo(\()p Fz(\031)256 2136 y Fj(\001)294
|
|
2879 |
2127 y Fo(\000\))24 b(\()p Fz(l)r(am)p Fo(\()p Fz(c;)14
|
|
2880 |
b Fo(\()p Fz(c)27 b(\031)828 2136 y Fj(\001)866 2127
|
|
2881 |
y Fz(a)p Fo(\))942 2136 y Fj(\001)981 2127 y Fz(\031)1031
|
|
2882 |
2136 y Fj(\001)1069 2127 y Fz(M)9 b Fo(\)\))24 b(\()p
|
|
2883 |
Fz(\034)33 b Fv(!)23 b Fz(\033)s Fo(\))g Fz(x)-150 2275
|
|
2884 |
y FC(Because)f Fz(c)j Fo(#)g Fz(\031)354 2284 y Fj(\001)393
|
|
2885 |
2275 y Fz(a)d FC(and)e Fz(c)26 b Fo(#)f Fz(\031)806 2284
|
|
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
|
|
2887 |
(ho)n(we)n(v)o(er)m(,)-150 2375 y(that)135 2523 y Fz(l)r(am)p
|
|
2888 |
Fo(\()p Fz(c;)14 b Fo(\()p Fz(c)27 b(\031)529 2532 y
|
|
2889 |
Fj(\001)567 2523 y Fz(a)p Fo(\))643 2532 y Fj(\001)682
|
|
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(\()p Fz(\031)1229 2532
|
|
2892 |
y Fj(\001)1267 2523 y Fz(a;)14 b(\031)1398 2532 y Fj(\001)1436
|
|
2893 |
2523 y Fz(M)9 b Fo(\))-150 2671 y FC(and)20 b(we)g(are)g(done.)p
|
|
2894 |
1782 2671 4 57 v 1786 2619 50 4 v 1786 2671 V 1835 2671
|
|
2895 |
4 57 v -50 2831 a(W)m(ith)g(this)h(induction)d(principle)h(at)i(our)f
|
|
2896 |
(disposal,)f(the)i(proof)d(of)-150 2930 y(the)i(weak)o(ening)f(lemma)h
|
|
2897 |
(is)h(simple.)p 0 TeXcolorgray -150 3089 a Fx(Pr)l(oof)f(of)g(the)h(W)
|
|
2898 |
-8 b(eak)o(ening)19 b(Lemma.)p 0 TeXcolorgray 28 w FC(Perform)49
|
|
2899 |
b(a)h(rule)g(induction)-150 3189 y(o)o(v)o(er)19 b Fo(\000)68
|
|
2900 |
3201 y Fu(1)128 3189 y Fv(`)k Fz(M)31 b Fo(:)24 b Fz(\034)30
|
|
2901 |
b FC(using)20 b(the)g(induction)e(hypothesis)211 3337
|
|
2902 |
y Fo(\000)263 3349 y Fu(1)324 3337 y Fv(\022)k Fo(\000)463
|
|
2903 |
3349 y Fu(2)523 3337 y Fv(\))i Fp(valid)10 b Fo(\(\000)892
|
|
2904 |
3349 y Fu(2)929 3337 y Fo(\))24 b Fv(\))f Fo(\000)1143
|
|
2905 |
3349 y Fu(2)1203 3337 y Fv(`)g Fz(M)31 b Fo(:)23 b Fz(\034)-150
|
|
2906 |
3485 y FC(That)d(is,)h(we)f(instantiate)g(Thm.)g(1)g(with)-96
|
|
2907 |
3620 y Fz(P)107 b Fo(=)83 b Fz(\025)p Fo(\000)312 3632
|
|
2908 |
y Fu(1)363 3620 y Fz(M)23 b(\034)g Fo(\000)578 3632 y
|
|
2909 |
Fu(2)615 3620 y Fz(:)46 b Fo(\000)736 3632 y Fu(1)797
|
|
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
|
|
2914 |
Fo(\000)102 b(=)83 b(\000)264 3731 y Fu(1)-108 3819 y
|
|
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
|
|
2917 |
y Fu(2)-150 4158 y FC(where)16 b Fo(\000)122 4170 y Fu(2)182
|
|
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
|
|
2919 |
(es)g(the)f(follo)n(wing)g(three)-150 4257 y(sub-goals:)-150
|
|
2920 |
4398 y Fo(\(1\))47 b Fp(valid)11 b Fo(\(\000)266 4368
|
|
2921 |
y Fq(0)266 4418 y Fu(1)303 4398 y Fo(\))42 b Fv(^)g Fo(\()p
|
|
2922 |
Fz(a)23 b Fo(:)g Fz(\034)9 b Fo(\))24 b Fv(2)g Fo(\000)851
|
|
2923 |
4368 y Fq(0)851 4418 y Fu(1)929 4398 y Fv(^)42 b Fo(\000)1078
|
|
2924 |
4368 y Fq(0)1078 4418 y Fu(1)1138 4398 y Fv(\022)23 b
|
|
2925 |
Fo(\000)1278 4368 y Fq(0)1278 4418 y Fu(2)1356 4398 y
|
|
2926 |
Fv(^)42 b Fp(valid)11 b Fo(\(\000)1716 4368 y Fq(0)1716
|
|
2927 |
4418 y Fu(2)1753 4398 y Fo(\))3 4497 y Fv(\))23 b Fo(\000)161
|
|
2928 |
4467 y Fq(0)161 4518 y Fu(2)222 4497 y Fv(`)f Fp(var)10
|
|
2929 |
b Fo(\()p Fz(a)p Fo(\))23 b(:)h Fz(\034)-150 4621 y Fo(\(2\))47
|
|
2930 |
b(\000)55 4591 y Fq(0)55 4641 y Fu(1)116 4621 y Fv(`)22
|
|
2931 |
b Fz(M)270 4633 y Fu(1)330 4621 y Fo(:)h Fz(\034)33 b
|
|
2932 |
Fv(!)23 b Fz(\033)45 b Fv(^)d Fo(\000)792 4591 y Fq(0)792
|
|
2933 |
4641 y Fu(1)852 4621 y Fv(`)23 b Fz(M)1007 4633 y Fu(2)1067
|
|
2934 |
4621 y Fo(:)g Fz(\034)33 b Fv(^)3 4720 y Fo(\()p Fv(8)p
|
|
2935 |
Fo(\000)134 4690 y Fq(0)134 4741 y Fu(3)171 4720 y Fz(:)23
|
|
2936 |
b Fo(\000)269 4690 y Fq(0)269 4741 y Fu(1)329 4720 y
|
|
2937 |
Fv(\022)g Fo(\000)469 4690 y Fq(0)469 4741 y Fu(3)529
|
|
2938 |
4720 y Fv(\))g Fp(valid)10 b Fo(\(\000)897 4690 y Fq(0)897
|
|
2939 |
4741 y Fu(3)935 4720 y Fo(\))23 b Fv(\))g Fo(\000)1148
|
|
2940 |
4690 y Fq(0)1148 4741 y Fu(3)1208 4720 y Fv(`)g Fz(M)1363
|
|
2941 |
4732 y Fu(1)1423 4720 y Fo(:)g Fz(\034)33 b Fv(!)23 b
|
|
2942 |
Fz(\033)s Fo(\))h Fv(^)3 4820 y Fo(\()p Fv(8)p Fo(\000)134
|
|
2943 |
4790 y Fq(0)134 4840 y Fu(3)171 4820 y Fz(:)f Fo(\000)269
|
|
2944 |
4790 y Fq(0)269 4840 y Fu(1)329 4820 y Fv(\022)g Fo(\000)469
|
|
2945 |
4790 y Fq(0)469 4840 y Fu(3)529 4820 y Fv(\))g Fp(valid)10
|
|
2946 |
b Fo(\(\000)897 4790 y Fq(0)897 4840 y Fu(3)935 4820
|
|
2947 |
y Fo(\))23 b Fv(\))g Fo(\000)1148 4790 y Fq(0)1148 4840
|
|
2948 |
y Fu(3)1208 4820 y Fv(`)g Fz(M)1363 4832 y Fu(2)1423
|
|
2949 |
4820 y Fo(:)g Fz(\034)9 b Fo(\))24 b Fv(^)3 4920 y Fo(\000)55
|
|
2950 |
4889 y Fq(0)55 4940 y Fu(1)116 4920 y Fv(\022)e Fo(\000)255
|
|
2951 |
4889 y Fq(0)255 4940 y Fu(2)334 4920 y Fv(^)42 b Fp(valid)10
|
|
2952 |
b Fo(\(\000)693 4889 y Fq(0)693 4940 y Fu(2)730 4920
|
|
2953 |
y Fo(\))3 5019 y Fv(\))23 b Fo(\000)161 4989 y Fq(0)161
|
|
2954 |
5040 y Fu(2)222 5019 y Fv(`)f Fp(app)7 b Fo(\()p Fz(M)541
|
|
2955 |
5031 y Fu(1)578 5019 y Fz(;)14 b(M)696 5031 y Fu(2)733
|
|
2956 |
5019 y Fo(\))23 b(:)g Fz(\033)-150 5142 y Fo(\(3\))47
|
|
2957 |
b Fz(a)23 b Fo(#)h(\000)215 5112 y Fq(0)215 5163 y Fu(2)293
|
|
2958 |
5142 y Fv(^)42 b Fz(a)23 b Fo(#)g(\000)601 5112 y Fq(0)601
|
|
2959 |
5163 y Fu(1)680 5142 y Fv(^)42 b Fo(\()p Fz(a)23 b Fo(:)g
|
|
2960 |
Fz(\034)5 b(;)14 b Fo(\000)1052 5112 y Fq(0)1052 5163
|
|
2961 |
y Fu(1)1089 5142 y Fo(\))24 b Fv(`)e Fz(M)32 b Fo(:)23
|
|
2962 |
b Fz(\033)k Fv(^)3 5242 y Fo(\()p Fv(8)p Fo(\000)134
|
|
2963 |
5212 y Fq(0)134 5263 y Fu(3)171 5242 y Fz(:)c Fo(\()p
|
|
2964 |
Fz(a)g Fo(:)g Fz(\034)5 b(;)14 b Fo(\000)492 5212 y Fq(0)492
|
|
2965 |
5263 y Fu(1)529 5242 y Fo(\))24 b Fv(\022)e Fo(\000)724
|
|
2966 |
5212 y Fq(0)724 5263 y Fu(3)808 5242 y Fv(\))h Fp(valid)10
|
|
2967 |
b Fo(\(\000)1176 5212 y Fq(0)1176 5263 y Fu(3)1214 5242
|
|
2968 |
y Fo(\))46 b Fv(\))g Fo(\000)1473 5212 y Fq(0)1473 5263
|
|
2969 |
y Fu(3)1533 5242 y Fv(`)23 b Fz(M)32 b Fo(:)23 b Fz(\033)s
|
|
2970 |
Fo(\))h Fv(^)3 5342 y Fo(\000)55 5312 y Fq(0)55 5362
|
|
2971 |
y Fu(1)116 5342 y Fv(\022)e Fo(\000)255 5312 y Fq(0)255
|
|
2972 |
5362 y Fu(2)334 5342 y Fv(^)d Fp(valid)10 b Fo(\(\000)670
|
|
2973 |
5312 y Fq(0)670 5362 y Fu(2)707 5342 y Fo(\))3 5441 y
|
|
2974 |
Fv(\))23 b Fo(\000)161 5411 y Fq(0)161 5462 y Fu(2)222
|
|
2975 |
5441 y Fv(`)f Fp(lam)7 b Fo(\()p Fz(a;)14 b(M)9 b Fo(\))23
|
|
2976 |
b(:)g Fz(\034)33 b Fv(!)23 b Fz(\033)p 0 TeXcolorgray
|
|
2977 |
0 TeXcolorgray 2042 66 a FC(where)31 b(the)h(\002rst)g(tw)o(o)g(are)g
|
|
2978 |
(tri)n(vial.)f(F)o(or)h Fo(\(3\))g FC(we)g(instantiate)g
|
|
2979 |
Fv(8)p Fo(\000)3998 36 y Fq(0)3998 87 y Fu(3)2042 166
|
|
2980 |
y FC(with)24 b Fo(\()p Fz(a)30 b Fo(:)g Fz(\034)5 b(;)14
|
|
2981 |
b Fo(\000)2503 136 y Fq(0)2503 187 y Fu(2)2541 166 y
|
|
2982 |
Fo(\))p FC(.)24 b(The)g(f)o(act)g Fo(\()p Fz(a)30 b Fo(:)h
|
|
2983 |
Fz(\034)5 b(;)14 b Fo(\000)3210 136 y Fq(0)3210 187 y
|
|
2984 |
Fu(1)3247 166 y Fo(\))30 b Fv(\022)g Fo(\()p Fz(a)g Fo(:)g
|
|
2985 |
Fz(\034)5 b(;)14 b Fo(\000)3693 136 y Fq(0)3693 187 y
|
|
2986 |
Fu(2)3730 166 y Fo(\))25 b FC(follo)n(ws)2042 266 y(from)31
|
|
2987 |
b Fo(\000)2288 236 y Fq(0)2288 286 y Fu(1)2371 266 y
|
|
2988 |
Fv(\022)45 b Fo(\000)2533 236 y Fq(0)2533 286 y Fu(2)2570
|
|
2989 |
266 y FC(;)34 b Fp(valid)10 b Fo(\()p Fz(a)46 b Fo(:)g
|
|
2990 |
Fz(\034)5 b(;)14 b Fo(\000)3126 236 y Fq(0)3126 286 y
|
|
2991 |
Fu(2)3163 266 y Fo(\))33 b FC(follo)n(ws)f(from)f Fp(valid)11
|
|
2992 |
b Fo(\(\000)3965 236 y Fq(0)3965 286 y Fu(2)4002 266
|
|
2993 |
y Fo(\))2042 365 y FC(and)32 b Fz(a)45 b Fo(#)h(\000)2451
|
|
2994 |
335 y Fq(0)2451 386 y Fu(2)2488 365 y FC(.)33 b(This)g(gi)n(v)o(es)f
|
|
2995 |
(us)g Fo(\()p Fz(a)46 b Fo(:)g Fz(\034)5 b(;)14 b Fo(\000)3355
|
|
2996 |
335 y Fq(0)3355 386 y Fu(2)3392 365 y Fo(\))46 b Fv(`)g
|
|
2997 |
Fz(M)54 b Fo(:)46 b Fz(\033)s FC(.)33 b(No)n(w)2042 465
|
|
2998 |
y(we)22 b(immediately)f(obtain)h Fo(\000)2882 435 y Fq(0)2882
|
|
2999 |
486 y Fu(2)2946 465 y Fv(`)27 b Fp(lam)7 b Fo(\()p Fz(a;)14
|
|
3000 |
b(M)9 b Fo(\))27 b(:)g Fz(\034)37 b Fv(!)27 b Fz(\033)f
|
|
3001 |
FC(using)c(the)2042 565 y(de\002nition)15 b(of)h(the)g(typing)f
|
|
3002 |
(relation)h(and)f(the)i(f)o(act)f(that)h Fz(a)23 b Fo(#)g(\000)3829
|
|
3003 |
534 y Fq(0)3829 585 y Fu(2)3866 565 y FC(.)p 3974 565
|
|
3004 |
V 3978 512 50 4 v 3978 565 V 4027 565 4 57 v 2141 724
|
|
3005 |
a(This)17 b(e)o(xample)e(also)i(sho)n(ws)g(why)e(the)i(ne)n(w)f
|
|
3006 |
(induction)f(principle)2042 823 y(needs)25 b(to)h(ha)n(v)o(e)e(uni)n(v)
|
|
3007 |
o(ersal)h(quanti\002cations)f(o)o(v)o(er)g(the)h(conte)o(xts)g(in)2042
|
|
3008 |
923 y(the)e(premises.)g(F)o(or)g(e)o(xample,)f(in)i(the)f(lambda-case)f
|
|
3009 |
(the)h(assumed)2042 1022 y(implication)c(has)h(the)g(premise)g
|
|
3010 |
Fo(\()p Fv(8)p Fz(z)t(:)i(P)35 b Fo(\()p Fz(a)23 b Fo(:)g
|
|
3011 |
Fz(\034)5 b(;)14 b Fo(\000\))23 b Fz(M)32 b(\033)26 b(z)t
|
|
3012 |
Fo(\))p FC(:)2104 1170 y Fv(8)p Fz(x)14 b(a)g Fo(\000)g
|
|
3013 |
Fz(M)22 b(\034)h(\033)n(:)47 b(a)23 b Fo(#)g Fz(x)42
|
|
3014 |
b Fv(^)19 b Fz(a)k Fo(#)g(\000)c Fv(^)f Fo(\()p Fz(a)24
|
|
3015 |
b Fo(:)f Fz(\034)5 b(;)14 b Fo(\000\))23 b Fv(`)g Fz(M)31
|
|
3016 |
b Fo(:)23 b Fz(\033)k Fv(^)2613 1270 y Fo(\()p Fv(8)p
|
|
3017 |
Fz(z)t(:)22 b(P)35 b Fo(\()p Fz(a)23 b Fo(:)g Fz(\034)5
|
|
3018 |
b(;)14 b Fo(\000\))23 b Fz(M)32 b(\033)26 b(z)t Fo(\))46
|
|
3019 |
b Fv(\))2613 1369 y Fz(P)35 b Fo(\000)23 b(\()p Fp(lam)7
|
|
3020 |
b Fo(\()p Fz(a;)14 b(M)9 b Fo(\)\))23 b(\()p Fz(\034)33
|
|
3021 |
b Fv(!)24 b Fz(\033)s Fo(\))f Fz(x)2042 1508 y FC(If)g(we)h(had)e
|
|
3022 |
(stated)i(the)f(induction)f(principle)f(using)i(the)h(follo)n(wing)2042
|
|
3023 |
1608 y(simpler)c(implication)2692 1577 y Fs(3)2104 1755
|
|
3024 |
y Fv(8)p Fz(x)14 b(a)g Fo(\000)g Fz(M)22 b(\034)h(\033)n(:)47
|
|
3025 |
b(a)23 b Fo(#)g Fz(x)42 b Fv(^)19 b Fz(a)k Fo(#)g(\000)c
|
|
3026 |
Fv(^)f Fo(\()p Fz(a)24 b Fo(:)f Fz(\034)5 b(;)14 b Fo(\000\))23
|
|
3027 |
b Fv(`)g Fz(M)31 b Fo(:)23 b Fz(\033)k Fv(^)2613 1855
|
|
3028 |
y Fz(P)35 b Fo(\()p Fz(a)23 b Fo(:)g Fz(\034)5 b(;)14
|
|
3029 |
b Fo(\000\))24 b Fz(M)31 b(\033)c(x)46 b Fv(\))2613 1954
|
|
3030 |
y Fz(P)35 b Fo(\000)23 b(\()p Fp(lam)7 b Fo(\()p Fz(a;)14
|
|
3031 |
b(M)9 b Fo(\)\))23 b(\()p Fz(\034)33 b Fv(!)24 b Fz(\033)s
|
|
3032 |
Fo(\))f Fz(x)2042 2093 y FC(then)37 b(the)g(induction)e(hypothesis)h
|
|
3033 |
(with)i(which)e(we)i(pro)o(v)o(ed)d(the)2042 2193 y(weak)o(ening)18
|
|
3034 |
b(lemma,)i(namely)2403 2340 y Fo(\000)2455 2352 y Fu(1)2515
|
|
3035 |
2340 y Fv(\022)j Fo(\000)2655 2352 y Fu(2)2715 2340 y
|
|
3036 |
Fv(\))g Fp(valid)11 b Fo(\(\000)3084 2352 y Fu(2)3121
|
|
3037 |
2340 y Fo(\))23 b Fv(\))g Fo(\000)3334 2352 y Fu(2)3395
|
|
3038 |
2340 y Fv(`)f Fz(M)32 b Fo(:)23 b Fz(\034)2042 2488 y
|
|
3039 |
FC(w)o(ould)17 b(not)g(ha)n(v)o(e)h(been)f(strong)g(enough.)e(W)-7
|
|
3040 |
b(e)19 b(w)o(ould)e(ha)n(v)o(e)g(to)h(mak)o(e)2042 2588
|
|
3041 |
y(it)j(stronger)e(as)h(follo)n(ws)2312 2735 y Fv(8)p
|
|
3042 |
Fo(\000)2411 2747 y Fu(2)2448 2735 y Fz(:)j Fo(\000)2546
|
|
3043 |
2747 y Fu(1)2606 2735 y Fv(\022)g Fo(\000)2746 2747 y
|
|
3044 |
Fu(2)2806 2735 y Fv(\))g Fp(valid)10 b Fo(\(\000)3174
|
|
3045 |
2747 y Fu(2)3212 2735 y Fo(\))23 b Fv(\))g Fo(\000)3425
|
|
3046 |
2747 y Fu(2)3485 2735 y Fv(`)g Fz(M)32 b Fo(:)23 b Fz(\034)2042
|
|
3047 |
2883 y FC(b)n(ut)28 b(then)f(we)h(w)o(ould)g(not)f(be)h(able)g(to)g
|
|
3048 |
(use)g(the)g(assumption)f Fz(a)37 b Fo(#)2042 2982 y(\000)2094
|
|
3049 |
2994 y Fu(2)2131 2982 y FC(,)h(which)g(w)o(as)g(vital)h(in)f(the)g
|
|
3050 |
(weak)o(ening)e(lemma)i(to)g(get)g(the)2042 3082 y(lambda-case)27
|
|
3051 |
b(through.)f(In)i(ef)n(fect,)g(we)h(w)o(ould)e(ha)n(v)o(e)h(to)h
|
|
3052 |
(perform)2042 3182 y(renamings.)d(W)m(ith)i(the)f(v)o(ersion)g(of)g
|
|
3053 |
(the)h(rule)f(induction)f(we)i(ha)n(v)o(e)2042 3281 y(gi)n(v)o(en,)18
|
|
3054 |
b(this)j(is)g(unnecessary)-5 b(.)2042 3433 y Fn(3.2)82
|
|
3055 |
b(Substituti)o(vity)19 b(of)h(One-Reduction)2042 3566
|
|
3056 |
y FC(The)34 b(central)h(lemma)f(in)h(proof)e(gi)n(v)o(en)h(in)h([2)o(])
|
|
3057 |
g(for)f(the)h(Church-)2042 3666 y(Rosser)22 b(property)d(of)j
|
|
3058 |
(beta-reduction)c(is)23 b(the)f(substituti)n(vity)f(of)g(the)2042
|
|
3059 |
3765 y @beginspecial @setspecial
|
|
3060 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3061 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3062 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3063 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3064 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3065 |
0 setlinecap stroke grestore end
|
|
3066 |
|
|
3067 |
@endspecial 2106 3776
|
|
3068 |
a Fm(1)2208 3765 y FC(-reduction)29 b(sho)n(wn)i(in)h(\(3\))o(.)g(The)f
|
|
3069 |
(induction)f(principle)h(that)2042 3865 y(comes)20 b(with)g(this)h
|
|
3070 |
(de\002nition)e(is)i(as)g(follo)n(ws:)2186 3988 y Fv(8)p
|
|
3071 |
Fz(M)t(:)h(P)35 b(M)d(M)2186 4111 y Fv(8)p Fz(a)14 b(M)21
|
|
3072 |
b(M)2483 4081 y Fq(0)2506 4111 y Fz(:)2352 4211 y(M)9
|
|
3073 |
b @beginspecial @setspecial
|
|
3074 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3075 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3076 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3077 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3078 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3079 |
0 setlinecap stroke grestore end
|
|
3080 |
|
|
3081 |
@endspecial 2506 4222 a
|
|
3082 |
Fm(1)2608 4211 y Fz(M)2698 4181 y Fq(0)2739 4211 y Fv(^)19
|
|
3083 |
b Fz(P)35 b(M)c(M)3103 4181 y Fq(0)3149 4211 y Fv(\))2352
|
|
3084 |
4311 y Fz(P)k Fo(\()p Fp(lam)7 b Fo(\()p Fz(a;)14 b(M)9
|
|
3085 |
b Fo(\)\))23 b(\()p Fp(lam)8 b Fo(\()p Fz(a;)14 b(M)3274
|
|
3086 |
4281 y Fq(0)3296 4311 y Fo(\)\))2186 4434 y Fv(8)p Fz(M)21
|
|
3087 |
b(M)2425 4404 y Fq(0)2462 4434 y Fz(N)i(N)2628 4404 y
|
|
3088 |
Fq(0)2651 4434 y Fz(:)2352 4534 y(M)9 b @beginspecial
|
|
3089 |
@setspecial
|
|
3090 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3091 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3092 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3093 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3094 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3095 |
0 setlinecap stroke grestore end
|
|
3096 |
|
|
3097 |
@endspecial 2506 4545 a Fm(1)2608 4534 y
|
|
3098 |
Fz(M)2698 4503 y Fq(0)2739 4534 y Fv(^)19 b Fz(P)35 b(M)c(M)3103
|
|
3099 |
4503 y Fq(0)3126 4534 y Fv(^)2352 4633 y Fz(N)9 b @beginspecial
|
|
3100 |
@setspecial
|
|
3101 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3102 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3103 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3104 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3105 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3106 |
0 setlinecap stroke grestore end
|
|
3107 |
|
|
3108 |
@endspecial 2492 4644 a Fm(1)2594 4633 y
|
|
3109 |
Fz(N)2670 4603 y Fq(0)2711 4633 y Fv(^)19 b Fz(P)35 b(N)d(N)3048
|
|
3110 |
4603 y Fq(0)3094 4633 y Fv(\))2352 4733 y Fz(P)j Fo(\()p
|
|
3111 |
Fp(app)7 b Fo(\()p Fz(M)t(;)14 b(N)9 b Fo(\)\))23 b(\()p
|
|
3112 |
Fp(app)7 b Fo(\()p Fz(M)3209 4703 y Fq(0)3232 4733 y
|
|
3113 |
Fz(;)14 b(N)3345 4703 y Fq(0)3368 4733 y Fo(\)\))2186
|
|
3114 |
4856 y Fv(8)p Fz(a)g(M)21 b(M)2483 4826 y Fq(0)2520 4856
|
|
3115 |
y Fz(N)h(N)2685 4826 y Fq(0)2709 4856 y Fz(:)2352 4956
|
|
3116 |
y(M)9 b @beginspecial @setspecial
|
|
3117 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3118 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3119 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3120 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3121 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3122 |
0 setlinecap stroke grestore end
|
|
3123 |
|
|
3124 |
@endspecial 2506 4967
|
|
3125 |
a Fm(1)2608 4956 y Fz(M)2698 4926 y Fq(0)2739 4956 y
|
|
3126 |
Fv(^)19 b Fz(P)35 b(M)c(M)3103 4926 y Fq(0)3126 4956
|
|
3127 |
y Fv(^)2352 5055 y Fz(N)9 b @beginspecial @setspecial
|
|
3128 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3129 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3130 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3131 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3132 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3133 |
0 setlinecap stroke grestore end
|
|
3134 |
|
|
3135 |
|
|
3136 |
@endspecial 2492 5066 a Fm(1)2594 5055 y Fz(N)2670 5025
|
|
3137 |
y Fq(0)2711 5055 y Fv(^)19 b Fz(P)35 b(N)d(N)3048 5025
|
|
3138 |
y Fq(0)3094 5055 y Fv(\))2352 5155 y Fz(P)j Fo(\()p Fp(app)7
|
|
3139 |
b Fo(\()p Fp(lam)g Fo(\()p Fz(a;)14 b(M)9 b Fo(\))p Fz(;)14
|
|
3140 |
b(N)9 b Fo(\)\))23 b(\()p Fz(M)3332 5125 y Fq(0)3355
|
|
3141 |
5155 y Fo([)p Fz(a)g Fo(:=)g Fz(N)3632 5125 y Fq(0)3655
|
|
3142 |
5155 y Fo(]\))p 2186 5205 1566 4 v 2577 5278 a Fz(M)9
|
|
3143 |
b @beginspecial @setspecial
|
|
3144 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3145 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3146 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3147 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3148 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3149 |
0 setlinecap stroke grestore end
|
|
3150 |
|
|
3151 |
@endspecial 2731 5289 a
|
|
3152 |
Fm(1)2833 5278 y Fz(N)55 b Fv(\))46 b Fz(P)35 b(M)d(N)544
|
|
3153 |
b FC(\(12\))p 0 TeXcolorgray 2042 5355 997 3 v 2042 5406
|
|
3154 |
a Fk(3)2079 5430 y Fw(This)16 b(v)o(ersion)h(is)f(similar)h(in)f(style)
|
|
3155 |
h(to)f(the)h(structural)i(induction)f(principle)h(in)d([14)q(].)p
|
|
3156 |
0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray eop end
|
|
3157 |
%%Page: 7 7
|
|
3158 |
TeXDict begin 7 6 bop 0 TeXcolorgray 0 TeXcolorgray 0
|
|
3159 |
TeXcolorgray -150 66 a FC(Our)15 b(technique)f(deri)n(v)o(es)h(the)h
|
|
3160 |
(follo)n(wing)e(ne)n(w)h(induction)f(principle:)p 0 TeXcolorgray
|
|
3161 |
-150 207 a Fn(Theor)o(em)27 b(2.)p 0 TeXcolorgray 46
|
|
3162 |
w Fx(F)-9 b(or)28 b(all)g Fz(\013)p Fx(-equated)e Fz(\025)p
|
|
3163 |
Fx(-terms)i Fz(M)37 b Fx(and)26 b Fz(N)37 b Fx(and)27
|
|
3164 |
b(all)-150 306 y(conte)n(xts)20 b Fz(x)k Fv(2)f Fx(fs-pset,)d(the)h
|
|
3165 |
(following)e(implication)g(holds:)-120 470 y Fv(8)p Fz(x)14
|
|
3166 |
b(M)t(:)23 b(P)35 b(M)c(M)h(x)-120 593 y Fv(8)p Fz(x)14
|
|
3167 |
b(a)g(M)22 b(M)239 563 y Fq(0)262 593 y Fz(:)46 693 y(a)h
|
|
3168 |
Fo(#)g Fz(x)c Fv(^)g Fz(M)9 b @beginspecial @setspecial
|
|
3169 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3170 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3171 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3172 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3173 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3174 |
0 setlinecap stroke grestore end
|
|
3175 |
|
|
3176 |
|
|
3177 |
@endspecial 499 704 a Fe(1)601 693 y Fz(M)691 663 y
|
|
3178 |
Fq(0)732 693 y Fv(^)19 b Fo(\()p Fv(8)p Fz(z)t(:)j(P)35
|
|
3179 |
b(M)c(M)1263 663 y Fq(0)1309 693 y Fz(z)t Fo(\))46 b
|
|
3180 |
Fv(\))46 792 y Fz(P)35 b Fo(\()p Fp(lam)7 b Fo(\()p Fz(a;)14
|
|
3181 |
b(M)9 b Fo(\)\))24 b(\()p Fp(lam)7 b Fo(\()p Fz(a;)14
|
|
3182 |
b(M)968 762 y Fq(0)991 792 y Fo(\)\))23 b Fz(x)-120 892
|
|
3183 |
y Fv(8)p Fz(x)14 b(M)22 b(M)181 862 y Fq(0)218 892 y
|
|
3184 |
Fz(N)g(N)383 862 y Fq(0)406 892 y Fz(:)46 992 y(M)9 b
|
|
3185 |
@beginspecial @setspecial
|
|
3186 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3187 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3188 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3189 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3190 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3191 |
0 setlinecap stroke grestore end
|
|
3192 |
|
|
3193 |
@endspecial 200 1003 a Fe(1)302
|
|
3194 |
992 y Fz(M)392 962 y Fq(0)433 992 y Fv(^)19 b Fo(\()p
|
|
3195 |
Fv(8)p Fz(z)t(:)j(P)35 b(M)c(M)964 962 y Fq(0)1010 992
|
|
3196 |
y Fz(z)t Fo(\))23 b Fv(^)46 1091 y Fz(N)9 b @beginspecial
|
|
3197 |
@setspecial
|
|
3198 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3199 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3200 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3201 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3202 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3203 |
0 setlinecap stroke grestore end
|
|
3204 |
|
|
3205 |
@endspecial 186 1102 a Fe(1)288 1091 y Fz(N)364
|
|
3206 |
1061 y Fq(0)406 1091 y Fv(^)18 b Fo(\()p Fv(8)p Fz(z)t(:)k(P)35
|
|
3207 |
b(N)d(N)909 1061 y Fq(0)955 1091 y Fz(z)t Fo(\))46 b
|
|
3208 |
Fv(\))46 1191 y Fz(P)35 b Fo(\()p Fp(app)7 b Fo(\()p
|
|
3209 |
Fz(M)t(;)14 b(N)9 b Fo(\)\))24 b(\()p Fp(app)6 b Fo(\()p
|
|
3210 |
Fz(M)903 1161 y Fq(0)927 1191 y Fz(;)14 b(N)1040 1161
|
|
3211 |
y Fq(0)1063 1191 y Fo(\)\))23 b Fz(x)-120 1314 y Fv(8)p
|
|
3212 |
Fz(x)14 b(a)g(M)22 b(M)239 1284 y Fq(0)276 1314 y Fz(N)g(N)441
|
|
3213 |
1284 y Fq(0)464 1314 y Fz(:)46 1414 y(a)h Fo(#)g(\()p
|
|
3214 |
Fz(x;)14 b(N)t(;)g(N)505 1384 y Fq(0)529 1414 y Fo(\))19
|
|
3215 |
b Fv(^)g Fz(M)9 b @beginspecial @setspecial
|
|
3216 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3217 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3218 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3219 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3220 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3221 |
0 setlinecap stroke grestore end
|
|
3222 |
|
|
3223 |
@endspecial
|
|
3224 |
808 1425 a Fe(1)909 1414 y Fz(M)999 1384 y Fq(0)1041
|
|
3225 |
1414 y Fv(^)19 b Fo(\()p Fv(8)p Fz(z)t(:)i(P)35 b(M)d(M)1572
|
|
3226 |
1384 y Fq(0)1618 1414 y Fz(z)t Fo(\))22 b Fv(^)46 1513
|
|
3227 |
y Fz(N)9 b @beginspecial @setspecial
|
|
3228 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3229 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3230 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3231 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3232 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3233 |
0 setlinecap stroke grestore end
|
|
3234 |
|
|
3235 |
@endspecial 186
|
|
3236 |
1524 a Fe(1)288 1513 y Fz(N)364 1483 y Fq(0)406 1513
|
|
3237 |
y Fv(^)18 b Fo(\()p Fv(8)p Fz(z)t(:)k(P)35 b(N)d(N)909
|
|
3238 |
1483 y Fq(0)955 1513 y Fz(z)t Fo(\))46 b Fv(\))46 1613
|
|
3239 |
y Fz(P)35 b Fo(\()p Fp(app)7 b Fo(\()p Fp(lam)g Fo(\()p
|
|
3240 |
Fz(a;)14 b(M)9 b Fo(\))p Fz(;)14 b(N)9 b Fo(\)\))23 b(\()p
|
|
3241 |
Fz(M)1026 1583 y Fq(0)1050 1613 y Fo([)p Fz(a)g Fo(:=)f
|
|
3242 |
Fz(N)1326 1583 y Fq(0)1349 1613 y Fo(]\))i Fz(x)p -120
|
|
3243 |
1663 1933 4 v 420 1736 a(M)9 b @beginspecial @setspecial
|
|
3244 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3245 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3246 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3247 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3248 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3249 |
0 setlinecap stroke grestore end
|
|
3250 |
|
|
3251 |
|
|
3252 |
@endspecial 573 1747 a Fe(1)675 1736 y Fz(N)55 b Fv(\))46
|
|
3253 |
b Fz(P)35 b(M)d(N)g(x)p 0 TeXcolorgray -150 1909 a Fx(Pr)l(oof)20
|
|
3254 |
b(\(Sk)o(etc)o(h\).)p 0 TeXcolorgray 27 w FC(The)j(proof)f(is)i
|
|
3255 |
(similar)g(to)g(the)f(proof)f(of)i(Thm.)e(1.)-150 2008
|
|
3256 |
y(W)-7 b(e)24 b(need)e(to)h(strengthen)e(the)i(induction)e(hypothesis)g
|
|
3257 |
(to)i(be)g(of)f(the)-150 2108 y(form:)-29 2280 y Fv(8)p
|
|
3258 |
Fz(\031)16 b(M)23 b(N)f(x)i Fv(2)f Fx(fs-pset)p Fz(:)g
|
|
3259 |
Fo(\()p Fz(:)14 b(:)g(:)p Fo(\))46 b Fv(\))h Fz(P)35
|
|
3260 |
b Fo(\()p Fz(\031)1193 2289 y Fj(\001)1231 2280 y Fz(M)9
|
|
3261 |
b Fo(\))23 b(\()p Fz(\031)1458 2289 y Fj(\001)1497 2280
|
|
3262 |
y Fz(N)9 b Fo(\))23 b Fz(x)h(:)-150 2453 y FC(In)j(the)g(second)g(and)f
|
|
3263 |
(fourth)g(rule)h(we)g(can)g(chose)g(a)h(fresh)f(atom)g
|
|
3264 |
Fz(c)-150 2552 y FC(w)-5 b(.r)g(.t.)24 b Fo(\()p Fz(x;)14
|
|
3265 |
b(N)t(;)g(N)338 2522 y Fq(0)362 2552 y Fo(\))25 b FC(since)f
|
|
3266 |
Fz(\013)p FC(-equated)f Fz(\025)p FC(-terms)i(and)f Fz(x)h
|
|
3267 |
FC(are)f(\002nitely)-150 2652 y(supported.)18 b(W)-7
|
|
3268 |
b(e)21 b(must)g(pro)o(v)o(e)d(equi)n(v)n(ariance)g(for)h
|
|
3269 |
@beginspecial @setspecial
|
|
3270 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3271 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3272 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3273 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3274 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3275 |
0 setlinecap stroke grestore end
|
|
3276 |
|
|
3277 |
@endspecial 1360 2663 a Fm(1)1462
|
|
3278 |
2652 y FC(,)i(namely)203 2824 y Fv(8)p Fz(\031)s(:)h(M)9
|
|
3279 |
b @beginspecial @setspecial
|
|
3280 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3281 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3282 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3283 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3284 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3285 |
0 setlinecap stroke grestore end
|
|
3286 |
|
|
3287 |
@endspecial 499 2835 a Fm(1)601
|
|
3288 |
2824 y Fz(N)55 b Fv(\))46 b Fo(\()p Fz(\031)934 2833
|
|
3289 |
y Fj(\001)973 2824 y Fz(M)9 b Fo(\))p @beginspecial @setspecial
|
|
3290 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3291 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3292 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3293 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3294 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3295 |
0 setlinecap stroke grestore end
|
|
3296 |
|
|
3297 |
|
|
3298 |
@endspecial 1159 2835 a Fm(1)1261 2824 y Fo(\()p Fz(\031)1343
|
|
3299 |
2833 y Fj(\001)1382 2824 y Fz(N)g Fo(\))-150 2997 y FC(in)23
|
|
3300 |
b(order)e(to)i(apply)e(the)i(assumed)f(implications)f(\(this)i(can)f
|
|
3301 |
(be)h(eas-)-150 3096 y(ily)h(established)g(using)g(the)g(original)f
|
|
3302 |
(induction)f(principle)h(sho)n(wn)-150 3196 y(in)d(\(12\))o(\).)p
|
|
3303 |
1782 3196 4 57 v 1786 3143 50 4 v 1786 3196 V 1835 3196
|
|
3304 |
4 57 v -50 3360 a(Using)g(the)g(ne)n(w)g(induction)e(principle)h(to)i
|
|
3305 |
(pro)o(v)o(e)-137 3532 y Fz(M)9 b @beginspecial @setspecial
|
|
3306 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3307 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3308 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3309 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3310 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3311 |
0 setlinecap stroke grestore end
|
|
3312 |
|
|
3313 |
|
|
3314 |
@endspecial 17 3543 a Fm(1)119 3532 y Fz(M)209 3498
|
|
3315 |
y Fq(0)255 3532 y Fv(\))23 b Fz(N)9 b @beginspecial @setspecial
|
|
3316 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3317 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3318 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3319 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3320 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3321 |
0 setlinecap stroke grestore end
|
|
3322 |
|
|
3323 |
|
|
3324 |
@endspecial 501 3543 a Fm(1)603 3532 y Fz(N)679 3498
|
|
3325 |
y Fq(0)725 3532 y Fv(\))23 b Fz(M)9 b Fo([)p Fz(x)23
|
|
3326 |
b Fo(:=)g Fz(N)9 b Fo(])p @beginspecial @setspecial
|
|
3327 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3328 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3329 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3330 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3331 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3332 |
0 setlinecap stroke grestore end
|
|
3333 |
|
|
3334 |
@endspecial
|
|
3335 |
1288 3543 a Fm(1)1390 3532 y Fz(M)1480 3498 y Fq(0)1503
|
|
3336 |
3532 y Fo([)p Fz(x)23 b Fo(:=)g Fz(N)1783 3498 y Fq(0)1806
|
|
3337 |
3532 y Fo(])-150 3705 y FC(leads)c(to)g(a)g(v)o(ery)e(simple)i
|
|
3338 |
(substituti)n(vity)f(proof:)f(all)i(cases)h(are)e(quite)-150
|
|
3339 |
3804 y(simple)26 b(calculations)f(about)g(substitutions.)g(In)g(the)h
|
|
3340 |
(second)f(case,)-150 3904 y(we)36 b(ha)n(v)o(e)g Fz(M)9
|
|
3341 |
b @beginspecial @setspecial
|
|
3342 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3343 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3344 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3345 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3346 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3347 |
0 setlinecap stroke grestore end
|
|
3348 |
|
|
3349 |
@endspecial 328 3915 a Fm(1)430
|
|
3350 |
3904 y Fz(M)520 3874 y Fq(0)579 3904 y FC(being)35 b
|
|
3351 |
Fp(lam)7 b Fo(\()p Fz(a;)14 b(P)e Fo(\))p @beginspecial
|
|
3352 |
@setspecial
|
|
3353 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3354 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3355 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3356 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3357 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3358 |
0 setlinecap stroke grestore end
|
|
3359 |
|
|
3360 |
@endspecial 1213 3915 a Fm(1)1315 3904 y
|
|
3361 |
Fp(lam)6 b Fo(\()p Fz(a;)14 b(P)1630 3874 y Fq(0)1654
|
|
3362 |
3904 y Fo(\))37 b FC(and)-150 4003 y Fz(a)j Fo(#)g(\()p
|
|
3363 |
Fz(x;)14 b(N)t(;)g(N)343 3973 y Fq(0)367 4003 y Fo(\))p
|
|
3364 |
FC(.)30 b(The)f(latter)g(assumption)g(allo)n(ws)g(us)h(to)g(mo)o(v)o(e)
|
|
3365 |
-150 4103 y(the)d(substitutions)f Fo([)p Fz(x)35 b Fo(:=)g
|
|
3366 |
Fz(N)9 b Fo(])27 b FC(and)f Fo([)p Fz(x)35 b Fo(:=)g
|
|
3367 |
Fz(N)1231 4073 y Fq(0)1254 4103 y Fo(])27 b FC(freely)f(under)f(the)
|
|
3368 |
-150 4203 y(binder)19 b(and)h(back)f(out.)-50 4302 y(In)h(the)g(fourth)
|
|
3369 |
e(case,)j(we)f(ha)n(v)o(e)g Fz(M)9 b @beginspecial @setspecial
|
|
3370 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3371 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3372 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3373 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3374 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3375 |
0 setlinecap stroke grestore end
|
|
3376 |
|
|
3377 |
|
|
3378 |
@endspecial 1016 4313 a Fm(1)1118 4302 y Fz(M)1208 4272
|
|
3379 |
y Fq(0)1251 4302 y FC(being)239 4475 y Fp(app)e Fo(\()p
|
|
3380 |
Fp(lam)g Fo(\()p Fz(a;)14 b(P)e Fo(\))p Fz(;)i(Q)p Fo(\))p
|
|
3381 |
@beginspecial @setspecial
|
|
3382 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3383 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3384 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3385 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3386 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3387 |
0 setlinecap stroke grestore end
|
|
3388 |
|
|
3389 |
@endspecial 951 4486 a Fm(1)1053
|
|
3390 |
4475 y Fz(P)e Fo([)p Fz(a)23 b Fo(:=)g Fz(Q)p Fo(])f
|
|
3391 |
Fz(:)-150 4647 y FC(Because)32 b(of)f(the)h(assumption)e(in)i(this)g
|
|
3392 |
(case)g(that)f Fz(a)h FC(is)h(fresh)e(for)-150 4747 y
|
|
3393 |
Fo(\()p Fz(x;)14 b(Q;)g(Q)135 4716 y Fq(0)158 4747 y
|
|
3394 |
Fz(;)g(N)t(;)g(N)379 4716 y Fq(0)402 4747 y Fo(\))21
|
|
3395 |
b FC(we)g(ha)n(v)o(e)26 4914 y Fp(app)6 b Fo(\()p Fp(lam)h
|
|
3396 |
Fo(\()p Fz(a;)14 b(P)e Fo(\))p Fz(;)i(Q)p Fo(\)[)p Fz(x)24
|
|
3397 |
b Fo(:=)f Fz(N)9 b Fo(])23 b(=)275 5014 y Fp(app)6 b
|
|
3398 |
Fo(\()p Fp(lam)h Fo(\()p Fz(a;)14 b(P)e Fo([)p Fz(x)24
|
|
3399 |
b Fo(:=)f Fz(N)9 b Fo(]\))p Fz(;)14 b(Q)p Fo([)p Fz(x)23
|
|
3400 |
b Fo(:=)f Fz(N)9 b Fo(]\))1704 4965 y FC(\(13\))-150
|
|
3401 |
5177 y(and)20 b(kno)n(w)f(by)h(the)g(induction)e(hypotheses)113
|
|
3402 |
5342 y Fz(N)9 b @beginspecial @setspecial
|
|
3403 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3404 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3405 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3406 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3407 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3408 |
0 setlinecap stroke grestore end
|
|
3409 |
|
|
3410 |
@endspecial
|
|
3411 |
253 5353 a Fm(1)355 5342 y Fz(N)431 5312 y Fq(0)500 5342
|
|
3412 |
y Fv(\))46 b Fz(P)12 b Fo([)p Fz(x)24 b Fo(:=)e Fz(N)9
|
|
3413 |
b Fo(])p @beginspecial @setspecial
|
|
3414 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3415 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3416 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3417 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3418 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3419 |
0 setlinecap stroke grestore end
|
|
3420 |
|
|
3421 |
@endspecial 1062
|
|
3422 |
5353 a Fm(1)1163 5342 y Fz(P)1228 5312 y Fq(0)1251 5342
|
|
3423 |
y Fo([)p Fz(x)24 b Fo(:=)f Fz(N)1532 5312 y Fq(0)1555
|
|
3424 |
5342 y Fo(])113 5441 y Fz(N)9 b @beginspecial @setspecial
|
|
3425 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3426 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3427 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3428 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3429 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3430 |
0 setlinecap stroke grestore end
|
|
3431 |
|
|
3432 |
|
|
3433 |
@endspecial 253 5452 a Fm(1)355 5441 y Fz(N)431 5411
|
|
3434 |
y Fq(0)500 5441 y Fv(\))46 b Fz(Q)p Fo([)p Fz(x)23 b
|
|
3435 |
Fo(:=)g Fz(N)9 b Fo(])p @beginspecial @setspecial
|
|
3436 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3437 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3438 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3439 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3440 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3441 |
0 setlinecap stroke grestore end
|
|
3442 |
|
|
3443 |
@endspecial
|
|
3444 |
1062 5452 a Fm(1)1164 5441 y Fz(Q)1230 5411 y Fq(0)1253
|
|
3445 |
5441 y Fo([)p Fz(x)24 b Fo(:=)e Fz(N)1533 5411 y Fq(0)1556
|
|
3446 |
5441 y Fo(])p 0 TeXcolorgray 0 TeXcolorgray 2042 66 a
|
|
3447 |
FC(\(we)16 b(also)h(ha)n(v)o(e)f Fz(N)9 b @beginspecial
|
|
3448 |
@setspecial
|
|
3449 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3450 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3451 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3452 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3453 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3454 |
0 setlinecap stroke grestore end
|
|
3455 |
|
|
3456 |
@endspecial 2645 77 a Fm(1)2747 66 y Fz(N)2823
|
|
3457 |
36 y Fq(0)2846 66 y FC(\).)17 b(The)f(de\002nition)g(of)g
|
|
3458 |
@beginspecial @setspecial
|
|
3459 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3460 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3461 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3462 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3463 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3464 |
0 setlinecap stroke grestore end
|
|
3465 |
|
|
3466 |
@endspecial 3544 77 a Fm(1)3663
|
|
3467 |
66 y FC(tells)i(us)f(that)2042 166 y(the)j(right-hand)e(side)i(of)g
|
|
3468 |
(\(13\))f(reduces)g(to:)2511 347 y Fz(P)2576 312 y Fq(0)2599
|
|
3469 |
347 y Fo([)p Fz(x)24 b Fo(:=)f Fz(N)2880 312 y Fq(0)2903
|
|
3470 |
347 y Fo(][)p Fz(a)g Fo(:=)f Fz(Q)3192 312 y Fq(0)3215
|
|
3471 |
347 y Fo([)p Fz(x)i Fo(:=)f Fz(N)3496 312 y Fq(0)3519
|
|
3472 |
347 y Fo(]])2042 527 y FC(No)n(w)29 b(the)g(freshness)g(constraints)f
|
|
3473 |
Fz(a)40 b Fo(#)g Fz(x)30 b FC(and)f Fz(a)40 b Fo(#)g
|
|
3474 |
Fz(N)3779 497 y Fq(0)3831 527 y FC(match)2042 627 y(e)o(xactly)18
|
|
3475 |
b(the)h(pre-conditions)d(for)j(the)g(substitution)f(lemma,)g(which)2042
|
|
3476 |
727 y(gi)n(v)o(es)h(us)2651 826 y Fz(P)2716 792 y Fq(0)2740
|
|
3477 |
826 y Fo([)p Fz(a)k Fo(:=)f Fz(Q)3006 792 y Fq(0)3029
|
|
3478 |
826 y Fo(][)p Fz(x)i Fo(:=)e Fz(N)3332 792 y Fq(0)3356
|
|
3479 |
826 y Fo(])h Fz(:)2042 975 y FC(This)d(completes)g(the)g(proof.)2042
|
|
3480 |
1173 y FA(4.)99 b(Related)26 b(W)-7 b(ork)2042 1306 y
|
|
3481 |
FC(The)15 b(prettiest)h(formal)f(proof)g(of)g(the)h(weak)o(ening)f
|
|
3482 |
(lemma)g(we)i(found)2042 1406 y(in)k(the)f(e)o(xisting)g(literature)g
|
|
3483 |
(is)i(that)f(in)g([12)n(].)g(Pitts')-5 b(s)22 b(proof)e(uses)h(the)2042
|
|
3484 |
1505 y(equi)n(v)n(ariance)h(property)g(of)i(the)h(typing)e(relation,)h
|
|
3485 |
(and)g(includes)f(a)2042 1605 y(renaming)i(step)i(using)f
|
|
3486 |
(permutations.)f(Because)i(of)f(the)h(pleasant)2042 1704
|
|
3487 |
y(properties)16 b(that)j(permutations)d(enjo)o(y)h(\(the)o(y)g(are)h
|
|
3488 |
(bijecti)n(v)o(e)f(renam-)2042 1804 y(ings,)29 b(in)h(contrast)f(to)h
|
|
3489 |
(substitutions)g(which)f(might)g(identify)g(tw)o(o)2042
|
|
3490 |
1904 y(names\),)c(the)i(renaming)d(can)i(be)g(done)g(with)g(minimal)g
|
|
3491 |
(o)o(v)o(erhead.)2042 2003 y(Our)18 b(contrib)n(ution)f(is)i(that)g(we)
|
|
3492 |
g(ha)n(v)o(e)f(ef)n(fecti)n(v)o(ely)f(b)n(uilt)i(this)g(renam-)2042
|
|
3493 |
2103 y(ing)i(into)g(the)g(induction)f(principles)g(once)h(and)g(for)f
|
|
3494 |
(all.)i(Proofs)f(us-)2042 2203 y(ing)31 b(our)f(principles)h(do)g(not)g
|
|
3495 |
(need)g(to)g(perform)e(e)o(xplicit)i(renam-)2042 2302
|
|
3496 |
y(ing)22 b(steps)i(at)f(all.)g(Furthermore,)d(we)k(ha)n(v)o(e)e
|
|
3497 |
(created)g(a)h(full)g(reason-)2042 2402 y(ing)g(frame)n(w)o(ork)e(in)j
|
|
3498 |
(HOL4)f(and)g(Isabelle/HOL)g(in)h(which)f(results)2042
|
|
3499 |
2501 y(about)i(calculi)i(with)f(binders)g(can)g(be)g(pro)o(v)o(ed)f(at)
|
|
3500 |
i(least)g(as)g(con)m(v)o(e-)2042 2601 y(niently)19 b(as)i(in)f(other)g
|
|
3501 |
(mechanisations.)2141 2701 y(Some)n(what)g(similar)h(to)f(our)g
|
|
3502 |
(approach)e(is)k(the)e(w)o(ork)g(of)g(Pollack)2042 2800
|
|
3503 |
y(and)f(McKinna)f([9)o(].)i(Starting)e(from)h(the)g(standard)f
|
|
3504 |
(induction)g(prin-)2042 2900 y(ciple)25 b(that)h(is)h(associated)e
|
|
3505 |
(with)h(an)g(inducti)n(v)o(e)e(de\002nition,)g(we)i(de-)2042
|
|
3506 |
3000 y(ri)n(v)o(ed)20 b(an)g(induction)f(principle)h(that)h(allo)n(ws)g
|
|
3507 |
(emulation)f(of)g(Baren-)2042 3099 y(dre)o(gt')-5 b(s)27
|
|
3508 |
b(v)n(ariable)h(con)m(v)o(ention.)d(Pollack)i(and)h(McKinna,)f(in)i
|
|
3509 |
(con-)2042 3199 y(trast,)21 b(ga)n(v)o(e)e(a)i(\223weak\224)f(and)g
|
|
3510 |
(\223strong\224)f(v)o(ersion)g(of)h(the)h(typing)e(rela-)2042
|
|
3511 |
3298 y(tion.)c(These)g(v)o(ersions)f(dif)n(fer)g(in)i(the)f(w)o(ay)h
|
|
3512 |
(the)f(rule)g(for)g(abstractions)2042 3398 y(is)21 b(stated:)2318
|
|
3513 |
3546 y Fz(x)i Fo(#)h Fz(M)91 b Fo(\()p Fz(x)24 b Fo(:)f
|
|
3514 |
Fz(\034)5 b(;)14 b Fo(\000\))23 b Fv(`)g Fz(M)9 b Fo([)p
|
|
3515 |
Fz(y)26 b Fo(:=)c Fz(x)p Fo(])i(:)f Fz(\033)p 2318 3587
|
|
3516 |
1224 4 v 2522 3666 a Fo(\000)g Fv(`)g Fp(lam)6 b Fo(\()p
|
|
3517 |
Fz(y)s(;)14 b(M)9 b Fo(\))23 b(:)g Fz(\034)33 b Fv(!)23
|
|
3518 |
b Fz(\033)3583 3615 y FC(weak)2228 3834 y Fv(8)p Fz(x:)f(x)i
|
|
3519 |
Fo(#)f(\000)g Fv(\))g Fo(\()p Fz(x)h Fo(:)f Fz(\034)5
|
|
3520 |
b(;)14 b Fo(\000\))23 b Fv(`)g Fz(M)9 b Fo([)p Fz(y)26
|
|
3521 |
b Fo(:=)c Fz(x)p Fo(])i(:)f Fz(\033)p 2228 3875 1372
|
|
3522 |
4 v 2506 3954 a Fo(\000)g Fv(`)f Fp(lam)7 b Fo(\()p Fz(y)s(;)14
|
|
3523 |
b(M)9 b Fo(\))23 b(:)g Fz(\034)33 b Fv(!)23 b Fz(\033)3641
|
|
3524 |
3890 y FC(strong)2042 4102 y(The)o(y)d(then)g(sho)n(wed)g(that)h(both)f
|
|
3525 |
(v)o(ersions)g(deri)n(v)o(e)f(the)i(same)g(typing)2042
|
|
3526 |
4202 y(judgements.)16 b(W)m(ith)i(this)h(the)o(y)e(pro)o(v)o(ed)f(the)i
|
|
3527 |
(weak)o(ening)e(lemma)i(us-)2042 4301 y(ing)g(the)i(\223strong\224)d(v)
|
|
3528 |
o(ersion)h(of)h(the)g(principle,)f(while)h(kno)n(wing)e(that)2042
|
|
3529 |
4401 y(the)i(result)g(held)f(for)h(the)g(\223weak\224)f(relation)g(as)i
|
|
3530 |
(well.)f(The)g(main)f(dif-)2042 4501 y(ference)30 b(between)g(this)h
|
|
3531 |
(and)g(our)f(w)o(ork)g(seems)h(to)g(be)g(of)g(con)m(v)o(e-)2042
|
|
3532 |
4600 y(nience:)g(we)h(can)f(relati)n(v)o(ely)g(easily)h(deri)n(v)o(e,)e
|
|
3533 |
(in)i(a)g(uniform)d(w)o(ay)-5 b(,)2042 4700 y(an)30 b(induction)e
|
|
3534 |
(principle)h(for)g(equi)n(v)n(araint)f(relations)i(that)g(allo)n(ws)
|
|
3535 |
2042 4799 y(the)c(v)n(ariable)f(con)m(v)o(ention)e(\(we)j(ha)n(v)o(e)f
|
|
3536 |
(illustrated)h(this)g(point)g(with)2042 4899 y(tw)o(o)g(e)o(xamples\).)
|
|
3537 |
f(Achie)n(ving)f(the)j(same)f(uniformity)e(in)i(the)g(style)2042
|
|
3538 |
4999 y(of)20 b(McKinna)f(and)h(Pollack)f(does)h(not)g(seem)h(as)g
|
|
3539 |
(straightforw)o(ard.)2042 5197 y FA(5.)99 b(Conclusion)2042
|
|
3540 |
5330 y FC(In)21 b(the)j(P)t(O)t(P)t(L)t Fw(M)t(A)t(R)t(K)h
|
|
3541 |
FC(Challenge)c([1)o(],)h(the)g(proof)e(of)h(the)h(weak)o(en-)2042
|
|
3542 |
5430 y(ing)h(lemma)g(is)h(described)f(as)h(a)g(\223straightforw)o(ard)d
|
|
3543 |
(induction\224.)g(In)p 0 TeXcolorgray 0 TeXcolorgray
|
|
3544 |
eop end
|
|
3545 |
%%Page: 8 8
|
|
3546 |
TeXDict begin 8 7 bop 0 TeXcolorgray 0 TeXcolorgray 0
|
|
3547 |
TeXcolorgray -150 66 a FC(f)o(act,)23 b(mechanising)f(this)i(informal)e
|
|
3548 |
(proof)g(is)j Fx(not)g FC(straightforw)o(ard)-150 166
|
|
3549 |
y(at)30 b(all)h(\(see)f(for)f(e)o(xample)g([9)o(,)h(4,)g(12)o(]\).)f(W)
|
|
3550 |
-7 b(e)31 b(ha)n(v)o(e)f(gi)n(v)o(en)e(a)j(no)o(v)o(el)-150
|
|
3551 |
266 y(rule)g(induction)e(principle)h(for)h(the)g(typing)f(relation)h
|
|
3552 |
(that)g(mak)o(es)-150 365 y(pro)o(ving)h(the)j(weak)o(ening)e(lemma)h
|
|
3553 |
(mechanically)f(as)j(simple)e(as)-150 465 y(the)25 b(performing)c(the)k
|
|
3554 |
(informal)e(proof.)g(W)-7 b(e)26 b(ha)n(v)o(e)e(also)g(illustrated)-150
|
|
3555 |
565 y(our)h(technique)g(with)h(another)e(typical)i(proof)e(tak)o(en)i
|
|
3556 |
(from)e(the)i Fz(\025)p FC(-)-150 664 y(calculus.)20
|
|
3557 |
b(W)-7 b(e)23 b(see)e(no)g(problems)f(in)h(e)o(xtending)e(this)i
|
|
3558 |
(technique)f(to)-150 764 y(other)f(calculi)h(with)h(bound)d(names.)-50
|
|
3559 |
863 y(One)27 b(remaining)f(challenge)g(is)j(to)e(pro)o(vide)f(machine)g
|
|
3560 |
(support)-150 963 y(to)19 b(deri)n(v)o(e)f(our)g(ne)n(w)h(rule)f
|
|
3561 |
(induction)g(principles)g(automatically)-5 b(.)17 b(At)-150
|
|
3562 |
1063 y(the)k(moment,)f(we)h(ha)n(v)o(e)f(pro)o(v)o(ed)f(the)i
|
|
3563 |
(principles)f(manually)-5 b(.)19 b(There)-150 1162 y(is)i(clearly)e(a)h
|
|
3564 |
(pattern)f(in)h(the)g(statement)f(of)h(the)f(re)n(vised)g(principles,)
|
|
3565 |
-150 1262 y(and)h(in)g(their)g(proof:)p 0 TeXcolorgray
|
|
3566 |
-110 1408 a Fd(\017)p 0 TeXcolorgray -42 1417 a FC(bound)c(v)n
|
|
3567 |
(ariables)h(that)h(appear)f(in)h(rules)g(can)g(be)g(assumed)f(to)h(be)
|
|
3568 |
-42 1517 y(fresh)e(with)i(respect)e(both)h(to)g(free)f(v)n(ariables)h
|
|
3569 |
(in)g(those)g(rules)g(and)-42 1617 y(with)j(respect)g(to)h(an)f
|
|
3570 |
(additional)e(\223conte)o(xt\224)h(parameter;)g(and)p
|
|
3571 |
0 TeXcolorgray -110 1740 a Fd(\017)p 0 TeXcolorgray -42
|
|
3572 |
1749 a FC(proofs)h(proceed)g(by)h(sho)n(wing)g(equi)n(v)n(ariance)e
|
|
3573 |
(for)i(the)g(relation,)-42 1849 y(and)j(then)h(using)f(the)h(original)e
|
|
3574 |
(induction)h(principles)f(to)i(sho)n(w)-42 1949 y(that)e(an)f
|
|
3575 |
(induction)f(parameter)g Fz(P)34 b FC(holds)22 b(for)g(all)h(possible)g
|
|
3576 |
(per)n(-)-42 2048 y(mutations)c(of)h(its)h(parameters.)-150
|
|
3577 |
2204 y(The)39 b(\002rst)g(element)g(of)g(the)g(pattern)f(is)i(not)e
|
|
3578 |
(yet)h(rigorous.)e(F)o(or)-150 2303 y(e)o(xample,)24
|
|
3579 |
b(in)i(the)f(last)i(rule)e(of)g(the)h(principle)e(in)i(Theorem)e(2,)h
|
|
3580 |
(the)-150 2403 y(bound)16 b(atom)i Fz(a)g FC(can)g(be)f(assumed)h
|
|
3581 |
(fresh)f(with)h(respect)g(to)g(v)n(ariables)-150 2503
|
|
3582 |
y Fz(N)42 b FC(and)33 b Fz(N)189 2472 y Fq(0)212 2503
|
|
3583 |
y FC(,)g(b)n(ut)h(not)e Fz(M)43 b FC(and)32 b Fz(M)911
|
|
3584 |
2472 y Fq(0)934 2503 y FC(.)h(As)h Fz(a)g FC(binds)e(o)o(v)o(er)g
|
|
3585 |
Fz(M)42 b FC(it)34 b(is)-150 2602 y(reasonable)e(that)h(it)h(not)f(be)g
|
|
3586 |
(forced)f(to)h(be)h(free)e(there,)h(b)n(ut)g(it)h(is)-150
|
|
3587 |
2702 y(not)d(syntactically)g(clear)h(why)f Fz(M)899 2672
|
|
3588 |
y Fq(0)954 2702 y FC(is)i(e)o(xcluded.)d(Semantically)-5
|
|
3589 |
b(,)-150 2801 y(it)23 b Fx(is)f FC(clear:)g Fz(M)9 b
|
|
3590 |
@beginspecial @setspecial
|
|
3591 |
tx@Dict begin STP newpath 0.28453 SLW 0 setgray /ArrowA { moveto
|
|
3592 |
} def /ArrowB { BeginArrow 1. 1. scale false 0.6 1.4 1.5 2. Arrow
|
|
3593 |
0 h T gsave newpath false 0.6 1.4 1.5 2. Arrow CP grestore CP newpath
|
|
3594 |
moveto 2 copy L stroke moveto EndArrow } def [ 17.0 3.15005 3.0 3.15005
|
|
3595 |
/Lineto /lineto load def false Line gsave 0.28453 SLW 0 setgray
|
|
3596 |
0 setlinecap stroke grestore end
|
|
3597 |
|
|
3598 |
@endspecial 357 2812 a Fm(1)459
|
|
3599 |
2801 y Fz(M)549 2771 y Fq(0)572 2801 y FC(,)22 b(and)f(so)i
|
|
3600 |
Fz(a)f FC(may)f(also)i(appear)d(in)i Fz(M)1662 2771 y
|
|
3601 |
Fq(0)1685 2801 y FC(.)g(F)o(or)-150 2901 y(arbitrary)28
|
|
3602 |
b(relations,)h(this)i(may)e(not)h(al)o(w)o(ays)g(hold,)f(and)g(we)i
|
|
3603 |
(may)-150 3001 y(ha)n(v)o(e)20 b(to)g(content)f(ourselv)o(es)g(with)i
|
|
3604 |
(syntactic)e(heuristics.)-50 3100 y(In)24 b(an)o(y)g(case,)i(requiring)
|
|
3605 |
d(one)h(simple,)h(stereotyped)e(induction)-150 3200 y(in)k(order)e(to)i
|
|
3606 |
(reproduce)e(the)h(ease-of-use)g(of)g(Barendre)o(gt')-5
|
|
3607 |
b(s)26 b(V)-9 b(ari-)-150 3300 y(able)27 b(Con)m(v)o(ention)e(seems)i
|
|
3608 |
(a)h(v)o(ery)e(small)h(price)g(to)g(pay)-5 b(.)26 b(W)-7
|
|
3609 |
b(e)29 b(ha)n(v)o(e)-150 3399 y(sho)n(wn)j(this)i(by)e(implementing)f
|
|
3610 |
(our)h(results)i(in)f(HOL4)g(and)f(Is-)-150 3499 y(abelle/HOL.)-150
|
|
3611 |
3677 y Fy(Ac)o(kno)n(wledgements)82 b FC(W)-7 b(e)24
|
|
3612 |
b(are)e(v)o(ery)g(grateful)f(to)i(Andre)n(w)f(Pitts,)-150
|
|
3613 |
3776 y(for)g(the)h(man)o(y)f(discussions)h(with)g(him)g(on)g(the)g
|
|
3614 |
(subject)g(of)f(the)i(pa-)-150 3876 y(per)m(,)i(and)f(to)i(Ren)5
|
|
3615 |
b(\264)-33 b(e)27 b(V)-9 b(ester)o(gaard,)23 b(who)j(pro)o(vided)e(us)j
|
|
3616 |
(with)g(e)o(xcel-)-150 3976 y(lent)h(w)o(orking)f(conditions)g(at)h
|
|
3617 |
(the)h(recent)e(\223Binding)g(W)-7 b(orkshop\224)-150
|
|
3618 |
4075 y(at)22 b(J)-5 b(AIST)f(.)22 b(The)f(\002rst)i(author)d(is)j
|
|
3619 |
(supported)d(by)h(a)h(fello)n(wship)f(from)-150 4175
|
|
3620 |
y(the)f(Ale)o(xander)n(-v)n(on-Humboldt)15 b(F)o(oundation.)-150
|
|
3621 |
4417 y FA(Refer)n(ences)p 0 TeXcolorgray -99 4541 a Fc([1])p
|
|
3622 |
0 TeXcolorgray 29 w(B.)i(E.)f(A)-7 b(ydemir)m(,)17 b(A.)f(Bohannon,)j
|
|
3623 |
(M.)e(F)o(airbairn,)f(J.)g(N.)h(F)o(oster)m(,)f(B.)g(C.)17
|
|
3624 |
4633 y(Pierce,)g(P)-8 b(.)15 b(Se)n(well,)g(D.)h(Vytiniotis,)g(G.)f(W)
|
|
3625 |
-6 b(ashb)o(urn,)17 b(S.)e(W)-6 b(eirich,)16 b(and)17
|
|
3626 |
4724 y(S.)23 b(Zdance)n(wic.)42 b(Mechanized)26 b(metatheory)f(for)e
|
|
3627 |
(the)h(masses:)f(the)17 4815 y(POPLmark)18 b(challenge.)28
|
|
3628 |
b(In)19 b(Hurd)g(and)h(Melham)g([8].)p 0 TeXcolorgray
|
|
3629 |
-99 4940 a([2])p 0 TeXcolorgray 29 w(H.)e(Barendre)o(gt.)25
|
|
3630 |
b Fb(The)18 b(Lambda)h(Calculus:)f(its)g(Syntax)h(and)f(Seman-)17
|
|
3631 |
5031 y(tics)p Fc(,)j(v)o(olume)h(103)g(of)g Fb(Studies)g(in)f(Lo)o(gic)
|
|
3632 |
h(and)g(the)g(F)-8 b(oundations)23 b(of)17 5122 y(Mathematics)p
|
|
3633 |
Fc(.)28 b(North-Holland,)19 b(1981.)p 0 TeXcolorgray
|
|
3634 |
-99 5247 a([3])p 0 TeXcolorgray 29 w(M.)k(J.)g(Gabbay)h(and)g(A.)f(M.)g
|
|
3635 |
(Pitts.)39 b(A)23 b(ne)n(w)h(approach)g(to)f(abstract)17
|
|
3636 |
5338 y(syntax)e(with)f(v)n(ariable)h(binding.)31 b Fb(F)-8
|
|
3637 |
b(ormal)20 b(Aspects)g(of)g(Computing)p Fc(,)17 5430
|
|
3638 |
y(13:341\226363,)i(2001.)p 0 TeXcolorgray 0 TeXcolorgray
|
|
3639 |
0 TeXcolorgray 2093 66 a([4])p 0 TeXcolorgray 29 w(J.)29
|
|
3640 |
b(Gallier)l(.)61 b Fb(Lo)o(gic)30 b(for)g(Computer)g(Science:)h(F)-8
|
|
3641 |
b(oundations)31 b(of)2209 158 y(A)o(utomatic)19 b(Theor)m(em)g(Pr)m(o)o
|
|
3642 |
(ving)p Fc(.)27 b(Harper)19 b(&)g(Ro)n(w)-5 b(,)19 b(1986.)p
|
|
3643 |
0 TeXcolorgray 2093 282 a([5])p 0 TeXcolorgray 29 w(A.)h(D.)f(Gordon.)
|
|
3644 |
32 b(A)20 b(mechanisation)i(of)e(name-carrying)h(syntax)g(up)2209
|
|
3645 |
374 y(to)i(alpha-con)m(v)o(ersion.)41 b(In)23 b Fb(Pr)m(oceedings)g(of)
|
|
3646 |
g(Higher)o(-or)m(der)h(Lo)o(gic)2209 465 y(Theor)m(em)j(Pr)m(o)o(ving)g
|
|
3647 |
(and)g(its)f(Applications)h(\(HUG'93\))p Fc(,)f(v)o(olume)2209
|
|
3648 |
556 y(780)d(of)g Fb(Lectur)m(e)f(Notes)g(in)g(Computer)h(Science)p
|
|
3649 |
Fc(,)g(pages)g(414\226426.)2209 648 y(Springer)m(,)c(1994.)p
|
|
3650 |
0 TeXcolorgray 2093 772 a([6])p 0 TeXcolorgray 29 w(A.)h(D.)g(Gordon)h
|
|
3651 |
(and)g(T)-6 b(.)20 b(Melham.)33 b(Fi)n(v)o(e)20 b(axioms)h(of)f(alpha)h
|
|
3652 |
(con)m(v)o(er)o(-)2209 863 y(sion.)42 b(In)23 b(J.)g(v)o(on)h(Wright,)e
|
|
3653 |
(J.)h(Grundy)-5 b(,)25 b(and)f(J.)f(Harrison,)g(editors,)2209
|
|
3654 |
955 y Fb(Theor)m(em)f(Pr)m(o)o(ving)f(in)g(Higher)h(Or)m(der)g(Lo)o
|
|
3655 |
(gics:)f(9th)h(International)2209 1046 y(Confer)m(ence)o(,)j(TPHOLs'96)
|
|
3656 |
p Fc(,)d(v)o(olume)h(1125)i(of)e Fb(Lectur)m(e)h(Notes)f(in)2209
|
|
3657 |
1137 y(Computer)d(Science)p Fc(,)f(pages)h(173\226190.)h(Springer)o(-V)
|
|
3658 |
-8 b(erlag,)18 b(1996.)p 0 TeXcolorgray 2093 1262 a([7])p
|
|
3659 |
0 TeXcolorgray 29 w(P)-8 b(.)22 b(Homeier)l(.)41 b(A)23
|
|
3660 |
b(proof)g(of)h(the)f(Church-Rosser)h(theorem)g(for)f(the)2209
|
|
3661 |
1353 y(lambda)30 b(calculus)g(in)f(higher)h(order)f(logic.)60
|
|
3662 |
b(In)29 b(R.)f(J.)h(Boulton)2209 1445 y(and)35 b(P)-8
|
|
3663 |
b(.)34 b(B.)g(Jackson,)h(editors,)g Fb(TPHOLs'01:)e(Supplemental)2209
|
|
3664 |
1536 y(Pr)m(oceedings)p Fc(,)k(pages)g(207\226222.)h(Di)n(vision)e(of)g
|
|
3665 |
(Informatics,)2209 1627 y(Uni)n(v)o(ersity)30 b(of)f(Edinb)o(ur)o(gh,)h
|
|
3666 |
(September)g(2001.)62 b(A)-6 b(v)n(ailable)30 b(as)2209
|
|
3667 |
1719 y(Informatics)19 b(Research)h(Report)f(EDI-INF-RR-0046.)p
|
|
3668 |
0 TeXcolorgray 2093 1843 a([8])p 0 TeXcolorgray 29 w(J.)h(Hurd)g(and)h
|
|
3669 |
(T)-6 b(.)20 b(Melham,)g(editors.)31 b Fb(Theor)m(em)21
|
|
3670 |
b(Pr)m(o)o(ving)f(in)g(Higher)2209 1934 y(Or)m(der)k(Lo)o(gics,)f(18th)
|
|
3671 |
h(International)g(Confer)m(ence)p Fc(,)g(v)o(olume)g(3603)2209
|
|
3672 |
2026 y(of)19 b Fb(Lectur)m(e)g(Notes)g(in)g(Computer)h(Science)p
|
|
3673 |
Fc(.)f(Springer)m(,)g(2005.)p 0 TeXcolorgray 2093 2150
|
|
3674 |
a([9])p 0 TeXcolorgray 29 w(J.)k(McKinna)h(and)g(R.)f(Pollack.)41
|
|
3675 |
b(Some)23 b(type)h(theory)g(and)g(lambda)2209 2242 y(calculus)d
|
|
3676 |
(formalised.)30 b Fb(J)n(ournal)21 b(of)f(A)o(utomated)g(Reasoning)p
|
|
3677 |
Fc(,)g(23\(1-)2209 2333 y(4\),)f(1999.)p 0 TeXcolorgray
|
|
3678 |
2056 2457 a([10])p 0 TeXcolorgray 29 w(M.)24 b(Norrish.)44
|
|
3679 |
b(Mechanising)26 b Fa(\025)p Fc(-calculus)f(using)g(a)f(classical)g
|
|
3680 |
(\002rst)2209 2549 y(order)g(theory)g(of)f(terms)g(with)f(permutation.)
|
|
3681 |
42 b Fb(Higher)23 b(Or)m(der)h(and)2209 2640 y(Symbolic)c(Computation)p
|
|
3682 |
Fc(.)28 b(T)-6 b(o)18 b(appear)l(.)p 0 TeXcolorgray 2056
|
|
3683 |
2765 a([11])p 0 TeXcolorgray 29 w(B.)27 b(C.)f(Pierce.)54
|
|
3684 |
b Fb(T)-6 b(ypes)28 b(and)g(Pr)m(o)o(gr)o(amming)g(Langua)o(g)o(es)p
|
|
3685 |
Fc(.)56 b(MIT)2209 2856 y(Press,)18 b(2002.)p 0 TeXcolorgray
|
|
3686 |
2056 2980 a([12])p 0 TeXcolorgray 29 w(A.)24 b(M.)h(Pitts.)45
|
|
3687 |
b(Nominal)25 b(logic:)g(A)f(\002rst)g(order)i(theory)f(of)g(names)2209
|
|
3688 |
3072 y(and)e(binding.)40 b(In)23 b Fb(Theor)m(etical)g(Aspects)f(of)h
|
|
3689 |
(Computer)g(Softwar)m(e)o(,)2209 3163 y(4th)k(International)h
|
|
3690 |
(Symposium,)g(T)l(A)n(CS)e(2001,)i(Sendai,)g(J)m(apan,)2209
|
|
3691 |
3254 y(October)22 b(29-31,)h(2001,)f(Pr)m(oceedings)p
|
|
3692 |
Fc(,)h(v)o(olume)f(2215)h(of)e Fb(Lectur)m(e)2209 3346
|
|
3693 |
y(Notes)d(in)g(Computer)h(Science)p Fc(,)f(pages)h(219\226242.)h
|
|
3694 |
(Springer)o(-V)-8 b(erlag,)2209 3437 y(2001.)p 0 TeXcolorgray
|
|
3695 |
2056 3562 a([13])p 0 TeXcolorgray 29 w(A.)34 b(M.)g(Pitts.)74
|
|
3696 |
b(Alpha-structural)35 b(recursion)f(and)h(induction)2209
|
|
3697 |
3653 y(\(e)o(xtended)28 b(abstract\).)52 b(In)27 b(Hurd)g(and)g(Melham)
|
|
3698 |
h([8],)e(pages)h(17\226)2209 3744 y(34.)p 0 TeXcolorgray
|
|
3699 |
2056 3869 a([14])p 0 TeXcolorgray 29 w(C.)35 b(Urban)h(and)g(C.)f(T)-6
|
|
3700 |
b(asson.)81 b(Nominal)36 b(techniques)h(in)e(Is-)2209
|
|
3701 |
3960 y(abelle/HOL.)41 b(In)23 b Fb(Pr)m(oc.)g(of)g(the)g(20th)h
|
|
3702 |
(International)h(Confer)m(ence)2209 4051 y(on)f(A)o(utomated)f
|
|
3703 |
(Deduction)i(\(CADE\))p Fc(,)c(v)o(olume)j(3632)g(of)g
|
|
3704 |
Fb(Lectur)m(e)2209 4143 y(Notes)19 b(in)g(Computer)g(Science)p
|
|
3705 |
Fc(,)h(pages)g(38\22653,)g(2005.)p 0 TeXcolorgray 0 TeXcolorgray
|
|
3706 |
eop end
|
|
3707 |
%%Trailer
|
|
3708 |
|
|
3709 |
userdict /end-hook known{end-hook}if
|
|
3710 |
%%EOF
|