matita/matita/contribs/lambdadelta/basic_2/rt_computation/cnuw_simple.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 "static_2/syntax/tweq_simple.ma".
  16 include "basic_2/rt_computation/cpms_cpms.ma".
  17 include "basic_2/rt_computation/cnuw.ma".
  18
  19 (* NORMAL TERMS FOR T-UNUNBOUND WHD RT-TRANSITION ***************************)
  20
  21 (* Advanced forward lemma with with simple terms ****************************)
  22 (*
  23 lemma cnuw_fwd_appl_simple (h) (G) (L):
  24       ∀V,T. ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] ⓐV.T → 𝐒⦃T⦄.
  25 #h #G #L #V #T #HT
  26 elim (simple_dec_ex T) [ // ] * #p #I #W #U #H destruct
  27 *)
  28 (* Advanced properties with simple terms ************************************)
  29
  30 lemma cnuw_appl_simple (h) (G) (L):
  31       ∀V,T. 𝐒⦃T⦄ → ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] T → ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] ⓐV.T.
  32 #h #G #L #V1 #T1 #H1T1 #H2T1 #n #X #H
  33 elim (cpms_inv_appl_sn … H) -H *
  34 [ #V2 #T2 #_ #HT12 #H destruct -H1T1
  35   /3 width=2 by tweq_appl/
  36 | #n1 #n2 #p #V2 #T2 #HT12 #_ #_ -n -n2
  37   lapply (H2T1 … HT12) -H2T1 -n1 #H
  38   lapply (tweq_simple_trans … H H1T1) -H -H1T1 #H
  39   elim (simple_inv_bind … H)
  40 | #n1 #n2 #p #V2 #W2 #W #T2 #_ #_ #HT12 #_ #_ -n -n2 -V2 -W2
  41   lapply (H2T1 … HT12) -H2T1 -n1 #H
  42   lapply (tweq_simple_trans … H H1T1) -H -H1T1 #H
  43   elim (simple_inv_bind … H)
  44 ]
  45 qed.