matita/matita/contribs/lambdadelta/static_2/etc/scl/scl_scl.etc

   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 "static_2/relocation/scl.ma".
  16
  17 (* CLEAR FOR LOCAL ENVIRONMENTS ON SELECTED ENTRIES *************************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem scl_fix: ∀f,L1,L. L1 ⊐ⓧ[f] L →
  22                  ∀L2. L ⊐ⓧ[f] L2 → L = L2.
  23 #f #L1 #L #H @(scl_ind … H) -f -L1 -L
  24 [ #f #L2 #H
  25   >(scl_inv_atom_sn … H) -L2 //
  26 | #f #I #K1 #K2 #_ #IH #L2 #H
  27   elim (scl_inv_push_sn … H) -H /3 width=1 by eq_f2/
  28 | #f #I #K1 #K2 #_ #IH #L2 #H
  29   elim (scl_inv_next_sn … H) -H /3 width=1 by eq_f2/
  30 ]
  31 qed-.
  32
  33 theorem scl_trans: ∀f. Transitive … (scl f).
  34 #f #L1 #L #H1 #L2 #H2
  35 <(scl_fix … H1 … H2) -L2 //
  36 qed-.