proposition: Lemma par_red_red : forall M N, par_red M N -> red M N.
proof: Proof. simple induction 1. simple induction 1; intros; auto with coc core arith sets. apply trans_red with (App (Abs T M') N'); auto with coc core arith sets. intros. apply trans_red_red with y; auto with coc core arith sets. Qed.
imports: Arith Compare_dec Relations