:: Field Properties of Complex Numbers - Requirements
:: by Library Committee
::
:: Received May 29, 2003
:: Copyright (c) 2003-2016 Association of Mizar Users

0 in NAT
;

then reconsider Z = 0 as Element of REAL by NUMBERS:19;

1 in NAT
;

then reconsider J = 1 as Element of REAL by NUMBERS:19;

theorem Th1: :: ARITHM:1

for x being Complex holds x + 0 = x

proof end;

Lm1: - 0 = 0

proof end;

Lm2: opp Z = 0

proof end;

theorem Th2: :: ARITHM:2

for x being Complex holds x * 0 = 0

proof end;

theorem Th3: :: ARITHM:3

for x being Complex holds 1 * x = x

proof end;

theorem :: ARITHM:4

for x being Complex holds x - 0 = x

proof end;

theorem :: ARITHM:5

for x being Complex holds 0 / x = 0

proof end;

Lm3: 1 " = 1

proof end;

theorem :: ARITHM:6

for x being Complex holds x / 1 = x

proof end;