(* (c) Copyright 2006-2015 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) Require Import mathcomp.ssreflect.ssreflect. Variables P G : Prop. Lemma test1 : (P -> G) -> P -> G. Proof. move=> pg p. have suff {pg} H : P. match goal with |- P -> G => move=> _; exact: pg p | _ => fail end. match goal with H : P -> G |- G => exact: H p | _ => fail end. Qed. Lemma test2 : (P -> G) -> P -> G. Proof. move=> pg p. have suffices {pg} H : P. match goal with |- P -> G => move=> _;exact: pg p | _ => fail end. match goal with H : P -> G |- G => exact: H p | _ => fail end. Qed. Lemma test3 : (P -> G) -> P -> G. Proof. move=> pg p. suff have {pg} H : P. match goal with H : P |- G => exact: pg H | _ => fail end. match goal with |- (P -> G) -> G => move=> H; exact: H p | _ => fail end. Qed. Lemma test4 : (P -> G) -> P -> G. Proof. move=> pg p. suffices have {pg} H: P. match goal with H : P |- G => exact: pg H | _ => fail end. match goal with |- (P -> G) -> G => move=> H; exact: H p | _ => fail end. Qed. (* Lemma test5 : (P -> G) -> P -> G. Proof. move=> pg p. suff have {pg} H : P := pg H. match goal with |- (P -> G) -> G => move=> H; exact: H p | _ => fail end. Qed. *) (* Lemma test6 : (P -> G) -> P -> G. Proof. move=> pg p. suff have {pg} H := pg H. match goal with |- (P -> G) -> G => move=> H; exact: H p | _ => fail end. Qed. *) Lemma test7 : (P -> G) -> P -> G. Proof. move=> pg p. have suff {pg} H : P := pg. match goal with H : P -> G |- G => exact: H p | _ => fail end. Qed. Lemma test8 : (P -> G) -> P -> G. Proof. move=> pg p. have suff {pg} H := pg. match goal with H : P -> G |- G => exact: H p | _ => fail end. Qed. Goal forall x y : bool, x = y -> x = y. move=> x y E. by have {x E} -> : x = y by []. Qed.