matita/matita/contribs/lambdadelta/apps_2/etc/models/model_lift.etc

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2/substitution/lift.ma".
  16 include "apps_2/models/model_lower.ma".
  17 include "apps_2/models/model_sound.ma".
  18
  19 (* MODEL ********************************************************************)
  20
  21 (* Forward lemmas on basic relocation ***************************************)
  22
  23 lemma sound_fwd_lift: ∀M. sound M → extensional M →
  24                       ∀sv,gv,T1,T2,l,m. ⬆[l, m] T1 ≡ T2 →
  25                       ∀lv. 〚T1〛{sv, gv, ↓[l, m]⦋M⦌ lv} = 〚T2〛{sv, gv, lv}.
  26 #M #H1M #H2M #sv #gv #T1 #T2 #l #m #H elim H -T1 -T2 -l -m
  27 [ #k #l #m #lv >(m1 … H1M) >(m1 … H1M) -H1M //
  28 | #i #l #m #Hil #lv >(m2 … H1M) >(m2 … H1M) -H1M >lower_lt //
  29 | #i #l #m #Hli #lv >(m2 … H1M) >(m2 … H1M) -H1M >lower_ge //
  30 | #p #l #m #lv >(m3 … H1M) >(m3 … H1M) -H1M //
  31 | #a * #V1 #V2 #T1 #T2 #l #m #_ #_ #IHV12 #IHT12 #lv
  32   [ >(m4 … H1M) >(m4 … H1M) /3 width=1 by raise_lower_lt, sound_ti_eq_l/
  33   | @(mx … H2M) /3 width=1 by raise_lower_lt, sound_ti_eq_l/
  34   ]
  35 | * #V1 #V2 #T1 #T2 #l #m #_ #_ #IHV12 #IHT12 #lv
  36   [ >(m6 … H1M) >(m6 … H1M) /3 width=1 by eq_f2/
  37   | >(m7 … H1M) >(m7 … H1M) /2 width=1 by/
  38   ]
  39 ]
  40 qed-.