proposition: Lemma complete_incr_left : forall {tar} `{DS.WF tar} {tar'} `{DS.WF tar'} l, tar <T= tar' -> tar +++l <T= tar' +++ l.
proof: Proof. intros tar Hwf tar' Hwf' l; revert tar Hwf tar' Hwf'. induction l as [|[x y] l IHl]; intros tar Hwf tar' Hwf' Hle; [ apply Hle|]. simpl. apply IHl; ti_auto. apply DSUtils.le_incr, Hle. 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_StateSetSets) ATBR(Utils_WF) Coq(Relations) Coq(List)