matita/matita/contribs/lambdadelta/basic_2/relocation/fqu_fqu.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/lleq_lleq.ma".
  16 include "basic_2/relocation/fqu.ma".
  17
  18 (* SUPCLOSURE ***************************************************************)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma lleq_fqu_trans: ∀G1,G2,L2,K2,T,U. ⦃G1, L2, T⦄ ⊃ ⦃G2, K2, U⦄ →
  23                       ∀L1. L1 ⋕[T] L2 →
  24                       ∃∃K1. ⦃G1, L1, T⦄ ⊃ ⦃G2, K1, U⦄ & K1 ⋕[U] K2.
  25 #G1 #G2 #L2 #K2 #T #U #H elim H -G1 -G2 -L2 -K2 -T -U
  26 [ #I #G #L2 #V #L1 #H elim (lleq_inv_lref_dx … H I L2 V) -H //
  27   #K1 #H1 #H2 lapply (ldrop_inv_O2 … H1) -H1
  28   #H destruct /2 width=3 by fqu_lref_O, ex2_intro/
  29 | * [ #a ] #I #G #L2 #V #T #L1 #H
  30   [ elim (lleq_inv_bind … H)
  31   | elim (lleq_inv_flat … H)
  32   ] -H
  33   /2 width=3 by fqu_pair_sn, ex2_intro/
  34 | #a #I #G #L2 #V #T #L1 #H elim (lleq_inv_bind … H) -H
  35   /2 width=3 by fqu_bind_dx, ex2_intro/
  36 | #I #G #L2 #V #T #L1 #H elim (lleq_inv_flat … H) -H
  37   /2 width=3 by fqu_flat_dx, ex2_intro/
  38 | #G #L2 #K2 #T #U #e #HLK2 #HTU #L1 #HL12
  39   elim (ldrop_O1_le (e+1) L1)
  40   [ /3 width=11 by fqu_drop, lleq_inv_lift, ex2_intro/
  41   | lapply (ldrop_fwd_length_le2 … HLK2) -K2
  42     lapply (lleq_fwd_length … HL12) -T -U //
  43   ]
  44 ]
  45 qed-.