(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
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(*                 The Calculus of Inductive Constructions                  *)
(*                                                                          *)
(*                                Projet Coq                                *)
(*                                                                          *)
(*                     INRIA                        ENS-CNRS                *)
(*              Rocquencourt                        Lyon                    *)
(*                                                                          *)
(*                                Coq V5.10                                 *)
(*                              Nov 25th 1994                               *)
(*                                                                          *)
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(*                            Nat_complements.v                             *)
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simple destruct n; auto with arith.
Qed.
intros; elim n; simpl in |- *.
auto with arith.
intros; rewrite H; elim mult_n_Sm; auto with arith.
Qed.
unfold mult in |- *; auto with arith.
Qed.

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Lemma technical_lemma :
forall y m : nat, S (y * m + (y + m) + m) = S y * m + (S y + m).