apply OrI1;is_ass.
apply OrI2;is_ass.
apply AndI;is_ass.
eapply OrE;[|eapply ImpE with A|mp]; is_ass.
eapply AndE1;is_ass.
eapply AndE2;is_ass.
mp;mp;is_ass.
is_ass.
apply BotC;apply ImpE with ¬A;is_ass.
Qed.

(* Specifications: *)
Theorem Hc_to_Nc : forall Γ A, Γ ⊢H A -> Γ ⊢ A.
induction 1.