:: Field Properties of Complex Numbers - Requirements
:: by Library Committee
::
:: Received May 29, 2003
:: Copyright (c) 2003-2021 Association of Mizar Users
:: (Stowarzyszenie Uzytkownikow Mizara, Bialystok, Poland).
:: This code can be distributed under the GNU General Public Licence
:: version 3.0 or later, or the Creative Commons Attribution-ShareAlike
:: License version 3.0 or later, subject to the binding interpretation
:: detailed in file COPYING.interpretation.
:: See COPYING.GPL and COPYING.CC-BY-SA for the full text of these
:: licenses, or see http://www.gnu.org/licenses/gpl.html and
:: http://creativecommons.org/licenses/by-sa/3.0/.
environ
vocabularies XCMPLX_0, ARYTM_3, CARD_1, NUMBERS, SUBSET_1, ARYTM_0, ARYTM_1,
RELAT_1;
notations TARSKI, SUBSET_1, ORDINAL1, NUMBERS, ARYTM_0, XCMPLX_0;
constructors FUNCT_4, ARYTM_0, XCMPLX_0, NUMBERS;
registrations XCMPLX_0, ORDINAL1;
requirements NUMERALS, SUBSET, BOOLE;
begin
:: This file contains statements which are obvious for Mizar checker if
:: "requirements ARITHM" is included in the environment description
:: of an article. "requirements NUMERALS" is also required.
:: They are published for testing purposes only.
:: Users should use appropriate requirements instead of referencing
:: to these theorems.
:: Some of these items need also other requirements for proper work.
reserve x for Complex;
theorem :: ARITHM:1
x + 0 = x;
theorem :: ARITHM:2
x * 0 = 0;
theorem :: ARITHM:3
1 * x = x;
theorem :: ARITHM:4
x - 0 = x;
theorem :: ARITHM:5
0 / x = 0;
theorem :: ARITHM:6
x / 1 = x;