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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)           *)
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(*         *     GNU Lesser General Public License Version 2.1          *)
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(* (c) Copyright 2006-2016 Microsoft Corporation and Inria.                  *)
by move=> x y f; rewrite [_.+1](addnC x.+1).
Qed.
by move=> x y f; rewrite {2}[in f _]addnC.
Qed.
by move=> x y f; rewrite [in f _](addnC y).
Qed.
by move=> x y f; rewrite {1 3}[in f _](addnC y).
Qed.
by move=> x y f; rewrite [in f _](addnC x). (* put y when bound var will be OK *)
Qed.

Lemma test3 : forall x y f, x + f (x + y) (f (y + x) x) = x + f (x + y) (f (x + y) x).