update in basic_2 and ground_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma
new file mode 100644 (file)
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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_computation/fpbg.ma".
+include "basic_2/rt_computation/cpms_fpbs.ma".
+include "basic_2/dynamic/cnv.ma".
+
+(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+(* Inductive premises for the preservation results **************************)
+
+definition IH_cnv_cpm_trans_lpr (a) (h): relation3 genv lenv term ≝
+                                λG,L1,T1. ⦃G, L1⦄ ⊢ T1 ![a,h] →
+                                ∀n,T2. ⦃G, L1⦄ ⊢ T1 ➡[n,h] T2 →
+                                ∀L2. ⦃G, L1⦄ ⊢ ➡[h] L2 → ⦃G, L2⦄ ⊢ T2 ![a,h].
+
+definition IH_cnv_cpms_trans_lpr (a) (h): relation3 genv lenv term ≝
+                                 λG,L1,T1. ⦃G, L1⦄ ⊢ T1 ![a,h] →
+                                 ∀n,T2. ⦃G, L1⦄ ⊢ T1 ➡*[n,h] T2 →
+                                 ∀L2. ⦃G, L1⦄ ⊢ ➡[h] L2 → ⦃G, L2⦄ ⊢ T2 ![a,h].
+
+definition IH_cnv_cpm_conf_lpr (a) (h): relation3 genv lenv term ≝
+                               λG,L0,T0. ⦃G, L0⦄ ⊢ T0 ![a,h] →
+                               ∀n1,T1. ⦃G, L0⦄ ⊢ T0 ➡[n1,h] T1 → ∀n2,T2. ⦃G, L0⦄ ⊢ T0 ➡[n2,h] T2 →
+                               ∀L1. ⦃G, L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡[h] L2 →
+                               ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G, L2⦄ ⊢ T2 ➡*[n1-n2,h] T.
+
+definition IH_cnv_cpms_strip_lpr (a) (h): relation3 genv lenv term ≝
+                                 λG,L0,T0. ⦃G, L0⦄ ⊢ T0 ![a,h] →
+                                 ∀n1,T1. ⦃G, L0⦄ ⊢ T0 ➡*[n1,h] T1 → ∀n2,T2. ⦃G, L0⦄ ⊢ T0 ➡[n2,h] T2 →
+                                 ∀L1. ⦃G, L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡[h] L2 →
+                                 ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G, L2⦄ ⊢ T2 ➡*[n1-n2,h] T.
+
+definition IH_cnv_cpms_conf_lpr (a) (h): relation3 genv lenv term ≝
+                                λG,L0,T0. ⦃G, L0⦄ ⊢ T0 ![a,h] →
+                                ∀n1,T1. ⦃G, L0⦄ ⊢ T0 ➡*[n1,h] T1 → ∀n2,T2. ⦃G, L0⦄ ⊢ T0 ➡*[n2,h] T2 →
+                                ∀L1. ⦃G, L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡[h] L2 →
+                                ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G, L2⦄ ⊢ T2 ➡*[n1-n2,h] T.
+
+(* Auxiliary properties for preservation ************************************)
+
+fact cnv_cpms_trans_lpr_sub (a) (h) (o):
+                            ∀G0,L0,T0.
+                            (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpm_trans_lpr a h G1 L1 T1) →
+                            ∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_trans_lpr a h G1 L1 T1.
+#a #h #o #G0 #L0 #T0 #IH #G1 #L1 #T1 #H01 #HT1 #n #T2 #H
+@(cpms_ind_dx … H) -n -T2
+/4 width=7 by cpms_fwd_fpbs, fpbg_fpbs_trans/
+qed-.
+
+fact cnv_cpm_conf_lpr_sub (a) (h) (o):
+                          ∀G0,L0,T0.
+                          (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_conf_lpr a h G1 L1 T1) →
+                          ∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpm_conf_lpr a h G1 L1 T1.
+/3 width=8 by cpm_cpms/ qed-.
+
+fact cnv_cpms_strip_lpr_sub (a) (h) (o):
+                            ∀G0,L0,T0.
+                            (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_conf_lpr a h G1 L1 T1) →
+                            ∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_strip_lpr a h G1 L1 T1.
+/3 width=8 by cpm_cpms/ qed-.