proposition: Lemma build_max_label: forall a i e f A, i < max_label A -> i < max_label (build a e f A).
proof: Proof. induction a; intros i e f A Hi; rewrite (psurj A); simpl; auto. rewrite max_label_add_one. auto. num_simpl. eauto 2 using Nat.le_max_r with arith. 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)