matita/matita/contribs/lambdadelta/basic_2/unfold/lpss_lpss.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/unfold/lpss_cpss.ma".
  16
  17 (* SN PARALLEL UNFOLD ON LOCAL ENVIRONMENTS *********************************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem lpss_conf: confluent … lpss.
  22 /3 width=6 by lpx_sn_conf, cpss_conf_lpss/
  23 qed-.
  24
  25 theorem lpss_trans: Transitive … lpss.
  26 /3 width=5 by lpx_sn_trans, cpss_trans_lpss/
  27 qed-.
  28
  29 (* Advanced forward lemmas **************************************************)
  30
  31 lemma cpss_fwd_shift1: ∀L1,L,T1,T. L ⊢ L1 @@ T1 ▶* T →
  32                        ∃∃L2,T2. L @@ L1 ⊢ ▶* L @@ L2 & L @@ L1 ⊢ T1 ▶* T2 &
  33                                 T = L2 @@ T2.
  34 #L1 @(lenv_ind_dx … L1) -L1
  35 [ #L #T1 #T #HT1
  36   @ex3_2_intro [3: // |4,5: // |1,2: skip ] (**) (* /2 width=4/ does not work *)
  37 | #I #L1 #V1 #IH #L #T1 #T >shift_append_assoc #H <append_assoc
  38   elim (cpss_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
  39   elim (IH … HT12) -IH -HT12 #L2 #T #HL12 #HT1 #H destruct
  40   lapply (lpss_trans … HL12 (L.ⓑ{I}V2@@L2) ?) -HL12 /3 width=1/ #HL12
  41   @(ex3_2_intro … (⋆.ⓑ{I}V2@@L2)) [4: /2 width=3/ | skip ] <append_assoc // (**) (* explicit constructor *)
  42 ]
  43 qed-.