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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 (* This file was automatically generated: do not edit *********************)
19 (* $Id: Qmonoid.v,v 1.7 2004/04/08 08:20:33 lcf Exp $ *)
21 include "model/semigroups/Qsemigroup.ma".
23 include "algebra/CMonoids.ma".
25 (*#* **Examples of a monoid: $\langle$#⟨#[Q],[[+]]$\rangle$#⟩# and $\langle$#⟨#[Q],[[*]]$\rangle$#⟩#
26 ***$\langle$#⟨#[Q],[[+]]$\rangle$#⟩#
27 The rational numbers form with addition a CMonoid. [QZERO] is the unit.
30 inline procedural "cic:/CoRN/model/monoids/Qmonoid/ZEROQ_as_rht_unit3.con" as lemma.
32 inline procedural "cic:/CoRN/model/monoids/Qmonoid/ZEROQ_as_lft_unit3.con" as lemma.
34 inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_is_CMonoid.con" as definition.
36 inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_as_CMonoid.con" as definition.
38 (*#* ***$\langle$#⟨#[Q],[[*]]$\rangle$#⟩#
39 Also with multiplication Q forms a CMonoid. Here, the unit is [QONE].
42 inline procedural "cic:/CoRN/model/monoids/Qmonoid/ONEQ_as_rht_unit.con" as lemma.
44 inline procedural "cic:/CoRN/model/monoids/Qmonoid/ONEQ_as_lft_unit.con" as lemma.
46 inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_mul_is_CMonoid.con" as definition.
48 inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_mul_as_CMonoid.con" as definition.