matita/matita/contribs/lambdadelta/ground/relocation/tr_compose_compose.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 "ground/relocation/tr_compose_pap.ma".
  16 include "ground/relocation/tr_compose_tls.ma".
  17 include "ground/relocation/tr_eq.ma".
  18
  19 (* COMPOSITION FOR TOTAL RELOCATION MAPS ************************************)
  20
  21 (* Main constructions *******************************************************)
  22
  23 corec theorem tr_compose_assoc (f3) (f2) (f1):
  24               (f3 ∘ f2) ∘ f1 ≗ f3 ∘ (f2 ∘ f1).
  25 cases f1 -f1 #p1 #f1
  26 cases tr_compose_unfold cases tr_compose_unfold cases tr_compose_unfold
  27 cases tr_compose_tls
  28 /2 width=1 by stream_eq_cons/
  29 qed.