diff options
Diffstat (limited to 'doc/faq/axioms.eps')
| -rw-r--r-- | doc/faq/axioms.eps | 378 |
1 files changed, 378 insertions, 0 deletions
diff --git a/doc/faq/axioms.eps b/doc/faq/axioms.eps new file mode 100644 index 00000000..3f3c01c4 --- /dev/null +++ b/doc/faq/axioms.eps @@ -0,0 +1,378 @@ +%!PS-Adobe-2.0 EPSF-2.0 +%%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 +%%EndComments +/$F2psDict 200 dict def +$F2psDict begin +$F2psDict /mtrx matrix put +/col-1 {0 setgray} bind def +/col0 {0.000 0.000 0.000 srgb} bind def +/col1 {0.000 0.000 1.000 srgb} bind def +/col2 {0.000 1.000 0.000 srgb} bind def +/col3 {0.000 1.000 1.000 srgb} bind def +/col4 {1.000 0.000 0.000 srgb} bind def +/col5 {1.000 0.000 1.000 srgb} bind def +/col6 {1.000 1.000 0.000 srgb} bind def +/col7 {1.000 1.000 1.000 srgb} bind def +/col8 {0.000 0.000 0.560 srgb} bind def +/col9 {0.000 0.000 0.690 srgb} bind def +/col10 {0.000 0.000 0.820 srgb} bind def +/col11 {0.530 0.810 1.000 srgb} bind def +/col12 {0.000 0.560 0.000 srgb} bind def +/col13 {0.000 0.690 0.000 srgb} bind def +/col14 {0.000 0.820 0.000 srgb} bind def +/col15 {0.000 0.560 0.560 srgb} bind def +/col16 {0.000 0.690 0.690 srgb} bind def +/col17 {0.000 0.820 0.820 srgb} bind def +/col18 {0.560 0.000 0.000 srgb} bind def +/col19 {0.690 0.000 0.000 srgb} bind def +/col20 {0.820 0.000 0.000 srgb} bind def +/col21 {0.560 0.000 0.560 srgb} bind def +/col22 {0.690 0.000 0.690 srgb} bind def +/col23 {0.820 0.000 0.820 srgb} bind def +/col24 {0.500 0.190 0.000 srgb} bind def +/col25 {0.630 0.250 0.000 srgb} bind def +/col26 {0.750 0.380 0.000 srgb} bind def +/col27 {1.000 0.500 0.500 srgb} bind def +/col28 {1.000 0.630 0.630 srgb} bind def +/col29 {1.000 0.750 0.750 srgb} bind def +/col30 {1.000 0.880 0.880 srgb} bind def +/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 +/gr {grestore} bind def +/gs {gsave} bind def +/sa {save} bind def +/rs {restore} bind def +/l {lineto} bind def +/m {moveto} bind def +/rm {rmoveto} bind def +/n {newpath} bind def +/s {stroke} bind def +/sh {show} bind def +/slc {setlinecap} bind def +/slj {setlinejoin} bind def +/slw {setlinewidth} bind def +/srgb {setrgbcolor} bind def +/rot {rotate} bind def +/sc {scale} bind def +/sd {setdash} bind def +/ff {findfont} bind def +/sf {setfont} bind def +/scf {scalefont} bind def +/sw {stringwidth} bind def +/tr {translate} bind def +/tnt {dup dup currentrgbcolor + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} + 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 +8#240 /space 8#241 /exclamdown 8#242 /cent 8#243 /sterling +8#244 /currency 8#245 /yen 8#246 /brokenbar 8#247 /section 8#250 /dieresis +8#251 /copyright 8#252 /ordfeminine 8#253 /guillemotleft 8#254 /logicalnot +8#255 /hyphen 8#256 /registered 8#257 /macron 8#260 /degree 8#261 /plusminus +8#262 /twosuperior 8#263 /threesuperior 8#264 /acute 8#265 /mu 8#266 /paragraph +8#267 /periodcentered 8#270 /cedilla 8#271 /onesuperior 8#272 /ordmasculine +8#273 /guillemotright 8#274 /onequarter 8#275 /onehalf +8#276 /threequarters 8#277 /questiondown 8#300 /Agrave 8#301 /Aacute +8#302 /Acircumflex 8#303 /Atilde 8#304 /Adieresis 8#305 /Aring +8#306 /AE 8#307 /Ccedilla 8#310 /Egrave 8#311 /Eacute +8#312 /Ecircumflex 8#313 /Edieresis 8#314 /Igrave 8#315 /Iacute +8#316 /Icircumflex 8#317 /Idieresis 8#320 /Eth 8#321 /Ntilde 8#322 /Ograve +8#323 /Oacute 8#324 /Ocircumflex 8#325 /Otilde 8#326 /Odieresis 8#327 /multiply +8#330 /Oslash 8#331 /Ugrave 8#332 /Uacute 8#333 /Ucircumflex +8#334 /Udieresis 8#335 /Yacute 8#336 /Thorn 8#337 /germandbls 8#340 /agrave +8#341 /aacute 8#342 /acircumflex 8#343 /atilde 8#344 /adieresis 8#345 /aring +8#346 /ae 8#347 /ccedilla 8#350 /egrave 8#351 /eacute +8#352 /ecircumflex 8#353 /edieresis 8#354 /igrave 8#355 /iacute +8#356 /icircumflex 8#357 /idieresis 8#360 /eth 8#361 /ntilde 8#362 /ograve +8#363 /oacute 8#364 /ocircumflex 8#365 /otilde 8#366 /odieresis 8#367 /divide +8#370 /oslash 8#371 /ugrave 8#372 /uacute 8#373 /ucircumflex +8#374 /udieresis 8#375 /yacute 8#376 /thorn 8#377 /ydieresis] def +/Times-Roman /Times-Roman-iso isovec ReEncode +/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def +/$F2psEnd {$F2psEnteredState restore end} def + +$F2psBegin +10 setmiterlimit +0 slj 0 slc + 0.06000 0.06000 sc +% +% Fig objects follow +% +% +% here starts figure with depth 50 +% Arc +7.500 slw +gs clippath +3599 6933 m 3626 6879 l 3492 6812 l 3586 6893 l 3465 6865 l cp +eoclip +n 3600.0 6750.0 150.0 90.0 -90.0 arc +gs col0 s gr + gr + +% arrowhead +n 3465 6865 m 3586 6893 l 3492 6812 l 3465 6865 l cp gs 0.00 setgray ef gr col0 s +% Arc +gs clippath +3599 6633 m 3626 6579 l 3492 6512 l 3586 6593 l 3465 6565 l cp +eoclip +n 3600.0 6450.0 150.0 90.0 -90.0 arc +gs col0 s gr + gr + +% arrowhead +n 3465 6565 m 3586 6593 l 3492 6512 l 3465 6565 l cp gs 0.00 setgray ef gr col0 s +% Arc +gs clippath +3626 6020 m 3599 5966 l 3465 6034 l 3586 6007 l 3492 6087 l cp +3599 6333 m 3626 6279 l 3492 6212 l 3586 6293 l 3465 6265 l cp +eoclip +n 3600.0 6150.0 150.0 90.0 -90.0 arc +gs col0 s gr + gr + +% arrowhead +n 3492 6087 m 3586 6007 l 3465 6034 l 3492 6087 l cp gs 0.00 setgray ef gr col0 s +% arrowhead +n 3465 6265 m 3586 6293 l 3492 6212 l 3465 6265 l cp gs 0.00 setgray ef gr col0 s +% Arc +gs clippath +3626 6320 m 3599 6266 l 3465 6334 l 3586 6307 l 3492 6387 l cp +3599 6633 m 3626 6579 l 3492 6512 l 3586 6593 l 3465 6565 l cp +eoclip +n 3600.0 6450.0 150.0 90.0 -90.0 arc +gs col0 s gr + gr + +% arrowhead +n 3492 6387 m 3586 6307 l 3465 6334 l 3492 6387 l cp gs 0.00 setgray ef gr col0 s +% arrowhead +n 3465 6565 m 3586 6593 l 3492 6512 l 3465 6565 l cp gs 0.00 setgray ef gr col0 s +% Arc +gs clippath +3626 6620 m 3599 6566 l 3465 6634 l 3586 6607 l 3492 6687 l cp +3599 6933 m 3626 6879 l 3492 6812 l 3586 6893 l 3465 6865 l cp +eoclip +n 3600.0 6750.0 150.0 90.0 -90.0 arc +gs col0 s gr + gr + +% arrowhead +n 3492 6687 m 3586 6607 l 3465 6634 l 3492 6687 l cp gs 0.00 setgray ef gr col0 s +% arrowhead +n 3465 6865 m 3586 6893 l 3492 6812 l 3465 6865 l cp gs 0.00 setgray ef gr col0 s +% Arc +gs clippath +3626 6920 m 3599 6866 l 3465 6934 l 3586 6907 l 3492 6987 l cp +3599 7233 m 3626 7179 l 3492 7112 l 3586 7193 l 3465 7165 l cp +eoclip +n 3600.0 7050.0 150.0 90.0 -90.0 arc +gs col0 s gr + gr + +% arrowhead +n 3492 6987 m 3586 6907 l 3465 6934 l 3492 6987 l cp gs 0.00 setgray ef gr col0 s +% arrowhead +n 3465 7165 m 3586 7193 l 3492 7112 l 3465 7165 l cp gs 0.00 setgray ef gr col0 s +% Arc +gs clippath +4168 4060 m 4227 4068 l 4247 3919 l 4202 4034 l 4188 3911 l cp +eoclip +n 14032.5 5272.5 9908.2 -159.9 -172.9 arcn +gs col0 s gr + gr + +% arrowhead +n 4188 3911 m 4202 4034 l 4247 3919 l 4188 3911 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 +eoclip +n 4200 5175 m + 4200 5775 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 +% Polyline +gs clippath +4553 5749 m 4567 5807 l 4714 5771 l 4591 5771 l 4700 5713 l cp +eoclip +n 7050 5175 m + 4575 5775 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 +% Polyline +gs clippath +4170 4890 m 4230 4890 l 4230 4739 l 4200 4859 l 4170 4739 l cp +eoclip +n 4200 4275 m + 4200 4875 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 +% Polyline +gs clippath +7131 4907 m 7147 4850 l 7001 4810 l 7109 4871 l 6985 4868 l cp +eoclip +n 4950 4275 m + 7125 4875 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 +% Polyline +gs clippath +7167 4057 m 7225 4071 l 7262 3924 l 7204 4034 l 7204 3910 l cp +eoclip +n 7725 1950 m + 7200 4050 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 +% Polyline +n 4350 3075 m + 7350 1950 l gs col0 s gr +% Polyline +gs clippath +7170 4890 m 7230 4890 l 7230 4739 l 7200 4859 l 7170 4739 l cp +eoclip +n 7200 4275 m + 7200 4875 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 +% Polyline +n 3075 1875 m + 3975 1875 l gs col0 s gr +% 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 +eoclip +n 5550 3675 m + 5550 4050 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 +% arrowhead +n 5520 3914 m 5550 4034 l 5580 3914 l 5520 3914 l cp gs 0.00 setgray ef gr col0 s +% Polyline +n 4575 4050 m + 6450 4050 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 +eoclip +n 3525 1875 m + 3525 2250 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 +% arrowhead +n 3495 2114 m 3525 2234 l 3555 2114 l 3495 2114 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 +eoclip +n 2325 1875 m + 2250 3975 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 +% 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 +% here ends figure; +$F2psEnd +rs +showpage |