proposition: Lemma Forall_not_eq_count_eq_zero : forall P l, Forall (fun x => ~ P x) l = (count P l = 0).
proof: Proof. Proof using. intros. rewrite LibList.Forall_not_eq_count_eq_zero. unfold count. rewrite abs_nonneg; math. Qed.
imports: TLC(LibTactics LibLogic LibOperation LibReflect LibProd LibNat LibInt LibOption LibWf) TLC(LibInt)