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Diffstat (limited to 'doc/faq/axioms.eps')
| -rw-r--r-- | doc/faq/axioms.eps | 413 |
1 files changed, 226 insertions, 187 deletions
diff --git a/doc/faq/axioms.eps b/doc/faq/axioms.eps index 3f3c01c43..836afc347 100644 --- a/doc/faq/axioms.eps +++ b/doc/faq/axioms.eps @@ -1,11 +1,11 @@ -%!PS-Adobe-2.0 EPSF-2.0 +%!PS-Adobe-3.0 EPSF-3.0 %%Title: axioms.fig -%%Creator: fig2dev Version 3.2 Patchlevel 4 -%%CreationDate: Wed May 5 18:30:03 2004 -%%For: herbelin@limoux.polytechnique.fr (Hugo Herbelin) -%%BoundingBox: 0 0 437 372 -%%Magnification: 1.0000 +%%Creator: fig2dev Version 3.2 Patchlevel 5e +%%CreationDate: Sun Jul 26 08:23:54 2015 +%%BoundingBox: 0 0 647 514 +%Magnification: 1.0000 %%EndComments +%%BeginProlog /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put @@ -44,10 +44,6 @@ $F2psDict /mtrx matrix put /col31 {1.000 0.840 0.000 srgb} bind def end -save -newpath 0 372 moveto 0 0 lineto 437 0 lineto 437 372 lineto closepath clip newpath --90.0 435.2 translate -1 -1 scale /cp {closepath} bind def /ef {eofill} bind def @@ -80,51 +76,25 @@ newpath 0 372 moveto 0 0 lineto 437 0 lineto 437 372 lineto closepath clip newpa bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def -/reencdict 12 dict def /ReEncode { reencdict begin -/newcodesandnames exch def /newfontname exch def /basefontname exch def -/basefontdict basefontname findfont def /newfont basefontdict maxlength dict def -basefontdict { exch dup /FID ne { dup /Encoding eq -{ exch dup length array copy newfont 3 1 roll put } -{ exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall -newfont /FontName newfontname put newcodesandnames aload pop -128 1 255 { newfont /Encoding get exch /.notdef put } for -newcodesandnames length 2 idiv { newfont /Encoding get 3 1 roll put } repeat -newfontname newfont definefont pop end } def -/isovec [ -8#055 /minus 8#200 /grave 8#201 /acute 8#202 /circumflex 8#203 /tilde -8#204 /macron 8#205 /breve 8#206 /dotaccent 8#207 /dieresis -8#210 /ring 8#211 /cedilla 8#212 /hungarumlaut 8#213 /ogonek 8#214 /caron -8#220 /dotlessi 8#230 /oe 8#231 /OE 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7725 3900 m + 7200 6000 l gs col0 s gr gr + +% arrowhead +n 7204 5860 m 7204 5984 l 7262 5874 l 7204 5860 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath -4170 5790 m 4230 5790 l 4230 5639 l 4200 5759 l 4170 5639 l cp +7170 6914 m 7170 7065 l 7230 7065 l 7230 6914 l 7230 6914 l 7200 7034 l 7170 6914 l cp eoclip -n 4200 5175 m - 4200 5775 l gs col0 s gr gr +n 7200 6225 m + 7200 7050 l gs col0 s gr gr % arrowhead -n 4170 5639 m 4200 5759 l 4230 5639 l 4170 5639 l cp gs 0.00 setgray ef gr col0 s +n 7170 6914 m 7200 7034 l 7230 6914 l 7170 6914 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath -4553 5749 m 4567 5807 l 4714 5771 l 4591 5771 l 4700 5713 l cp +5520 5864 m 5520 6015 l 5580 6015 l 5580 5864 l 5580 5864 l 5550 5984 l 5520 5864 l cp +5580 5761 m 5580 5610 l 5520 5610 l 5520 5761 l 5520 5761 l 5550 5641 l 5580 5761 l cp eoclip -n 7050 5175 m - 4575 5775 l gs col0 s gr gr +n 5550 5625 m + 5550 6000 l gs col0 s gr gr % arrowhead -n 4700 5713 m 4591 5771 l 4714 5771 l 4700 5713 l cp gs 0.00 setgray ef gr col0 s +n 5580 5761 m 5550 5641 l 5520 5761 l 5580 5761 l cp gs 0.00 setgray ef gr col0 s +% arrowhead +n 5520 5864 m 5550 5984 l 5580 5864 l 5520 5864 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath -4170 4890 m 4230 4890 l 4230 4739 l 4200 4859 l 4170 4739 l cp +3345 3464 m 3345 3615 l 3405 3615 l 3405 3464 l 3405 3464 l 3375 3584 l 3345 3464 l cp +3405 3361 m 3405 3210 l 3345 3210 l 3345 3361 l 3345 3361 l 3375 3241 l 3405 3361 l cp eoclip -n 4200 4275 m - 4200 4875 l gs col0 s gr gr +n 3375 3225 m + 3375 3600 l gs col0 s gr gr % arrowhead -n 4170 4739 m 4200 4859 l 4230 4739 l 4170 4739 l cp gs 0.00 setgray ef gr col0 s +n 3405 3361 m 3375 3241 l 3345 3361 l 3405 3361 l cp gs 0.00 setgray ef gr col0 s +% arrowhead +n 3345 3464 m 3375 3584 l 3405 3464 l 3345 3464 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath -7131 4907 m 7147 4850 l 7001 4810 l 7109 4871 l 6985 4868 l cp +3344 2114 m 3346 2265 l 3406 2264 l 3404 2113 l 3404 2113 l 3376 2234 l 3344 2114 l cp eoclip -n 4950 4275 m - 7125 4875 l gs col0 s gr gr +n 3373 1950 m + 3376 2250 l gs col0 s gr gr % arrowhead -n 6985 4868 m 7109 4871 l 7001 4810 l 6985 4868 l cp gs 0.00 setgray ef gr col0 s +n 3344 2114 m 3376 2234 l 3404 2113 l 3344 2114 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath -7167 4057 m 7225 4071 l 7262 3924 l 7204 4034 l 7204 3910 l cp +3345 2864 m 3345 3015 l 3405 3015 l 3405 2864 l 3405 2864 l 3375 2984 l 3345 2864 l cp +3405 2761 m 3405 2610 l 3345 2610 l 3345 2761 l 3345 2761 l 3375 2641 l 3405 2761 l cp eoclip -n 7725 1950 m - 7200 4050 l gs col0 s gr gr +n 3375 2625 m + 3375 3000 l gs col0 s gr gr % arrowhead -n 7204 3910 m 7204 4034 l 7262 3924 l 7204 3910 l cp gs 0.00 setgray ef gr col0 s +n 3405 2761 m 3375 2641 l 3345 2761 l 3405 2761 l cp gs 0.00 setgray ef gr col0 s +% arrowhead +n 3345 2864 m 3375 2984 l 3405 2864 l 3345 2864 l cp gs 0.00 setgray ef gr col0 s % Polyline -n 4350 3075 m - 7350 1950 l gs col0 s gr +n 2175 3600 m + 3750 3600 l gs col0 s gr % Polyline gs clippath -7170 4890 m 7230 4890 l 7230 4739 l 7200 4859 l 7170 4739 l cp +2611 2445 m 2460 2445 l 2460 2505 l 2611 2505 l 2611 2505 l 2491 2475 l 2611 2445 l cp eoclip -n 7200 4275 m - 7200 4875 l gs col0 s gr gr +n 3075 2475 m + 2475 2475 l gs col0 s gr gr % arrowhead -n 7170 4739 m 7200 4859 l 7230 4739 l 7170 4739 l cp gs 0.00 setgray ef gr col0 s +n 2611 2445 m 2491 2475 l 2611 2505 l 2611 2445 l cp gs 0.00 setgray ef gr col0 s % Polyline -n 3075 1875 m - 3975 1875 l gs col0 s gr +gs clippath +3345 1289 m 3347 1440 l 3407 1439 l 3405 1288 l 3405 1288 l 3377 1409 l 3345 1289 l cp +eoclip +n 3374 1125 m + 3377 1425 l gs col0 s gr gr + +% arrowhead +n 3345 1289 m 3377 1409 l 3405 1288 l 3345 1289 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath -5520 4065 m 5580 4065 l 5580 3914 l 5550 4034 l 5520 3914 l cp -5580 3660 m 5520 3660 l 5520 3811 l 5550 3691 l 5580 3811 l cp +1711 945 m 1560 945 l 1560 1005 l 1711 1005 l 1711 1005 l 1591 975 l 1711 945 l cp eoclip -n 5550 3675 m - 5550 4050 l gs col0 s gr gr +n 3075 975 m + 1575 975 l gs col0 s gr gr % arrowhead -n 5580 3811 m 5550 3691 l 5520 3811 l 5580 3811 l cp gs 0.00 setgray ef gr col0 s +n 1711 945 m 1591 975 l 1711 1005 l 1711 945 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +2161 1695 m 2010 1695 l 2010 1755 l 2161 1755 l 2161 1755 l 2041 1725 l 2161 1695 l cp +eoclip +n 3075 1725 m + 2025 1725 l gs col0 s gr gr + % arrowhead -n 5520 3914 m 5550 4034 l 5580 3914 l 5520 3914 l cp gs 0.00 setgray ef gr col0 s +n 2161 1695 m 2041 1725 l 2161 1755 l 2161 1695 l cp gs 0.00 setgray ef gr col0 s % Polyline -n 4575 4050 m - 6450 4050 l gs col0 s gr +n 8025 5925 m 8250 5925 l 9000 4950 l + 9150 4950 l gs col0 s gr % Polyline gs clippath -3495 2265 m 3555 2265 l 3555 2114 l 3525 2234 l 3495 2114 l cp -3555 1860 m 3495 1860 l 3495 2011 l 3525 1891 l 3555 2011 l cp +8312 4025 m 8275 3878 l 8217 3892 l 8254 4039 l 8254 4039 l 8254 3916 l 8312 4025 l cp eoclip -n 3525 1875 m - 3525 2250 l gs col0 s gr gr +n 8625 5400 m + 8250 3900 l gs col0 s gr gr % arrowhead -n 3555 2011 m 3525 1891 l 3495 2011 l 3555 2011 l cp gs 0.00 setgray ef gr col0 s +n 8312 4025 m 8254 3916 l 8254 4039 l 8312 4025 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +4700 7888 m 4553 7924 l 4567 7982 l 4714 7946 l 4714 7946 l 4591 7946 l 4700 7888 l cp +eoclip +n 7050 7350 m + 4575 7950 l gs col0 s gr gr + % arrowhead -n 3495 2114 m 3525 2234 l 3555 2114 l 3495 2114 l cp gs 0.00 setgray ef gr col0 s +n 4700 7888 m 4591 7946 l 4714 7946 l 4700 7888 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath -2219 3988 m 2279 3991 l 2285 3840 l 2251 3959 l 2225 3838 l cp +4170 7814 m 4170 7965 l 4230 7965 l 4230 7814 l 4230 7814 l 4200 7934 l 4170 7814 l cp eoclip -n 2325 1875 m - 2250 3975 l gs col0 s gr gr +n 4200 7500 m + 4200 7950 l gs col0 s gr gr % arrowhead -n 2225 3838 m 2251 3959 l 2285 3840 l 2225 3838 l cp gs 0.00 setgray ef gr col0 s +n 4170 7814 m 4200 7934 l 4230 7814 l 4170 7814 l cp gs 0.00 setgray ef gr col0 s % Polyline -n 7800 1275 m - 2100 1275 l gs col0 s gr -/Times-Roman-iso ff 180.00 scf sf -6600 5100 m -gs 1 -1 sc (Proof-irrelevance) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -3675 4200 m -gs 1 -1 sc (Excluded-middle) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -6900 1800 m -gs 1 -1 sc (Predicate extensionality) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -3375 3525 m -gs 1 -1 sc (\(Diaconescu\)) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -4650 3600 m -gs 1 -1 sc (Propositional degeneracy) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -3825 1800 m -gs 1 -1 sc (Relational choice axiom) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -1725 1800 m -gs 1 -1 sc (Description principle) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -2550 2400 m -gs 1 -1 sc (Functional choice axiom) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -3600 5100 m -gs 1 -1 sc (Decidability of equality on $A$) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -4425 4575 m -gs 1 -1 sc (\(needs Prop-impredicativity\)) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -5025 4725 m -gs 1 -1 sc (\(Berardi\)) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -1500 3075 m -gs 1 -1 sc (\(if Set impredicative\)) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -1500 4200 m -gs 1 -1 sc (Not excluded-middle) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -3600 6000 m -gs 1 -1 sc (Axiom K on A) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -3600 7200 m -gs 1 -1 sc (Invariance by substitution of reflexivity proofs for equality on A) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -6150 4200 m -gs 1 -1 sc (Propositional extensionality) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -2100 1200 m -gs 1 -1 sc (The dependency graph of axioms in the Calculus of Inductive Constructions) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -3600 6900 m -gs 1 -1 sc (Injectivity of equality on sigma-types on A) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -3600 6300 m -gs 1 -1 sc (Uniqueness of reflexivity proofs for equality on A) col0 sh gr -/Times-Roman-iso ff 180.00 scf sf -3600 6600 m -gs 1 -1 sc (Uniqueness of equality proofs on A) col0 sh gr +gs clippath +1295 3398 m 1339 3543 l 1397 3526 l 1353 3381 l 1353 3381 l 1359 3505 l 1295 3398 l cp +1207 2893 m 1163 2748 l 1105 2765 l 1149 2910 l 1149 2910 l 1144 2787 l 1207 2893 l cp +eoclip +n 1139 2771 m + 1364 3521 l gs col0 s gr gr + +% arrowhead +n 1207 2893 m 1144 2787 l 1149 2910 l 1207 2893 l cp gs 0.00 setgray ef gr col0 s +% arrowhead +n 1295 3398 m 1359 3505 l 1353 3381 l 1295 3398 l cp gs 0.00 setgray ef gr col0 s +% Polyline +n 4425 4875 m + 7350 3825 l gs col0 s gr +% Polyline +gs clippath +1019 1289 m 1021 1440 l 1081 1439 l 1079 1288 l 1079 1288 l 1051 1409 l 1019 1289 l cp +eoclip +n 1048 1125 m + 1051 1425 l gs col0 s gr gr + +% arrowhead +n 1019 1289 m 1051 1409 l 1079 1288 l 1019 1289 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +1020 2114 m 1022 2265 l 1082 2264 l 1080 2113 l 1080 2113 l 1052 2234 l 1020 2114 l cp +eoclip +n 1049 1950 m + 1052 2250 l gs col0 s gr gr + +% arrowhead +n 1020 2114 m 1052 2234 l 1080 2113 l 1020 2114 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +2104 5879 m 2151 6023 l 2208 6005 l 2161 5861 l 2161 5861 l 2170 5985 l 2104 5879 l cp +eoclip +n 1500 3900 m + 2175 6000 l gs col0 s gr gr + +% arrowhead +n 2104 5879 m 2170 5985 l 2161 5861 l 2104 5879 l cp gs 0.00 setgray ef gr col0 s +% Polyline +n 4575 6000 m + 6450 6000 l gs col0 s gr +% Polyline +gs clippath +6900 7063 m 7043 7113 l 7063 7056 l 6920 7006 l 6920 7006 l 7024 7075 l 6900 7063 l cp +eoclip +n 4714 6255 m + 7039 7080 l gs col0 s gr gr + +% arrowhead +n 6900 7063 m 7024 7075 l 6920 7006 l 6900 7063 l cp gs 0.00 setgray ef gr col0 s +% Polyline +gs clippath +4170 7064 m 4170 7215 l 4230 7215 l 4230 7064 l 4230 7064 l 4200 7184 l 4170 7064 l cp +eoclip +n 4200 6225 m + 4200 7200 l gs col-1 s gr gr + +% arrowhead +n 4170 7064 m 4200 7184 l 4230 7064 l 4170 7064 l cp gs 0.00 setgray ef gr col-1 s +% Polyline +2 slj +n 6450 7050 m 6448 7050 l 6444 7049 l 6437 7048 l 6425 7046 l 6408 7044 l + 6385 7040 l 6356 7036 l 6320 7030 l 6279 7024 l 6231 7017 l + 6177 7008 l 6118 6999 l 6054 6990 l 5986 6979 l 5915 6969 l + 5841 6958 l 5766 6946 l 5690 6935 l 5614 6924 l 5539 6913 l + 5464 6902 l 5391 6891 l 5320 6881 l 5252 6871 l 5185 6861 l + 5122 6852 l 5061 6843 l 5002 6835 l 4947 6827 l 4894 6820 l + 4843 6813 l 4796 6807 l 4750 6801 l 4707 6796 l 4666 6791 l + 4627 6786 l 4590 6782 l 4555 6778 l 4521 6774 l 4489 6771 l + 4458 6768 l 4429 6765 l 4400 6763 l 4350 6759 l 4303 6755 l + 4258 6753 l 4216 6751 l 4176 6751 l 4138 6750 l 4102 6751 l + 4068 6752 l 4037 6754 l 4008 6757 l 3980 6760 l 3955 6764 l + 3933 6768 l 3912 6773 l 3894 6778 l 3877 6784 l 3863 6790 l + 3850 6796 l 3839 6803 l 3829 6810 l 3820 6816 l 3813 6823 l + 3806 6830 l 3800 6838 l 3791 6850 l 3783 6863 l 3776 6878 l + 3771 6894 l 3766 6912 l 3762 6932 l 3759 6954 l 3756 6977 l + 3753 7000 l 3752 7021 l 3751 7036 l 3750 7045 l 3750 7049 l + + 3750 7050 l gs col0 s gr % here ends figure; -$F2psEnd -rs +pagefooter showpage +%%Trailer +%EOF |