matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpmre.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/notation/relations/predeval_6.ma".
  16 include "basic_2/rt_transition/cnr.ma".
  17 include "basic_2/rt_computation/cpms.ma".
  18
  19 (* EVALUATION FOR T-BOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION ON TERMS *)
  20
  21 (* Basic_2A1: uses: cpre *)
  22 definition cpmre (h) (n) (G) (L): relation2 term term ≝
  23            λT1,T2. ∧∧ ❪G,L❫ ⊢ T1 ➡*[h,n] T2 & ❪G,L❫ ⊢ ➡𝐍[h,0] T2.
  24
  25 interpretation "evaluation for t-bound context-sensitive parallel rt-transition (term)"
  26    'PRedEval h n G L T1 T2 = (cpmre h n G L T1 T2).
  27
  28 (* Basic properties *********************************************************)
  29
  30 lemma cpmre_intro (h) (n) (G) (L):
  31       ∀T1,T2. ❪G,L❫ ⊢ T1 ➡*[h,n] T2 → ❪G,L❫ ⊢ ➡𝐍[h,0] T2 → ❪G,L❫ ⊢ T1 ➡*𝐍[h,n] T2.
  32 /2 width=1 by conj/ qed.
  33
  34 (* Basic forward lemmas *****************************************************)
  35
  36 lemma cpmre_fwd_cpms (h) (n) (G) (L):
  37       ∀T1,T2. ❪G,L❫ ⊢ T1 ➡*𝐍[h,n] T2 → ❪G,L❫ ⊢ T1 ➡*[h,n] T2.
  38 #h #n #G #L #T1 #T2 * //
  39 qed-.