(* Basic_1: was by definition: ty3_bind *)
(* Basic_2A1: was by definition: nta_bind ntaa_bind *)
lemma nta_bind

(* Basic_2A1: was by definition: nta_pure ntaa_pure *)
lemma nta_pure

(* Basic_1: was: ty3_gen_bind *)
(* Basic_2A1: was: nta_inv_bind1 ntaa_inv_bind1 *)
lemma nta_inv_bind_sn

(* Basic_1: was by definition: ty3_abst *)
(* Basic_2A1: was by definition: nta_ldec *)
lemma nta_ldec_drops

(* Advanced properties ******************************************************)

| ntaa_cast: ∀L,T,U,W. ntaa h L T U → ntaa h L U W → ntaa h L (ⓝU. T) U

lemma nta_cast_alt: ∀h,L,T,W,U. ⦃h, L⦄ ⊢ T  : W → ⦃h, L⦄ ⊢ T : U → ⦃h, L⦄ ⊢ ⓝW.T : U.
#h #L #T #W #U #HTW #HTU
lapply (nta_mono … HTW … HTU) #HWU
elim (nta_fwd_correct … HTU) -HTU /3 width=3/
qed.