unfold Derivestar_P_A_2, Rstar, Derivestar_P_A in |- *.
intros x y Rstar_Der.
pattern x, y in |- *.
apply Rstar_Der.
intros.
apply Rstar_reflexive.
intros u v w Hyp1 Hyp2.
apply Rstar_R with v; auto.
Qed.
Hint Resolve Derivestar_P_A_2_imp_Derivestar_P_A.
(*seconde implication*)

Lemma Derive_P_A_imp_Derive_P_A_2 :
forall x y : Word * Word, Derive_P_A X d x y -> Derive_P_A_2 x y.