proposition: Lemma Dummy : forall t, Acc (one_step (@union term (@union term R1 R2) (@union term R3 (Pi pi V0 V1)))) t <-> Acc (one_step (@union term (@union term R1 R3) (@union term R2 (Pi pi V0 V1)))) t.
proof: Proof. intros t; split; apply Acc_incl; clear t; intros t1 t2; apply one_step_incl. clear t1 t2; intros t1 t2 [[H1 | H3] | [H2 | Hpi]]. left; left; trivial. right; left; trivial. left; right; trivial. right; right; trivial. clear t1 t2; intros t1 t2 [[H1 | H2] | [H3 | Hpi]]. left; left; trivial. right; left; trivial. left; right; trivial. right; right; trivial. Qed.
imports: Coq(List Relations Wellfounded Arith Recdef Setoid) CoLoR(closure more_list weaved_relation term equational_theory_spec dp)