adamc@616: (* Copyright (c) 2009, Adam Chlipala
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adamc@616: 
adamc@616: Set Implicit Arguments.
adamc@616: 
adamc@616: 
adamc@616: Axiom ext_eq : forall dom ran (f g : forall x : dom, ran x),
adamc@616:   (forall x, f x = g x)
adamc@616:   -> f = g.
adamc@616: 
adamc@616: Theorem ext_eq_forall : forall dom (f g : forall x : dom, Type),
adamc@616:   (forall x, f x = g x)
adamc@616:   -> (forall x, f x) = (forall x, g x).
adamc@616:   intros.
adamc@616:   rewrite (ext_eq _ f g H); reflexivity.
adamc@616: Qed.
adamc@616: 
adamc@616: Theorem ext_eq_forallS : forall dom (f g : forall x : dom, Set),
adamc@616:   (forall x, f x = g x)
adamc@616:   -> (forall x, f x) = (forall x, g x).
adamc@616:   intros.
adamc@616:   rewrite (ext_eq _ f g H); reflexivity.
adamc@616: Qed.