matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_rpx.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "static_2/static/rex_rex.ma".
  16 include "basic_2/rt_transition/rpx.ma".
  17
  18 (* EXTENDED PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS **********)
  19
  20 (* Main properties **********************************************************)
  21
  22 theorem rpx_bind (G):
  23         ∀L1,L2,V1. ❪G,L1❫ ⊢ ⬈[V1] L2 →
  24         ∀I,V2,T. ❪G,L1.ⓑ[I]V1❫ ⊢ ⬈[T] L2.ⓑ[I]V2 →
  25         ∀p. ❪G,L1❫ ⊢ ⬈[ⓑ[p,I]V1.T] L2.
  26 /2 width=2 by rex_bind/ qed.
  27
  28 theorem rpx_flat (G):
  29         ∀L1,L2,V. ❪G,L1❫ ⊢ ⬈[V] L2 →
  30         ∀I,T. ❪G,L1❫ ⊢ ⬈[T] L2 → ❪G,L1❫ ⊢ ⬈[ⓕ[I]V.T] L2.
  31 /2 width=1 by rex_flat/ qed.
  32
  33 theorem rpx_bind_void (G):
  34         ∀L1,L2,V. ❪G,L1❫ ⊢ ⬈[V] L2 →
  35         ∀T. ❪G,L1.ⓧ❫ ⊢ ⬈[T] L2.ⓧ →
  36         ∀p,I. ❪G,L1❫ ⊢ ⬈[ⓑ[p,I]V.T] L2.
  37 /2 width=1 by rex_bind_void/ qed.