proposition: Lemma split_last : forall x y l r s, (r,s) = split l -> split (l&(x,y)) = (r&x, s&y).
proof: Proof. Proof using. introv H. erewrite split_app; fequals. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)