matita/matita/contribs/lambdadelta/basic_2/rt_computation/lsubsx_lsubsx.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "basic_2/rt_computation/lsubsx.ma".
  16
  17 (* CLEAR OF STRONGLY NORMALIZING ENTRIES FOR UNBOUND RT-TRANSITION **********)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem lsubsx_fix: ∀h,f,G,L1,L. G ⊢ L1 ⊆ⓧ[h, f] L →
  22                     ∀L2. G ⊢ L ⊆ⓧ[h, f] L2 → L = L2.
  23 #h #f #G #L1 #L #H elim H -f -L1 -L
  24 [ #f #L2 #H
  25   >(lsubsx_inv_atom_sn … H) -L2 //
  26 | #f #I #K1 #K2 #_ #IH #L2 #H
  27   elim (lsubsx_inv_push_sn … H) -H /3 width=1 by eq_f2/
  28 | #f #I #K1 #K2 #_ #IH #L2 #H
  29   elim (lsubsx_inv_unit_sn … H) -H /3 width=1 by eq_f2/
  30 | #f #I #K1 #K2 #V #_ #_ #IH #L2 #H
  31   elim (lsubsx_inv_unit_sn … H) -H /3 width=1 by eq_f2/
  32 ]
  33 qed-.
  34
  35 theorem lsubsx_trans: ∀h,f,G. Transitive … (lsubsx h G f).
  36 #h #f #G #L1 #L #H1 #L2 #H2
  37 <(lsubsx_fix … H1 … H2) -L2 //
  38 qed-.