proposition: Lemma count_one : forall P x, count P (x::nil) = If P x then 1 else 0.
proof: Proof. Proof using. intros. unfold count. rew_listx. case_if~. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)