proposition: Lemma one_step_union_insert : forall R1 R2 l r, (one_step (union _ R1 R2) r l <-> one_step (union _ (union _ R1 Empty_R) R2) r l).
proof: Proof. intros R1 R2 l r. apply one_step_equiv;clear;intros l r. rewrite (union_sym (union _ R1 Empty_R)). rewrite <- union_assoc. rewrite Empty_R_neutral_union_l. apply union_sym. Qed.
imports: Coq(Relations List Setoid) CoLoR(weaved_relation closure equational_theory_spec dp modular_dp terminaison)