intros s x y Derive_P_A_2_x_y.
elim Derive_P_A_2_x_y.
intros w u x0 dans_x0_X.
exists (Append s (cons x0 nil)).
apply Derive3_X; assumption.
intros v w u x0 dans_couple.
intros; exists s.
apply Derive3_V; assumption.
Qed.

Lemma Derivestar_P_A_2_imp_Derivestar_P_A_3 :
forall x y : Conf,
Derivestar_P_A_2 x y ->
forall s : Word, exists s2 : Word, Derivestar_P_A_3 (s, x) (s2, y).