proposition: Lemma ac_one_step_at_top_size_eq : forall t1 t2, ac_one_step_at_top t1 t2 -> size t1 = size t2.
proof: Proof. intros t1 t2 H; destruct H; simpl; repeat rewrite Nat.add_0_r; auto with arith; rewrite (Nat.add_comm (size t1) (S (size t2 + size t3))); simpl; apply (f_equal (fun n => S (S n))); rewrite <- (Nat.add_assoc (size t1) (size t2) (size t3)); apply Nat.add_comm. Qed.
imports: Coq(Relations List Arith Morphisms) CoLoR(more_list list_permut list_sort term_spec term_o equational_theory_spec equational_theory)