proposition: Lemma dot'_dot: forall a b: regex, dot' a b == a * b.
proof: Proof. intros; unfold dot'; RegExp.destruct_tests; fold_regex; auto with algebra. Qed.
imports: ATBR(Common) ATBR(Classes) ATBR(Graph) ATBR(SemiLattice) ATBR(Monoid) ATBR(SemiRing) ATBR(KleeneAlgebra) ATBR(Model_RegExp) Coq(Bool)