apply ImpI;apply BotC;apply ImpE with (A ∧ B);
[is_ass|apply AndI;apply BotC;(apply ImpE with (¬A ∨ ¬B);[is_ass|])].
apply OrI1;is_ass.
apply OrI2;is_ass.
Qed.

Lemma Nc_list_weakening : forall Γ1 Γ2 Δ, (forall B, In B Γ1 -> In B Γ2) -> Γ1 ⊢⊢ Δ -> Γ2 ⊢⊢ Δ.
intros;induction Δ.