matita/matita/contribs/lambdadelta/ground/lib/stream_hdtl_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_hdtl.ma".
  16 include "ground/lib/stream_eq.ma".
  17
  18 (* HEAD AND TAIL FOR STREAMS ************************************************)
  19
  20 (* Constructions with stream_eq *********************************************)
  21
  22 lemma stream_hd_eq_repl (A):
  23       stream_eq_repl A (λt1,t2. ⇃t1 = ⇃t2).
  24 #A * #a1 #t1 * #a2 #t2 #H
  25 elim (stream_eq_inv_cons_bi … H) -H
  26 /2 width=7 by/
  27 qed.
  28
  29 lemma stream_tl_eq_repl (A):
  30       stream_eq_repl A (λt1,t2. ⇂t1 ≗ ⇂t2).
  31 #A * #a1 #t1 * #a2 #t2 #H
  32 elim (stream_eq_inv_cons_bi … H) -H
  33 /2 width=7 by/
  34 qed.