proposition: Lemma left_prefix : forall x y z : List, ltl (x ++ y) z -> ltl x z.
proof: Proof. simple induction x. - simple induction z. + simpl; intros H. inversion_clear H. + simpl; intros; apply (Lt_nil A leA). - intros a l HInd. simpl. intros. inversion_clear H. + apply (Lt_hd A leA); auto with sets. + apply (Lt_tl A leA). apply (HInd y y0); auto with sets. Qed.
imports: List Relation_Operators Operators_Properties Transitive_Closure