proposition: Lemma filter_nil_is_nil {A} : forall (l : list A) (pred : A -> bool), Nat.eqb (Datatypes.length l) 0 = true -> Nat.eqb (Datatypes.length (filter pred l)) 0 = true.
proof: Proof. induction l; intros; simpl; try inversion H. reflexivity. Qed.
imports: Fiat.Common.Coq__8_4__8_5__Compat Coq.ZArith.ZArith Coq.Lists.List Coq.Lists.SetoidList Coq.Bool.Bool Fiat.Common Fiat.Common.List.Operations Fiat.Common.Equality Fiat.Common.List.FlattenList Fiat.Common.LogicFacts