update in static_2 and app_2

[helm.git] / matita / matita / contribs / lambdadelta / apps_2 / models / tm_exteq.ma

diff --git a/matita/matita/contribs/lambdadelta/apps_2/models/tm_exteq.ma b/matita/matita/contribs/lambdadelta/apps_2/models/tm_exteq.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 "ground_2/lib/functions.ma".
+include "ground_2/lib/exteq.ma".
+include "apps_2/models/tm.ma".
+
+(* TERM MODEL ***************************************************************)
+
+(* Properties with extensional equivalencs of evaluations *******************) 
+
+lemma tm_gc_id: ∀j. ⇡[j]tm_gc ≐ tm_gc.
+// qed.
+
+lemma tm_lc_id: ⇡[0←#0]tm_lc ≐ tm_lc.
+#i elim (eq_or_gt i) #Hi destruct //
+>tm_vpush_gt // >(flifts_lref_uni 1) <(S_pred … Hi) in ⊢ (???%); -Hi //
+qed.
+
+lemma tm_vlift_comp (l): compatible_2 … (tm_vlift l) (exteq …) (exteq …).
+#l #gv1 #gv2 #Hgv #i
+>tm_vlift_rw >tm_vlift_rw //
+qed.
+
+lemma tm_vpush_comp (i): compatible_3 … (tm_vpush i) (eq …) (exteq …) (exteq …).
+#i #T1 #T2 #HT12 #lv1 #lv2 #Hlv #j
+elim (lt_or_eq_or_gt j i) #Hij destruct
+[ >tm_vpush_lt // >tm_vpush_lt //
+| >tm_vpush_eq >tm_vpush_eq //
+| >tm_vpush_gt // >tm_vpush_gt //
+]
+qed-.
+
+lemma tm_ti_comp (T): compatible_3 … (λgv,lv.tm_ti gv lv T) (exteq …) (exteq …) (eq …).
+#T elim T -T *
+[ //
+| #i #gv1 #gv2 #Hgv #lv1 #lv2 #Hlv
+  whd in ⊢ (??%%); //
+| #i #gv1 #gv2 #Hgv #lv1 #lv2 #Hlv
+  whd in ⊢ (??%%); //
+| #p #I #V #T #IHV #IHT #gv1 #gv2 #Hgv #lv1 #lv2 #Hlv
+  whd in ⊢ (??%%); /4 width=1 by tm_vlift_comp, tm_vpush_comp, eq_f3/
+| #I #V #T #IHV #IHT #gv1 #gv2 #Hgv #lv1 #lv2 #Hlv
+  whd in ⊢ (??%%); /3 width=1 by eq_f3/
+]
+qed-.
+
+lemma tm_ti_eq (T): tm_ti tm_gc tm_lc T = T.
+#T elim T -T * //
+[ #p #I #V #T #IHV #IHT
+  <IHV in ⊢ (???%); <IHT in ⊢ (???%); -IHV -IHT
+  whd in ⊢ (??%?); /3 width=1 by tm_ti_comp, eq_f3/
+| #I #V #T #IHV #IHT
+  <IHV in ⊢ (???%); <IHT in ⊢ (???%); -IHV -IHT //
+]
+qed.