:: Field Properties of Complex Numbers - Requirements
:: by Library Committee
::
:: Received May 29, 2003
:: Copyright (c) 2003-2012 Association of Mizar Users


begin

theorem Th1: :: ARITHM:1
for x being complex number holds x + 0 = x
proof end;

Lm1: - 0 = 0
proof end;

Lm2: opp 0 = 0
proof end;

theorem Th2: :: ARITHM:2
for x being complex number holds x * 0 = 0
proof end;

theorem Th3: :: ARITHM:3
for x being complex number holds 1 * x = x
proof end;

theorem :: ARITHM:4
for x being complex number holds x - 0 = x
proof end;

theorem :: ARITHM:5
for x being complex number holds 0 / x = 0
proof end;

Lm3: 1 " = 1
proof end;

theorem :: ARITHM:6
for x being complex number holds x / 1 = x
proof end;