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(*     SMTCoq                                                             *)
(*     Copyright (C) 2011 - 2019                                          *)
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(*     See file "AUTHORS" for the list of authors                         *)
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(*   This file is distributed under the terms of the CeCILL-C licence     *)
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Require Import SMTCoq.

Parameter g : Z -> Z.

Axiom g_2_linear : forall x, Zeq_bool (g (x + 1)) ((g x) + 2).

Lemma apply_lemma_multiple :
  forall x y, Zeq_bool (g (x + y)) ((g x) + y * 2).

Proof.
  verit g_2_linear.