proposition: Lemma bounded_add_one: forall i j A, belong i A -> belong j A -> bounded A -> bounded (add_one i j A).
proof: Proof. destruct A. intros Hi Hj [Hd He]. split; auto. intros s t Hst. apply epsilon_add_one in Hst as [Hst|[-> ->]]; auto. Qed.
imports: ATBR(Common) ATBR(Classes) ATBR(Graph) ATBR(Monoid) ATBR(SemiLattice) ATBR(SemiRing) ATBR(KleeneAlgebra) ATBR(MxGraph) ATBR(MxSemiLattice) ATBR(MxSemiRing) ATBR(MxKleeneAlgebra) ATBR(DKA_Definitions) ATBR(DKA_CheckLabels) ATBR(StrictStarForm) ATBR(Utils_WF) Coq(Relations)