matita/matita/contribs/lambdadelta/apps_2/models/veq_lifts.ma

   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/relocation/lifts.ma".
  16 include "apps_2/models/veq.ma".
  17
  18 (* EVALUATION EQUIVALENCE  **************************************************)
  19
  20 lemma pippo (M) (gv): is_model M → is_extensional M →
  21                       ∀f,T1,T2. ⬆*[f] T1 ≘ T2 → ∀n. ⫯*[n] 𝐔❴1❵ = f →
  22                       ∀lv,d. ⟦T1⟧[gv, lv] ≗{M} ⟦T2⟧[gv, ⫯[n←d]lv].
  23 #M #gv #H1M #H2M #f #T1 #T2 #H elim H -f -T1 -T2
  24 [ /4 width=3 by seq_trans, seq_sym, ms/
  25 | #f #i1 #i2 #Hi12 #n #Hn #lv #d
  26   @(mr … H1M) [4,5: @(seq_sym … H1M) @(ml … H1M) |1,2: skip ]
  27 | /4 width=3 by seq_trans, seq_sym, mg/
  28 | #f #p * #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #n #Hn #lv #d
  29   [ @(mr … H1M) [4,5: @(seq_sym … H1M) @(md … H1M) |1,2: skip ]
  30     @(seq_trans … H1M)
  31     [2: @(ti_comp_l … H1M) | skip ]
  32     [2: @(vlift_comp … lv lv) | skip ]
  33     [3: /2 width=1 by veq_refl/ ]
  34     [2: @(IHV … d) // | skip ]
  35     @(seq_trans … H1M) [2: @(IHT … d) // | skip ]
  36     /4 width=1 by seq_sym, ti_ext_l, vlift_swap/
  37   | @mx /2 width=1 by/ #d0 @(seq_trans … H1M)
  38     [3: @(seq_sym … H1M) @(ti_ext_l … H1M) | skip ]
  39     [2: @vlift_swap // | skip ]
  40     /2 width=1 by/
  41   ]
  42 | #f * #V1 #v2 #T1 #T2 #_ #_ #IHV #IHT #n #Hn #lv #d
  43   [ /4 width=5 by seq_sym, ma, mc, mr/
  44   | /4 width=5 by seq_sym, me, mr/
  45   ]
  46 ]