Qed.

Lemma weakening2 : forall Γ A, Γ ⊢ A -> forall Δ, (forall B, In B Γ -> In B Δ) -> Δ ⊢ A.
induction 1;[constructor|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];intros;in_solve;eauto.