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January 26, 2017 19:58
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Double negation elimination
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| Axiom a1 : forall A B, A -> (B -> A). | |
| Axiom a2 : forall A B, (~B -> ~A) -> (A -> B). | |
| Theorem dne : | |
| forall A, ~~A -> A. | |
| Proof. | |
| intros A P. | |
| generalize P. | |
| apply a2, a2, a1, P. | |
| Qed. | |
| Print dne. | |
| (* | |
| dne = | |
| fun (A : Prop) (P : ~ ~ A) => | |
| a2 (~ ~ A) A | |
| (a2 (~ A) (~ ~ ~ A) | |
| (a1 (~ ~ A) (~ ~ ~ ~ A) P)) P | |
| : forall A : Prop, ~ ~ A -> A | |
| Argument scopes are [type_scope _] | |
| *) |
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