proposition: Lemma xif_bool_incr: forall A B b c (x : X A B), (b=true -> c=true) -> xif b x 0 <== xif c x 0.
proof: Proof. intros. destruct b. rewrite H; auto. simpl. trivial with algebra. 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(Utils_WF) Coq(Relations) Coq(Eqdep_dec)