matita/matita/contribs/lambdadelta/static_2/relocation/seq_seq.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 "static_2/syntax/teq_ext_teq_ext.ma".
  16 include "static_2/relocation/sex_sex.ma".
  17
  18 (* SYNTACTIC EQUIVALENCE FOR SELECTED LOCAL ENVIRONMENTS ********************)
  19
  20 (* Main properties **********************************************************)
  21
  22 theorem seq_trans (f):
  23         Transitive … (seq f).
  24 /3 width=5 by sex_trans, ceq_ext_trans/ qed-.
  25
  26 theorem seq_canc_sn (f):
  27         left_cancellable … (seq f).
  28 /3 width=3 by sex_canc_sn, seq_trans, seq_sym/ qed-.
  29
  30 theorem seq_canc_dx (f):
  31         right_cancellable … (seq f).
  32 /3 width=3 by sex_canc_dx, seq_trans, seq_sym/ qed-.
  33
  34 theorem seq_join:
  35         ∀f1,L1,L2. L1 ≡[f1] L2 → ∀f2. L1 ≡[f2] L2 →
  36         ∀f. f1 ⋓ f2 ≘ f → L1 ≡[f] L2.
  37 /2 width=5 by sex_join/ qed-.
  38
  39 theorem seq_meet:
  40         ∀f1,L1,L2. L1 ≡[f1] L2 → ∀f2. L1 ≡[f2] L2 →
  41         ∀f. f1 ⋒ f2 ≘ f → L1 ≡[f] L2.
  42 /2 width=5 by sex_meet/ qed-.