matita/matita/contribs/lambdadelta/apps_2/models/veq_vdrop.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/models/vdrop_vlift.ma".
  16 include "apps_2/models/veq.ma".
  17
  18 (* EVALUATION EQUIVALENCE  **************************************************)
  19
  20 (* Properties with evaluation drop ******************************************)
  21
  22 lemma vdrop_comp (M): ∀i. compatible_2 … (vdrop M i) (veq M) (veq M).
  23 #M #i #lv1 #lv2 #Hlv12 #j elim (lt_or_ge j i) #Hji
  24 [ >vdrop_lt // >vdrop_lt //
  25 | >vdrop_ge // >vdrop_ge //
  26 ]
  27 qed.
  28
  29 (* Advanced inversion lemmas with evaluation evaluation lift ****************)
  30
  31 lemma veq_inv_vlift_sn (M): ∀lv1,y2,d1,i. ⫯[i←d1]lv1 ≗{M} y2 →
  32                             ∃∃lv2,d2. lv1 ≗ lv2 & d1 ≗ d2 & ⫯[i←d2]lv2 ≐ y2.
  33 #M #lv1 #y2 #d1 #i #H
  34 @(ex3_2_intro)
  35 [5: @exteq_sym @vlift_vdrop_eq |1,2: skip
  36 | #j elim (lt_or_ge j i) #Hji
  37   [ lapply (H j) -H >vlift_lt // >vdrop_lt //
  38   | lapply (H (↑j)) -H >vlift_gt /2 width=1 by monotonic_le_plus_l/ >vdrop_ge //
  39   ]
  40 | lapply (H i) >vlift_eq //
  41 ]
  42 qed-.