is_ass.
HImpI;assumption.
Hmp;eassumption.
Hmp;[aC|HImpI;assumption].
Hmp;[Hmp;[is_ax|]|];assumption.
Hmp;[Hmp;[Hmp|]|].
is_ax.
eassumption.
HImpI;assumption.
HImpI;assumption.
Qed.

Theorem Nc_equiv_Hc : forall Γ A, Γ ⊢ A <-> Γ ⊢H A.
split;[apply Nc_to_Hc|apply Hc_to_Nc].