proposition: Lemma Econv_Econv_prod : forall a b c d : term, Econv a b -> Econv c d -> Econv (Prod a c) (Prod b d).
proof: Proof. intros. apply trans_Econv_Econv with (Prod a d). elim H0; intros; auto with ecoc coc core arith sets. apply Etrans_conv_red with (Prod a P); auto with ecoc coc core arith sets. apply Etrans_conv_exp with (Prod a P); auto with ecoc coc core arith sets. elim H; intros; auto with ecoc coc core arith sets. apply Etrans_conv_red with (Prod P d); auto with ecoc coc core arith sets. apply Etrans_conv_exp with (Prod P d); auto with ecoc coc core arith sets. Qed.
imports: Termes Conv