annotate src/coq/Axioms.v @ 2307:6ae9a2784a45

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author Adam Chlipala <adam@chlipala.net>
date Sun, 20 Dec 2015 14:39:50 -0500 (2015-12-20)
parents be88d2d169f6
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adamc@616 27
adamc@616 28 Set Implicit Arguments.
adamc@616 29
adamc@616 30
adamc@616 31 Axiom ext_eq : forall dom ran (f g : forall x : dom, ran x),
adamc@616 32 (forall x, f x = g x)
adamc@616 33 -> f = g.
adamc@616 34
adamc@616 35 Theorem ext_eq_forall : forall dom (f g : forall x : dom, Type),
adamc@616 36 (forall x, f x = g x)
adamc@616 37 -> (forall x, f x) = (forall x, g x).
adamc@616 38 intros.
adamc@616 39 rewrite (ext_eq _ f g H); reflexivity.
adamc@616 40 Qed.
adamc@616 41
adamc@616 42 Theorem ext_eq_forallS : forall dom (f g : forall x : dom, Set),
adamc@616 43 (forall x, f x = g x)
adamc@616 44 -> (forall x, f x) = (forall x, g x).
adamc@616 45 intros.
adamc@616 46 rewrite (ext_eq _ f g H); reflexivity.
adamc@616 47 Qed.