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(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * Copyright INRIA, CNRS and contributors *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(* \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 TestSuite.ssr_mini_mathcomp.
Lemma test1 : forall a b : nat, a == b -> a == 0 -> b == 0.
Proof. move=> a b Eab Eac; congr (_ == 0) : Eac; exact: eqP Eab. Qed.
Definition arrow A B := A -> B.
Lemma test2 : forall a b : nat, a == b -> arrow (a == 0) (b == 0).
Proof. move=> a b Eab; congr (_ == 0); exact: eqP Eab. Qed.
Definition equals T (A B : T) := A = B.
Lemma test3 : forall a b : nat, a = b -> equals nat (a + b) (b + b).
Proof. move=> a b E; congr (_ + _); exact E. Qed.
Variable S : eqType.
Variable f : nat -> S.
Coercion f : nat >-> Equality.sort.
Lemma test4 : forall a b : nat, b = a -> @eq S (b + b) (a + a).
Proof. move=> a b Eba; congr (_ + _); exact: Eba. Qed.
Open Scope type_scope.
Lemma test5 : forall (P Q Q' : Type) (h : Q = Q'), P * Q = P * Q'.
Proof. move=>*; by congr (_ * _). Qed.
Lemma test6 : forall (P Q Q' : Type) (h : Q = Q'), P * Q -> P * Q'.
Proof. move=> P Q Q' h; by congr (_ * _). Qed.
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