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diff --git a/doc/faq/axioms.fig b/doc/faq/axioms.fig new file mode 100644 index 00000000..78e44886 --- /dev/null +++ b/doc/faq/axioms.fig @@ -0,0 +1,137 @@ +#FIG 3.2 +Landscape +Center +Inches +Letter +100.00 +Single +-2 +1200 2 +5 1 0 1 0 7 50 -1 -1 0.000 0 1 1 0 14032.500 7222.500 4725 3825 4425 4800 4200 6000 + 1 1 1.00 60.00 120.00 +5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 1 3600.000 8925.000 3600 9075 3450 8925 3600 8775 + 1 1 1.00 60.00 120.00 +5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 1 3600.000 8625.000 3600 8775 3450 8625 3600 8475 + 1 1 1.00 60.00 120.00 +5 1 0 1 0 7 50 -1 -1 0.000 0 0 1 1 3600.000 8325.000 3600 8475 3450 8325 3600 8175 + 1 1 1.00 60.00 120.00 + 1 1 1.00 60.00 120.00 +5 1 0 1 0 7 50 -1 -1 0.000 0 0 1 1 3600.000 8625.000 3600 8775 3450 8625 3600 8475 + 1 1 1.00 60.00 120.00 + 1 1 1.00 60.00 120.00 +5 1 0 1 0 7 50 -1 -1 0.000 0 0 1 1 3600.000 8925.000 3600 9075 3450 8925 3600 8775 + 1 1 1.00 60.00 120.00 + 1 1 1.00 60.00 120.00 +5 1 0 1 0 7 50 -1 -1 0.000 0 0 1 1 3600.000 9225.000 3600 9375 3450 9225 3600 9075 + 1 1 1.00 60.00 120.00 + 1 1 1.00 60.00 120.00 +5 1 0 1 0 7 50 -1 -1 0.000 0 1 1 0 6309.515 5767.724 4200 3825 3450 5550 3825 7200 + 1 1 1.00 60.00 120.00 +6 2025 300 7725 525 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2 + 7725 525 2025 525 +4 0 0 50 -1 0 12 0.0000 4 180 5700 2025 450 The dependency graph of axioms in the Calculus of Inductive Constructions\001 +-6 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 4200 6225 4200 7200 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 7725 3900 7200 6000 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 7200 6225 7200 7050 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 1 2 + 1 1 1.00 60.00 120.00 + 1 1 1.00 60.00 120.00 + 5550 5625 5550 6000 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2 + 4575 6000 6450 6000 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 1 2 + 1 1 1.00 60.00 120.00 + 1 1 1.00 60.00 120.00 + 3375 3225 3375 3600 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 3373 1950 3376 2250 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 1 2 + 1 1 1.00 60.00 120.00 + 1 1 1.00 60.00 120.00 + 3375 2625 3375 3000 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2 + 2175 3600 3750 3600 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 3075 2475 2475 2475 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 3374 1125 3377 1425 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1049 1950 1052 2250 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1048 1125 1051 1425 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 3075 975 1575 975 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 3075 1725 2025 1725 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 4 + 8025 5925 8250 5925 9000 4950 9150 4950 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 8625 5400 8250 3900 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 7050 7350 4575 7950 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 4200 7500 4200 7950 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 4714 6255 7039 7080 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2 + 1 1 1.00 60.00 120.00 + 1500 3900 2175 6000 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 1 2 + 1 1 1.00 60.00 120.00 + 1 1 1.00 60.00 120.00 + 1139 2771 1364 3521 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2 + 4425 4875 7350 3825 +3 0 0 1 0 7 50 -1 -1 0.000 0 0 0 4 + 6450 7050 4050 6675 3750 6825 3750 7050 + 0.000 1.000 1.000 0.000 +4 0 0 50 -1 0 12 0.0000 4 180 1830 6900 3750 Predicate extensionality\001 +4 0 0 50 -1 0 12 0.0000 4 135 1800 3825 3750 Relational choice axiom\001 +4 0 0 50 -1 0 12 0.0000 4 180 2100 6150 6150 Propositional extensionality\001 +4 0 0 50 -1 0 12 0.0000 4 180 1005 450 1050 Operator iota\001 +4 0 0 50 -1 2 12 0.0000 4 135 1020 450 1650 Constructive\001 +4 0 0 50 -1 2 12 0.0000 4 180 1530 450 1875 definite description\001 +4 0 0 50 -1 2 12 0.0000 4 180 2010 9000 5175 Functional extensionality\001 +4 0 0 50 -1 0 12 0.0000 4 180 4740 150 10050 Statements in boldface are the most "interesting" ones for Coq\001 +4 0 0 50 -1 0 12 0.0000 4 180 4800 3600 9375 Invariance by substitution of reflexivity proofs for equality on A\001 +4 0 0 50 -1 0 12 0.0000 4 180 3735 3600 8475 Uniqueness of reflexivity proofs for equality on A\001 +4 0 0 50 -1 0 12 0.0000 4 180 2670 3600 8775 Uniqueness of equality proofs on A\001 +4 0 0 50 -1 0 12 0.0000 4 135 1080 3600 8175 Axiom K on A\001 +4 0 0 50 -1 2 12 0.0000 4 135 1455 6450 7275 Proof-irrelevance\001 +4 0 0 50 -1 2 12 0.0000 4 180 3360 3600 9075 Injectivity of equality on Sigma-types on A\001 +4 0 0 50 -1 0 12 0.0000 4 180 2175 4950 6525 (needs Prop-impredicativity)\001 +4 0 0 50 -1 0 12 0.0000 4 180 705 6000 6750 (Berardi)\001 +4 0 0 50 -1 2 12 0.0000 4 135 1290 3675 6225 Excluded-middle\001 +4 0 0 50 -1 0 12 0.0000 4 180 1905 4950 5550 Propositional degeneracy\001 +4 0 0 50 -1 0 12 0.0000 4 180 1050 3750 5250 (Diaconescu)\001 +4 0 0 50 -1 0 12 0.0000 4 180 2475 3375 7425 Decidability of equality on any A\001 +4 0 0 50 -1 0 12 0.0000 4 180 1620 1275 5025 (if Set impredicative)\001 +4 0 0 50 -1 0 12 0.0000 4 135 1560 1575 6225 Not excluded-middle\001 +4 0 0 50 -1 0 12 0.0000 4 180 1770 450 2625 in propositional context\001 +4 0 0 50 -1 2 12 0.0000 4 135 1020 3150 1650 Constructive\001 +4 0 0 50 -1 2 12 0.0000 4 180 1665 3150 1875 indefinite description\001 +4 0 0 50 -1 0 12 0.0000 4 180 2610 3150 2400 Constructive indefinite description\001 +4 0 0 50 -1 0 12 0.0000 4 180 1770 3150 2625 in propositional context\001 +4 0 0 50 -1 2 12 0.0000 4 135 1935 3150 3150 Functional choice axiom\001 +4 0 0 50 -1 0 12 0.0000 4 135 2100 450 2400 Constructive definite descr.\001 +4 0 0 50 -1 2 12 0.0000 4 180 1845 450 3750 Axiom of unique choice\001 +4 0 0 50 -1 2 12 0.0000 4 180 1365 3150 1050 Operator epsilon\001 |