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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(*i $Id: Tactics.v 8100 2006-02-27 12:10:03Z letouzey $ i*)
Require Import Notations.
Require Import Logic.
(** Useful tactics *)
(* A shorter name for generalize + clear, can be seen as an anti-intro *)
Ltac revert H := generalize H; clear H.
(* to contradict an hypothesis without copying its type. *)
Ltac absurd_hyp h :=
let T := type of h in
absurd T.
(* Transforming a negative goal [ H:~A |- ~B ] into a positive one [ B |- A ]*)
Ltac swap H := intro; apply H; clear H.
(* A case with no loss of information. *)
Ltac case_eq x := generalize (refl_equal x); pattern x at -1; case x.
(* A tactic for easing the use of lemmas f_equal, f_equal2, ... *)
Ltac f_equal :=
let cg := try congruence in
let r := try reflexivity in
match goal with
| |- ?f ?a = ?f' ?a' => cut (a=a'); [cg|r]
| |- ?f ?a ?b = ?f' ?a' ?b' =>
cut (b=b');[cut (a=a');[cg|r]|r]
| |- ?f ?a ?b ?c = ?f' ?a' ?b' ?c'=>
cut (c=c');[cut (b=b');[cut (a=a');[cg|r]|r]|r]
| |- ?f ?a ?b ?c ?d= ?f' ?a' ?b' ?c' ?d'=>
cut (d=d');[cut (c=c');[cut (b=b');[cut (a=a');[cg|r]|r]|r]|r]
| |- ?f ?a ?b ?c ?d ?e= ?f' ?a' ?b' ?c' ?d' ?e'=>
cut (e=e');[cut (d=d');[cut (c=c');[cut (b=b');[cut (a=a');[cg|r]|r]|r]|r]|r]
| _ => idtac
end.
(* Rewriting in all hypothesis. *)
Ltac rewrite_all Eq := match type of Eq with
?a = ?b =>
generalize Eq; clear Eq;
match goal with
| H : context [a] |- _ => intro Eq; rewrite Eq in H; rewrite_all Eq
| _ => intro Eq; try rewrite Eq
end
end.
Ltac rewrite_all_rev Eq := match type of Eq with
?a = ?b =>
generalize Eq; clear Eq;
match goal with
| H : context [b] |- _ => intro Eq; rewrite <- Eq in H; rewrite_all_rev Eq
| _ => intro Eq; try rewrite <- Eq
end
end.
Tactic Notation "rewrite_all" "<-" constr(H) := rewrite_all_rev H.
|
