update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_preserve_cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_preserve_cpcs.ma
new file mode 100644 (file)
index 0000000..cbcd378
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_preserve_cpcs.ma
@@ -0,0 +1,62 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_cpcs.ma".
+include "basic_2/dynamic/nta_preserve.ma".
+
+(* NATIVE TYPE ASSIGNMENT FOR TERMS ****************************************)
+
+(* Properties based on type equivalence and preservation *******************)
+
+(* Basic_1: uses: ty3_tred *)
+lemma nta_cprs_trans (a) (h) (G) (L):
+      ∀T,U1. ⦃G,L⦄ ⊢ T :[a,h] U1 → ∀U2.  ⦃G,L⦄ ⊢ U1 ➡*[h] U2 → ⦃G,L⦄ ⊢ T :[a,h] U2.
+#a #h #G #L #T #U1 #H #U2 #HU12
+/4 width=4 by nta_conv_cnv, nta_fwd_cnv_dx, cnv_cpms_trans, cpcs_cprs_dx/
+qed-.
+
+(* Basic_1: uses: ty3_sred_back *)
+lemma cprs_nta_trans (a) (h) (G) (L):
+      ∀T1,U0. ⦃G,L⦄ ⊢ T1 :[a,h] U0 → ∀T2.  ⦃G,L⦄ ⊢ T1 ➡*[h] T2 →
+      ∀U. ⦃G,L⦄ ⊢ T2 :[a,h] U →  ⦃G,L⦄ ⊢ T1 :[a,h] U.
+#a #h #G #L #T1 #U0 #HT1 #T2 #HT12 #U #H
+lapply (nta_cprs_conf … HT1 … HT12) -HT12 #HT2
+/4 width=6 by nta_mono, nta_conv_cnv, nta_fwd_cnv_dx/
+qed-.
+
+lemma cprs_nta_trans_cnv (a) (h) (G) (L):
+      ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] → ∀T2.  ⦃G,L⦄ ⊢ T1 ➡*[h] T2 →
+      ∀U. ⦃G,L⦄ ⊢ T2 :[a,h] U →  ⦃G,L⦄ ⊢ T1 :[a,h] U.
+#a #h #G #L #T1 #HT1 #T2 #HT12 #U #H
+elim (cnv_nta_sn … HT1) -HT1 #U0 #HT1
+/2 width=3 by cprs_nta_trans/
+qed-.
+
+(* Basic_1: uses: ty3_sconv *)
+lemma nta_cpcs_conf (a) (h) (G) (L):
+      ∀T1,U. ⦃G,L⦄ ⊢ T1 :[a,h] U → ∀T2.  ⦃G,L⦄ ⊢ T1 ⬌*[h] T2 →
+      ∀U0. ⦃G,L⦄ ⊢ T2 :[a,h] U0 →  ⦃G,L⦄ ⊢ T2 :[a,h] U.
+#a #h #G #L #T1 #U #HT1 #T2 #HT12 #U0 #HT2
+elim (cpcs_inv_cprs … HT12) -HT12 #T0 #HT10 #HT02
+/3 width=5 by  cprs_nta_trans, nta_cprs_conf/
+qed-.
+
+(* Note: type preservation by valid r-equivalence *)
+lemma nta_cpcs_conf_cnv (a) (h) (G) (L):
+      ∀T1,U. ⦃G,L⦄ ⊢ T1 :[a,h] U →
+      ∀T2.  ⦃G,L⦄ ⊢ T1 ⬌*[h] T2 → ⦃G,L⦄ ⊢ T2 ![a,h] →  ⦃G,L⦄ ⊢ T2 :[a,h] U.
+#a #h #G #L #T1 #U #HT1 #T2 #HT12 #HT2
+elim (cnv_nta_sn … HT2) -HT2 #U0 #HT2
+/2 width=3 by nta_cpcs_conf/
+qed-.