- relation between native type and atomic arity proced

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / hod / ntas.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/dynamic/nta.ma".
+
+(* HIGHER ORDER NATIVE TYPE ASSIGNMENT ON TERMS *****************************)
+
+definition ntas: sh → lenv → relation term ≝
+                 λh,L. star … (nta h L).
+
+interpretation "higher order native type assignment (term)"
+   'NativeTypeStar h L T U = (ntas h L T U).
+
+(* Basic eliminators ********************************************************)
+(*
+lemma cprs_ind: ∀L,T1. ∀R:predicate term. R T1 →
+                (∀T,T2. L ⊢ T1 ➡* T → L ⊢ T ➡ T2 → R T → R T2) →
+                ∀T2. L ⊢ T1 ➡* T2 → R T2.
+#L #T1 #R #HT1 #IHT1 #T2 #HT12
+@(TC_star_ind … HT1 IHT1 … HT12) //
+qed-.
+*)
+axiom ntas_ind_dx: ∀h,L,T2. ∀R:predicate term. R T2 →
+                   (∀T1,T. ⦃h, L⦄ ⊢ T1 : T → ⦃h, L⦄ ⊢ T :* T2 → R T → R T1) →
+                   ∀T1. ⦃h, L⦄ ⊢ T1 :* T2 → R T1.
+(*
+#h #L #T2 #R #HT2 #IHT2 #T1 #HT12
+@(star_ind_dx … HT2 IHT2 … HT12) //
+qed-.
+*)
+(* Basic properties *********************************************************)
+
+lemma ntas_refl: ∀h,L,T. ⦃h, L⦄ ⊢ T :* T.
+// qed.
+
+lemma ntas_strap1: ∀h,L,T1,T,T2.
+                   ⦃h, L⦄ ⊢ T1 :* T → ⦃h, L⦄  ⊢ T : T2 → ⦃h, L⦄  ⊢ T1 :* T2.
+/2 width=3/ qed.
+
+lemma ntas_strap2: ∀h,L,T1,T,T2.
+                   ⦃h, L⦄  ⊢ T1 : T → ⦃h, L⦄ ⊢ T :* T2 → ⦃h, L⦄ ⊢ T1 :* T2.
+/2 width=3/ qed.