Definition Derivestar_P_A_2 := Rstar Conf Derive_P_A_2.

Lemma Derive_P_A_2_imp_Der_P_A_2_App : forall x y : Word, Derivestar_P_A_2 (x, y) (nil, nil) -> forall u v : Word, Append u v = x -> inmonoid X u -> ex2 (fun w : Word => Append u w = y) (fun w : Word => Derivestar_P_A_2 (v, w) (nil, nil)).