remember (A::Γ). revert Γ Heql. induction H;intros;subst.
destruct H.
subst. do 2 (Hmp;[|aK]). instantiate (2:=⊥). aS.
Hmp;[aK|is_ass].
Hmp;[aK|is_ax].
Hmp;[Hmp;[aS|]|];auto.
Hmp;[|is_ass]. eapply H_weakening;[|eassumption].
intros;in_solve.
Qed.
Ltac HImpI := apply H_Deduction_Theorem.

(* Specifications: *)
Theorem Nc_to_Hc : forall Γ A, Γ ⊢ A -> Γ ⊢H A.
induction 1;try (Hmp;[|eassumption];is_ax;fail).