induction a1; intuition.
rewrite vector_0 in *.
trivial.
destruct (vector_S a2).
destruct H2.
subst.
repeat rewrite <- splitVector.Vector_cons_app_assoc in H.
inversion H.
apply vector_cons_eq in H.
f_equal.
eapply IHa1.
eauto.
Qed.

Theorem WCR_h_star_pad_impl_h_star :
cAU.Adv_WCR _ _ h_star_pad
({ 0 , 1 }^c) Z <=
cAU.Adv_WCR _ _ h_star
({ 0 , 1 }^c) Y.