unfold Derivestar_P_A, Rstar, Derivestar_P_A_2 in |- *.
intros x y Der_star.
pattern x, y in |- *.
apply Der_star.
intros.
apply Rstar_reflexive.
intros u v w Deri_u_v Rstar_v_w.
apply Rstar_R with v; auto.
Qed.
Hint Resolve Derivestar_P_A_imp_Derivestar_P_A_2.
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(*Tout mot reconnu par la grammaire est reconnu par l'automate*)
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Theorem Derivestar_imp_Derivestar_P_A :
forall x y : Word,
Derivestar R x y -> inmonoid X y -> Derivestar_P_A X d (x, y) (nil, nil).