matita/matita/contribs/lambdadelta/apps_2/models/tm_props.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/rt_equivalence/cpcs_cpcs.ma".
  16 include "apps_2/models/model_props.ma".
  17 include "apps_2/models/tm.ma".
  18
  19 (* TERM MODEL ***************************************************************)
  20
  21 lemma tm_md (h): ∀T,V,gv,lv. ⟦+ⓓV.T⟧[gv,lv] ≗{TM h} ⟦T⟧[gv,⫯[O←⟦V⟧[gv,lv]]lv].
  22 #h #T elim T *
  23 [ /4 width=3 by cpc_cpcs, cpm_zeta, or_introl/
  24 | #i #V #gv #lv
  25   elim (eq_or_gt i) #Hi destruct
  26   [ elim (lifts_total (⟦V⟧[gv,lv]) (𝐔❴1❵)) #W #HVW
  27     >tm_ti_lref >vpush_eq
  28     >tm_ti_bind >tm_ti_lref >tm_vpush_eq
  29     /5 width=3 by cpc_cpcs, cpm_zeta, cpm_delta, or_introl/
  30   | >tm_ti_lref >vpush_gt //
  31     >tm_ti_bind >tm_ti_lref >tm_vpush_gt //
  32     /4 width=3 by cpc_cpcs, cpm_zeta, or_introl/
  33   ]
  34 | #l #V #gv #lv
  35   >tm_ti_bind >tm_ti_gref >tm_ti_gref
  36   /4 width=3 by cpc_cpcs, cpm_zeta, or_introl/
  37 | #p #I #W #T #IHW #IHT #V #gv #lv
  38   >tm_ti_bind in ⊢ (???%);
  39 (*
  40
  41   >tm_ti_bind >tm_ti_bind
  42   @cpc_cpcs @or_introl
  43   @cpm_bind
  44
  45   /4 width=3 by cpc_cpcs, cpm_zeta, or_introl/
  46
  47 definition is_tm (h): is_model (TM h) ≝ mk_is_model …. //
  48 [
  49 |
  50 | #gv #lv #p #V #T
  51   @cpcs_cprs_dx
  52   @cprs_step_sn
  53   [2: @cpm_bind // | skip ]
  54 *)