helm/software/matita/nlibrary/algebra/unital_magmas.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 "algebra/magmas.ma".
  16
  17 nrecord unital_magma_type : Type[1] ≝
  18  { umt_magma:> magma_type;
  19    unit: umt_magma;
  20    umt_is_neutral_l: ∀x. op ? unit x = x;
  21    umt_is_neutral_r: ∀x. op ? x unit = x
  22  }.
  23
  24 nrecord unital_magma (A: unital_magma_type) : Type[1] ≝
  25  { um_magma:> magma A;
  26    neutral_closed: unit A ∈ um_magma
  27  }.