proposition: Lemma star_dot_leq_star_plus: forall a b: regex, (a*b)# <== (a+b)#.
proof: Proof. intros a b. rewrite plus_com, star_distr. transitivity (1*(a*b#)#); [rewrite dot_neutral_left|]; auto with algebra. Qed.
imports: ATBR(Common) ATBR(Classes) ATBR(Graph) ATBR(SemiLattice) ATBR(Monoid) ATBR(SemiRing) ATBR(KleeneAlgebra) ATBR(Model_RegExp) Coq(Bool)