matita/matita/contribs/lambdadelta/basic_2A/multiple/lifts_lift_vector.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_2A/substitution/lift_lift_vector.ma".
  16 include "basic_2A/multiple/lifts_lift.ma".
  17 include "basic_2A/multiple/lifts_vector.ma".
  18
  19 (* GENERIC RELOCATION *******************************************************)
  20
  21 (* Main properties **********************************************************)
  22
  23 (* Basic_1: was: lifts1_xhg (right to left) *)
  24 lemma liftsv_liftv_trans_le: ∀T1s,Ts,cs. ⬆*[cs] T1s ≡ Ts →
  25                              ∀T2s:list term. ⬆[0, 1] Ts ≡ T2s →
  26                              ∃∃T0s. ⬆[0, 1] T1s ≡ T0s & ⬆*[cs + 1] T0s ≡ T2s.
  27 #T1s #Ts #cs #H elim H -T1s -Ts
  28 [ #T1s #H
  29   >(liftv_inv_nil1 … H) -T1s /2 width=3 by liftsv_nil, liftv_nil, ex2_intro/
  30 | #T1s #Ts #T1 #T #HT1 #_ #IHT1s #X #H
  31   elim (liftv_inv_cons1 … H) -H #T2 #T2s #HT2 #HT2s #H destruct
  32   elim (IHT1s … HT2s) -Ts #Ts #HT1s #HT2s
  33   elim (lifts_lift_trans_le … HT1 … HT2) -T /3 width=5 by liftsv_cons, liftv_cons, ex2_intro/
  34 ]
  35 qed-.