matita/matita/contribs/lambdadelta/basic_2/s_computation/fqup_drops.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/relocation/drops.ma".
  16 include "basic_2/s_computation/fqup.ma".
  17
  18 (* PLUS-ITERATED SUPCLOSURE *************************************************)
  19
  20 (* Properties with generic slicing for local environments *******************)
  21
  22 lemma fqup_drops_succ: ∀b,G,K,T,i,L,U. ⬇*[↑i] L ≘ K → ⬆*[↑i] T ≘ U →
  23                        ⦃G, L, U⦄ ⊐+[b] ⦃G, K, T⦄.
  24 #b #G #K #T #i elim i -i
  25 [ #L #U #HLK #HTU elim (drops_inv_succ … HLK) -HLK
  26   #I #Y #HY #H destruct <(drops_fwd_isid … HY) -K //
  27   /3 width=2 by fqu_fqup, fqu_drop/
  28 | #l #IH #L #U #HLK #HTU elim (drops_inv_succ … HLK) -HLK
  29   #I #Y #HY #H destruct
  30   elim (lifts_split_trans … HTU … (𝐔❴↑l❵) (𝐔❴1❵)) -HTU
  31   /4 width=5 by fqup_strap2, fqu_drop/
  32 ]
  33 qed.
  34
  35 lemma fqup_drops_strap1: ∀b,G1,G2,L1,K1,K2,T1,T2,U1,i. ⬇*[i] L1 ≘ K1 → ⬆*[i] T1 ≘ U1 →
  36                          ⦃G1, K1, T1⦄ ⊐[b] ⦃G2, K2, T2⦄ → ⦃G1, L1, U1⦄ ⊐+[b] ⦃G2, K2, T2⦄.
  37 #b #G1 #G2 #L1 #K1 #K2 #T1 #T2 #U1 *
  38 [ #HLK1 #HTU1 #HT12
  39   >(drops_fwd_isid … HLK1) -L1 //
  40   <(lifts_fwd_isid … HTU1) -U1 /2 width=1 by fqu_fqup/
  41 | /3 width=5 by fqup_strap1, fqup_drops_succ/
  42 ]
  43 qed-.
  44
  45 lemma fqup_lref: ∀b,I,G,L,K,V,i. ⬇*[i] L ≘ K.ⓑ{I}V → ⦃G, L, #i⦄ ⊐+[b] ⦃G, K, V⦄.
  46 /2 width=6 by fqup_drops_strap1/ qed.