+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/static/sh.ma".
+include "basic_2/equivalence/cpcs.ma".
+
+(* NATIVE TYPE ASSIGNMENT ON TERMS ******************************************)
+
+inductive nta (h:sh): lenv → relation term ≝
+| nta_sort: ∀L,k. nta h L (⋆k) (⋆(next h k))
+| nta_ldef: ∀L,K,V,W,U,i. ⇩[0, i] L ≡ K. ⓓV → nta h K V W →
+ ⇧[0, i + 1] W ≡ U → nta h L (#i) U
+| nta_ldec: ∀L,K,W,V,U,i. ⇩[0, i] L ≡ K. ⓛW → nta h K W V →
+ ⇧[0, i + 1] W ≡ U → nta h L (#i) U
+| nta_bind: ∀I,L,V,W,T,U. nta h L V W → nta h (L. ⓑ{I} V) T U →
+ nta h L (ⓑ{I}V.T) (ⓑ{I}V.U)
+| nta_appl: ∀L,V,W,U,T1,T2. nta h L V W → nta h L W U → nta h (L.ⓛW) T1 T2 →
+ nta h L (ⓐV.ⓛW.T1) (ⓐV.ⓛW.T2)
+| nta_pure: ∀L,V,W,T,U. nta h L T U → nta h L (ⓐV.U) W →
+ nta h L (ⓐV.T) (ⓐV.U)
+| nta_cast: ∀L,T,U. nta h L T U → nta h L (ⓣU. T) U
+| nta_conv: ∀L,T,U1,U2,V2. nta h L T U1 → L ⊢ U1 ⬌* U2 → nta h L U2 V2 →
+ nta h L T U2
+.
+
+interpretation "native type assignment (term)"
+ 'NativeType h L T U = (nta h L T U).
+
+(* Basic properties *********************************************************)
+
+(* Basic_1: was: ty3_cast *)
+lemma nta_cast_old: ∀h,L,W,T,U.
+ ⦃h, L⦄ ⊢ T : U → ⦃h, L⦄ ⊢ U : W → ⦃h, L⦄ ⊢ ⓣU.T : ⓣW.U.
+/4 width=3/ qed.
+
+(* Basic_1: was: ty3_typecheck *)
+lemma nta_typecheck: ∀h,L,T,U. ⦃h, L⦄ ⊢ T : U → ∃T0. ⦃h, L⦄ ⊢ ⓣU.T : T0.
+/3 width=2/ qed.
+
+(* Basic_1: removed theorems 1: ty3_getl_subst0 *)