matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_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 "basic_2/syntax/term_simple.ma".
  16 include "basic_2/relocation/lifts.ma".
  17
  18 (* GENERIC RELOCATION FOR TERMS *********************************************)
  19
  20 (* Forward lemmas with simple terms *****************************************)
  21
  22 (* Basic_2A1: includes: lift_simple_dx *)
  23 lemma lifts_simple_dx: ∀f,T1,T2. ⬆*[f] T1 ≘ T2 → 𝐒⦃T1⦄ → 𝐒⦃T2⦄.
  24 #f #T1 #T2 #H elim H -f -T1 -T2 //
  25 #f #p #I #V1 #V2 #T1 #T2 #_ #_ #_ #_ #H elim (simple_inv_bind … H)
  26 qed-.
  27
  28 (* Basic_2A1: includes: lift_simple_sn *)
  29 lemma lifts_simple_sn: ∀f,T1,T2. ⬆*[f] T1 ≘ T2 → 𝐒⦃T2⦄ → 𝐒⦃T1⦄.
  30 #f #T1 #T2 #H elim H -f -T1 -T2 //
  31 #f #p #I #V1 #V2 #T1 #T2 #_ #_ #_ #_ #H elim (simple_inv_bind … H)
  32 qed-.