update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / i_dynamic / ntas_cpcs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/i_dynamic/ntas_cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/i_dynamic/ntas_cpcs.ma
new file mode 100644 (file)
index 0000000..8438e03
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/i_dynamic/ntas_cpcs.ma
@@ -0,0 +1,36 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/i_dynamic/ntas.ma".
+
+(* ITERATED NATIVE TYPE ASSIGNMENT FOR TERMS ********************************)
+
+(* Properties with r-equivalence for terms **********************************)
+
+lemma ntas_zero (h) (a) (G) (L):
+      ∀T1,T2. ⦃G,L⦄ ⊢ T1 ![h,a] → ⦃G,L⦄ ⊢ T2 ![h,a] → ⦃G,L⦄ ⊢ T1 ⬌*[h] T2 → ⦃G,L⦄ ⊢ T1 :*[h,a,0] T2.
+#h #a #G #L #T1 #T2 #HT1 #HT2 #H
+elim (cpcs_inv_cprs … H) -H #T0 #HT10 #HT20
+/2 width=3 by ntas_intro/
+qed.
+
+(* Inversion lemmas with r-equivalence for terms ****************************)
+
+lemma ntas_inv_zero (h) (a) (G) (L):
+      ∀T1,T2. ⦃G,L⦄ ⊢ T1 :*[h,a,0] T2 →
+      ∧∧ ⦃G,L⦄ ⊢ T1 ![h,a] & ⦃G,L⦄ ⊢ T2 ![h,a] & ⦃G,L⦄ ⊢ T1 ⬌*[h] T2.
+#h #a #G #L #T1 #T2 * #T0 #HT1 #HT2 #HT20 #HT10
+/3 width=3 by cprs_div, and3_intro/ 
+qed-.