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(***********************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
(* \VV/ *************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(***********************************************************************)
(* $id$ *)
Require Export Eqdep_dec.
(* Congruence lemma *)
Theorem Congr_nodep: (A,B:Type)(f,g:A->B)(x,y:A)f==g->x==y->(f x)==(g y).
Intros A B f g x y eq1 eq2;Rewrite eq1;Rewrite eq2;Reflexivity.
Defined.
Theorem Congr_dep:
(A:Type; P:(A->Type); f,g:((a:A)(P a)); x:A)f==g->(f x)==(g x).
Intros A P f g x e;Rewrite e;Reflexivity.
Defined.
(* Basic application : try to prove that goal is equal to one hypothesis *)
Lemma convert_goal : (A,B:Prop)B->(A==B)->A.
Intros A B H E;Rewrite E;Assumption.
Save.
Tactic Definition CCsolve :=
Repeat (Match Context With
[ H: ?1 |- ?2] ->
(Assert Heq____:(?2==?1);[CC|(Rewrite Heq____;Exact H)])
|[ H: ?1; G: ?2 -> ?3 |- ?] ->
(Assert Heq____:(?2==?1) ;[CC|
(Rewrite Heq____ in G;Generalize (G H);Clear G;Intro G)])).
|
