matita/matita/contribs/lambdadelta/basic_2/static/fle_lsubf.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/static/frees_fqup.ma".
  16 include "basic_2/static/lsubf_lsubr.ma".
  17 include "basic_2/static/fle.ma".
  18
  19 (* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
  20
  21 (* Advanced forward lemmas ***************************************************)
  22
  23 lemma fle_fwd_pair_sn: ∀I1,I2,L1,L2,V1,V2,T1,T2. ⦃L1.ⓑ{I1}V1, T1⦄ ⊆ ⦃L2.ⓑ{I2}V2, T2⦄ →
  24                        ⦃L1.ⓧ, T1⦄ ⊆ ⦃L2.ⓑ{I2}V2, T2⦄.
  25 #I1 #I2 #L1 #L2 #V1 #V2 #T1 #T2 *
  26 #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HL12 #Hf12
  27 elim (lveq_inv_pair_pair … HL12) -HL12 #HL12 #H1 #H2 destruct
  28 elim (frees_total (L1.ⓧ) T1) #g1 #Hg1
  29 lapply (lsubr_lsubf … Hg1 … Hf1) -Hf1 /2 width=1 by lsubr_unit/ #Hfg1
  30 /5 width=10 by lsubf_fwd_sle, lveq_bind, sle_trans, ex4_4_intro/ (**) (* full auto too slow *)
  31 qed-.