proposition: Lemma Forall_filter : forall A (p : A -> bool) (P : A -> Prop) ls, Forall (fun x => p x = true -> P x) ls -> Forall P (filter p ls).
proof: Proof. induction 1; simpl; auto. destruct (p x); auto. Qed.
imports: Coq(FunctionalExtensionality Arith Lia) Coq(Arith.Peano_dec Arith.Compare_dec) Coq(Relations.Relation_Operators) Coq(List) Chapar(Predefs)