proposition: Lemma rdp_equiv_empty_pi : forall (R R':relation term) pi v1 v2 (Hpi:is_primary_pi pi R) x y, rdp_step (axiom (ddp (union _ (union _ R Empty_R) (Pi pi v1 v2)))) R' x y <-> rdp_step (axiom (ddp R)) R' x y.
proof: Proof. intros R R' pi v1 v2 Hpi x y. apply rdp_step_equiv_strong. intros;rewrite pi_no_dp. apply dp_equiv. clear; intros l r;apply Empty_R_neutral_union_l. intros s t H f. inversion_clear H. apply Hpi;exact H0. inversion H0. reflexivity. Qed.
imports: Coq(Relations List Setoid) CoLoR(weaved_relation closure equational_theory_spec dp modular_dp terminaison)