matita/matita/contribs/lambdadelta/ground/relocation/fr2_append.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "ground/notation/functions/black_circle_2.ma".
  16 include "ground/relocation/fr2_map.ma".
  17
  18 (* CONCATENATION FOR FINITE RELOCATION MAPS WITH PAIRS **********************)
  19
  20 (* Note: this is reverse compose *)
  21 (*** fr2_append *)
  22 rec definition fr2_append f1 f2 on f1 ≝ match f1 with
  23 [ fr2_empty        ⇒ f2
  24 | fr2_lcons d h f1 ⇒ ❨d, h❩◗ fr2_append f1 f2
  25 ].
  26
  27 interpretation
  28   "append (finite relocation maps with pairs)"
  29   'BlackCircle f1 f2 = (fr2_append f1 f2).
  30
  31 (* Basic constructions ******************************************************)
  32
  33 (*** mr2_append_nil *)
  34 lemma fr2_append_empty (f2):
  35       f2 = 𝐞 ● f2.
  36 // qed.
  37
  38 (*** mr2_append_cons *)
  39 lemma fr2_append_lcons (d) (h) (f1) (f2):
  40       ❨d, h❩◗ (f1 ● f2) = (❨d, h❩◗ f1) ● f2.
  41 // qed.