matita/matita/contribs/lambdadelta/ground/lib/stream_eq_eq.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/lib/stream_eq.ma".
  16
  17 (* EXTENSIONAL EQUIVALENCE FOR STREAMS **************************************)
  18
  19 (* Main constructions *******************************************************)
  20
  21 corec theorem stream_eq_trans (A):
  22               Transitive … (stream_eq A).
  23 #t1 #t * -t1 -t
  24 #a1 #a #t1 #t * #Ht1 * #a2 #t2 #H
  25 cases (stream_eq_inv_cons_bi A … H) -H -a
  26 /3 width=7 by stream_eq_cons/
  27 qed-.
  28
  29 theorem stream_eq_canc_sn (A):
  30         ∀t,t1,t2. t ≗ t1 → t ≗ t2 → t1 ≗{A} t2.
  31 /3 width=3 by stream_eq_trans, stream_eq_sym/ qed-.
  32
  33 theorem stream_eq_canc_dx (A):
  34         ∀t,t1,t2. t1 ≗ t → t2 ≗ t → t1 ≗{A} t2.
  35 /3 width=3 by stream_eq_trans, stream_eq_sym/ qed-.