proposition: Lemma clean_dot: forall (e f: regex), (cleaning_dot e f: regex) == e * f.
proof: Proof. intros. unfold cleaning_dot. destruct_tests; fold_regex; auto with algebra. Qed.
imports: ATBR(Common) ATBR(Classes) ATBR(Graph) ATBR(SemiLattice) ATBR(SemiRing) ATBR(KleeneAlgebra) ATBR(MxGraph) ATBR(Reification)