matita/matita/contribs/lambdadelta/basic_2/relocation/lreq_lreq.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   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/syntax/ceq_ext_ceq_ext.ma".
  16 include "basic_2/relocation/lexs_lexs.ma".
  17
  18 (* RANGED EQUIVALENCE FOR LOCAL ENVIRONMENTS ********************************)
  19
  20 (* Main properties **********************************************************)
  21
  22 theorem lreq_trans: ∀f. Transitive … (lreq f).
  23 /3 width=5 by lexs_trans, ceq_ext_trans/ qed-.
  24
  25 theorem lreq_canc_sn: ∀f. left_cancellable … (lreq f).
  26 /3 width=3 by lexs_canc_sn, lreq_trans, lreq_sym/ qed-.
  27
  28 theorem lreq_canc_dx: ∀f. right_cancellable … (lreq f).
  29 /3 width=3 by lexs_canc_dx, lreq_trans, lreq_sym/ qed-.
  30
  31 theorem lreq_join: ∀f1,L1,L2. L1 ≡[f1] L2 → ∀f2. L1 ≡[f2] L2 →
  32                    ∀f. f1 ⋓ f2 ≘ f → L1 ≡[f] L2.
  33 /2 width=5 by lexs_join/ qed-.
  34
  35 theorem lreq_meet: ∀f1,L1,L2. L1 ≡[f1] L2 → ∀f2. L1 ≡[f2] L2 →
  36                    ∀f. f1 ⋒ f2 ≘ f → L1 ≡[f] L2.
  37 /2 width=5 by lexs_meet/ qed-.