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authorherbelin2005-12-21 23:50:17 +0000
committerherbelin2005-12-21 23:50:17 +0000
commit4d4f08acb5e5f56d38289e5629173bc1b8b5fd57 (patch)
treec160d442d54dbd15cbd0ab3500cdf94d0a6da74e /test-suite/success/setoid_test_function_space.v8
parent960859c0c10e029f9768d0d70addeca8f6b6d784 (diff)
Abandon tests syntaxe v7; remplacement des .v par des fichiers en syntaxe v8
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@7693 85f007b7-540e-0410-9357-904b9bb8a0f7
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-Require Export Setoid.
-Set Implicit Arguments.
-Section feq.
-Variables A B:Type.
-Definition feq (f g: A -> B):=forall a, (f a)=(g a).
-Infix "=f":= feq (at level 80, right associativity).
-Hint Unfold feq.
-
-Lemma feq_refl: forall f, f =f f.
-intuition.
-Qed.
-
-Lemma feq_sym: forall f g, f =f g-> g =f f.
-intuition.
-Qed.
-
-Lemma feq_trans: forall f g h, f =f g-> g =f h -> f =f h.
-unfold feq. intuition.
-rewrite H.
-auto.
-Qed.
-End feq.
-Infix "=f":= feq (at level 80, right associativity).
-Hint Unfold feq. Hint Resolve feq_refl feq_sym feq_trans.
-
-Variable K:(nat -> nat)->Prop.
-Variable K_ext:forall a b, (K a)->(a =f b)->(K b).
-
-Add Relation (fun A B:Type => A -> B) feq
- reflexivity proved by feq_refl
- symmetry proved by feq_sym
- transitivity proved by feq_trans as funsetoid.
-
-Add Morphism K with signature feq ==> iff as K_ext1.
-intuition. apply (K_ext H0 H).
-intuition. assert (x2 =f x1);auto. apply (K_ext H0 H1).
-Qed.
-
-Lemma three:forall n, forall a, (K a)->(a =f (fun m => (a (n+m))))-> (K (fun m
-=> (a (n+m)))).
-intuition.
-setoid_rewrite <- H0.
-assumption.
-Qed.