proposition: Lemma right_filter i k k' j (s: X k' k) m m' u (u': X i k') v (v': X k' j): u == u'*s -> s*m == m'*s -> s*v == v' -> u'*m'#*v' == u*m#*v.
proof: Proof. intros Hu Hm Hv. rewrite Hu, <- Hv, dot_assoc. monoid_rewrite (comm_iter_right Hm). semiring_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(MyFSets) ATBR(MyFSetProperties) ATBR(MyFMapProperties)