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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 ssrfun ssrbool TestSuite.ssr_mini_mathcomp.
Lemma test1 n : n >= 0.
Proof.
have [:s1] @h m : 'I_(n+m).+1.
apply: Sub 0 _.
abstract: s1 m.
by auto.
cut (forall m, 0 < (n+m).+1); last assumption.
rewrite [_ 1 _]/= in s1 h *.
by [].
Qed.
Lemma test2 n : n >= 0.
Proof.
have [:s1] @h m : 'I_(n+m).+1 := Sub 0 (s1 m).
move=> m; reflexivity.
cut (forall m, 0 < (n+m).+1); last assumption.
by [].
Qed.
Lemma test3 n : n >= 0.
Proof.
Fail have [:s1] @h m : 'I_(n+m).+1 by apply: (Sub 0 (s1 m)); auto.
have [:s1] @h m : 'I_(n+m).+1 by apply: (Sub 0); abstract: s1 m; auto.
cut (forall m, 0 < (n+m).+1); last assumption.
by [].
Qed.
Lemma test4 n : n >= 0.
Proof.
have @h m : 'I_(n+m).+1 by apply: (Sub 0); abstract auto.
by [].
Qed.
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