proposition: Lemma Forall_app_bwd : forall A (P : A -> Prop) ls1 ls2, Forall P (ls1 ++ ls2) -> Forall P ls1 /\ Forall P ls2.
proof: Proof. induction ls1; simpl; eauto; inversion 1; subst. apply IHls1 in H3; intuition. Qed.
imports: Coq(FunctionalExtensionality Arith Lia) Coq(Arith.Peano_dec Arith.Compare_dec) Coq(Relations.Relation_Operators) Coq(List) Chapar(Predefs)