231_destruct.mlw 1.71 KB
 Sylvain Dailler committed Nov 07, 2018 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 `````` module T predicate p1 predicate p2 predicate p3 axiom H: p1 -> p2 -> p3 axiom H1: p1 /\ p2 /\ p3 axiom H2: p1 \/ p2 \/ p3 goal G : (p1 \/ p2 \/ p3) -> 1 = 1 end module T2 use int.Int predicate p1 int predicate p2 int predicate p3 int axiom H: forall x. p1 x -> p2 x-> p3 x axiom H1: exists x y z. p1 x /\ p2 y /\ p3 z axiom H2: exists x. p1 x \/ exists y. p2 y \/ exists z. p3 z goal G : (forall x. p1 x \/ p2 x \/ p3 x) -> 1 = 1 end `````` Sylvain Dailler committed Nov 29, 2018 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 ``````module Unsoundness predicate a predicate b predicate c (* Here if we do things badly we could use a on the right to prove the new hypothesis a on the left (and vice versa with b) This should not be provable. *) axiom H: (a -> (c /\ b)) /\ (b -> a) goal t1: c end module Incompleteness predicate a predicate b predicate c axiom H: (a -> (c /\ b)) /\ (b -> a) /\ a goal t1: c end `````` Sylvain Dailler committed Nov 07, 2018 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 ``````module Imbrication predicate p1 predicate p2 predicate p3 predicate p4 predicate p5 predicate p6 predicate p7 axiom H: (p1 /\ p2) \/ (p3 /\ p4 /\ (p5 \/ p6 \/ p7)) goal G: True end `````` Sylvain Dailler committed Nov 08, 2018 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 `````` (* TODO add more complex examples *) module Injection (* To avoid warning on axioms not containing local abstract symbol *) predicate p int constant z: int type t = | C int | D | E bool | F int axiom H: exists x. C x = D /\ p z axiom H1: C 1 = C 4 /\ p z axiom H2: E true = F 4 /\ p z goal G: True end module Injection2 (* To avoid warning on axioms not containing local abstract symbol *) predicate p int constant z: int type t = | C int | D | E bool | F int axiom H: exists x. C x <> D /\ p z axiom H1: C 1 <> C 4 /\ p z axiom H2: E true <> F 4 /\ p z goal G: True end``````