matita/matita/contribs/lambdadelta/apps_2/models/deq.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 "apps_2/notation/models/ringeq_4.ma".
  16 include "apps_2/models/model_li.ma".
  17 include "apps_2/models/model_props.ma".
  18
  19 (* DENOTATIONAL EQUIVALENCE  ************************************************)
  20
  21 definition deq (M): relation3 lenv term term ≝
  22                     λL,T1,T2. ∀gv,lv. lv ϵ ⟦L⟧[gv] → ⟦T1⟧[gv, lv] ≗{M} ⟦T2⟧[gv, lv].
  23
  24 interpretation "denotational equivalence (model)"
  25    'RingEq M L T1 T2 = (deq M L T1 T2).
  26
  27 (* Basic properties *********************************************************)
  28
  29 lemma deq_refl (M): is_model M →
  30                     c_reflexive … (deq M).
  31 /2 width=1 by mq/ qed.
  32 (*
  33 lemma veq_sym: ∀M. symmetric … (veq M).
  34 // qed-.
  35
  36 theorem veq_trans: ∀M. transitive … (veq M).
  37 // qed-.
  38 *)