Merge branch 'matita-lablgtk3' of ssh://matita.cs.unibo.it:/srv/git/helm into matita...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / nta_eval.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/cnv_eval.ma".
+include "basic_2/dynamic/nta_preserve.ma".
+
+(* NATIVE TYPE ASSIGNMENT FOR TERMS *****************************************)
+
+(* Properties with evaluations for rt-transition on terms *******************)
+
+lemma nta_typecheck_dec (h) (a) (G) (L): ac_props a →
+      ∀T,U. Decidable … (⦃G,L⦄ ⊢ T :[h,a] U).
+/2 width=1 by cnv_dec/ qed-.
+
+(* Basic_1: uses: ty3_inference *)
+lemma nta_inference_dec (h) (a) (G) (L) (T): ac_props a →
+      Decidable (∃U. ⦃G,L⦄ ⊢ T :[h,a] U).
+#h #a #G #L #T #Ha
+elim (cnv_dec h … G L T Ha) -Ha #HT
+[ /3 width=1 by cnv_nta_sn, or_introl/
+| @or_intror * #U #HTU
+  /3 width=2 by nta_fwd_cnv_sn/
+]
+qed-.