proposition: Lemma Forall_take : forall P n l, Forall P l -> Forall P (take n l).
proof: Proof. Proof using. introv E. forwards (q&K): take_is_prefix n l. rewrite K in E. rewrite* Forall_app_eq in E. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)