assumption.
destruct H;split.
assumption.
apply IHΔ1;apply H1.
Qed.
Ltac Ncl_solve := repeat match goal with
| |- _ ⊢ _     => idtac
| |- _ ⊢⊢ _::_ => split;[eassumption||(try (is_ass;fail))|]
| |- _ ⊢⊢ _++_ => apply Nc_list_app
| |- map_fold_right (Nc ?Γ) and True _ => change (map_fold_right (Nc Γ) and True) with (Ncl Γ)
| _            => eassumption||(apply Nc_list_contained;in_solve)
end.

(* Specifications: *)
Lemma G_to_Nc_Neg : forall Γ Δ, Γ ⊃ Δ -> Γ++¬l Δ ⊢ ⊥.
induction 1;try rewrite map_app in *;simpl in *.