proposition: Lemma conv_conv_subst : forall (a b c d : term) k, conv a b -> conv c d -> conv (subst_rec a c k) (subst_rec b d k).
proof: Proof. intros. apply trans_conv_conv with (subst_rec a d k). elim H0; intros; auto with coc core arith sets. apply trans_conv_red with (subst_rec a P k); auto with coc core arith sets. apply trans_conv_exp with (subst_rec a P k); auto with coc core arith sets. elim H; intros; auto with coc core arith sets. apply trans_conv_conv with (subst_rec P d k); auto with coc core arith sets. apply trans_conv_conv with (subst_rec P d k); auto with coc core arith sets. apply sym_conv; auto with coc core arith sets. Qed.
imports: Arith Compare_dec Relations