(************************************************************************) (* * The Rocq Prover / The Rocq 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. *)
Lemma test1 n : n >= 0. Proof.
have [:s1] @h m : 'I_(n+m).+1. apply: Sub 0 _.
abstract: s1 m. byauto. 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 byapply: (Sub 0 (s1 m)); auto.
have [:s1] @h m : 'I_(n+m).+1 byapply: (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 byapply: (Sub 0); abstract auto. by []. Qed.
Lemma test5 : True. Proof.
have @t : nat := 3.
have : t = 3 by []. by []. Qed.
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