view src/coq/Axioms.v @ 1145:6249df767d4c

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author Adam Chlipala <adamc@hcoop.net>
date Thu, 04 Feb 2010 13:07:12 -0500
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Set Implicit Arguments.


Axiom ext_eq : forall dom ran (f g : forall x : dom, ran x),
  (forall x, f x = g x)
  -> f = g.

Theorem ext_eq_forall : forall dom (f g : forall x : dom, Type),
  (forall x, f x = g x)
  -> (forall x, f x) = (forall x, g x).
  intros.
  rewrite (ext_eq _ f g H); reflexivity.
Qed.

Theorem ext_eq_forallS : forall dom (f g : forall x : dom, Set),
  (forall x, f x = g x)
  -> (forall x, f x) = (forall x, g x).
  intros.
  rewrite (ext_eq _ f g H); reflexivity.
Qed.