proposition: Lemma count_last : forall P l x, count P (l&x) = count P l + If P x then 1 else 0.
proof: Proof. Proof using. intros. rewrite count_app, count_one. math. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)