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(* (c) Copyright 2006-2016 Microsoft Corporation and Inria.                  *)
by move=> x y f; rewrite [_.+1](addnC x.+1).
Qed.

Lemma test2 : forall x y f, x + y + f (y + x) + f (y + x) = x + y + f (y + x) + f (x + y).