trivial.
destruct H0;split.
eapply weakening2;eassumption.
apply IHΔ;apply H1.
Qed.

(* Specifications: *)
Lemma Nc_list_impl : forall Γ A, Γ ⊢ A ->forall Δ, Δ ⊢⊢ Γ -> Δ ⊢ A.
induction 1;intros;[induction Γ;destruct H;[subst;apply H0|apply IHΓ;[assumption|apply H0]]
|constructor 2|econstructor 3|constructor 4|constructor 5|econstructor 6
|econstructor 7|constructor 8|constructor 9|econstructor 10];try eauto;
[apply IHNc..|apply IHNc2|try apply IHNc3];
(split;[is_ass|eapply Nc_list_weakening;[|eassumption];in_solve]).