proposition: Lemma sym_conv : forall M N, conv M N -> conv N M.
proof: Proof. simple induction 1; auto with coc core arith sets. simple induction 2; intros; auto with coc core arith sets. apply trans_conv_red with P0; auto with coc core arith sets. apply trans_conv_exp with P0; auto with coc core arith sets. simple induction 2; intros; auto with coc core arith sets. apply trans_conv_red with P0; auto with coc core arith sets. apply trans_conv_exp with P0; auto with coc core arith sets. Qed.
imports: Arith Compare_dec Relations