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(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
Require Import ssreflect.
Require Import ssrbool.
Require Import TestSuite.ssr_mini_mathcomp.
Variable T : Type.
Variables P : T -> Prop.
Definition f := fun x y : T => x.
Lemma test1 : forall x y : T, P (f x y) -> P x.
Proof.
move=> x y; set fxy := f x y; move=> Pfxy.
wlog H : @fxy Pfxy / P x.
match goal with |- (let fxy0 := f x y in P fxy0 -> P x -> P x) -> P x => by auto | _ => fail end.
exact: H.
Qed.
Lemma test2 : forall x y : T, P (f x y) -> P x.
Proof.
move=> x y; set fxy := f x y; move=> Pfxy.
wlog H : fxy Pfxy / P x.
match goal with |- (forall fxy, P fxy -> P x -> P x) -> P x => by auto | _ => fail end.
exact: H.
Qed.
Lemma test3 : forall x y : T, P (f x y) -> P x.
Proof.
move=> x y; set fxy := f x y; move=> Pfxy.
move: {1}@fxy (Pfxy) (Pfxy).
match goal with |- (let fxy0 := f x y in P fxy0 -> P fxy -> P x) => by auto | _ => fail end.
Qed.
Lemma test4 : forall n m z: bool, n = z -> let x := n in x = m && n -> x = m && n.
move=> n m z E x H.
case: true.
by rewrite {1 2}E in (x) H |- *.
by rewrite {1}E in x H |- *.
Qed.
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