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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.
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.
¤ Dauer der Verarbeitung: 0.14 Sekunden
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