proposition: Lemma length_filter {A} f (ls : list A) : length (filter f ls) <= length ls.
proof: Proof. induction ls as [|l ls IHls]; simpl. { reflexivity. } { edestruct f; simpl; try apply le_n_S; try apply le_S; apply IHls. } 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