update in basic_2 and static_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / nta_cpcs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_cpcs.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/rt_equivalence/cpcs_cprs.ma".
+include "basic_2/dynamic/nta.ma".
+
+(* NATIVE TYPE ASSIGNMENT FOR TERMS *****************************************)
+
+(* Properties with r-equivalence for terms **********************************)
+
+lemma nta_conv_cnv (a) (h) (G) (L) (T):
+                   ∀U1. ⦃G,L⦄ ⊢ T :[a,h] U1 →
+                   ∀U2. ⦃G,L⦄  ⊢ U1 ⬌*[h] U2 → ⦃G,L⦄ ⊢ U2 ![a,h] → ⦃G,L⦄ ⊢ T :[a,h] U2.
+#a #h #G #L #T #U1 #H1 #U2 #HU12 #HU2
+elim (cnv_inv_cast … H1) -H1 #X1 #HU1 #HT #HUX1 #HTX1
+lapply (cpcs_cprs_conf … HUX1 … HU12) -U1 #H
+elim (cpcs_inv_cprs … H) -H #X2 #HX12 #HU12
+/3 width=5 by cnv_cast, cpms_cprs_trans/
+qed-.
+
+(* Basic_1: was by definition: ty3_conv *)
+(* Basic_2A1: was by definition: nta_conv ntaa_conv *)
+lemma nta_conv (a) (h) (G) (L) (T):
+               ∀U1. ⦃G,L⦄ ⊢ T :[a,h] U1 →
+               ∀U2. ⦃G,L⦄  ⊢ U1 ⬌*[h] U2 →
+               ∀W2. ⦃G,L⦄ ⊢ U2 :[a,h] W2 → ⦃G,L⦄ ⊢ T :[a,h] U2.
+#a #h #G #L #T #U1 #H1 #U2 #HU12 #W2 #H2
+/3 width=3 by nta_conv_cnv, nta_fwd_cnv_sn/
+qed-.
+
+(* Inversion lemmas with r-equivalence for terms ***************************)
+
+(* Basic_1: was: ty3_gen_sort *)
+(* Basic_2A1: was: nta_inv_sort1 *)
+lemma nta_inv_sort_sn (a) (h) (G) (L) (X2):
+      ∀s. ⦃G,L⦄ ⊢ ⋆s :[a,h] X2 → ⦃G,L⦄ ⊢ ⋆(next h s) ⬌*[h] X2.
+#a #h #G #L #X2 #s #H
+elim (cnv_inv_cast … H) -H #X1 #HX2 #_ #HX21 #H
+lapply (cpms_inv_sort1 … H) -H #H destruct
+/2 width=1 by cpcs_cprs_sn/
+qed-.
+