proposition: Lemma bounded: forall (a: regex), eNFA.bounded (X_to_eNFA a).
proof: Proof. intro. destruct (@bounded_build a 1 2 empty refl_equal refl_equal bounded_empty) as [Hd He]. unfold X_to_eNFA. rewrite (psurj (build a 0 1 empty)). split; simpl. intros i b j Hj. apply (Hd b i j). apply StateSet.mem_1, Hj. intros i j Hj. apply (He i j). apply StateSet.mem_1, Hj. apply belong_build. reflexivity. apply belong_build. reflexivity. 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)