
theorem Th62:
  id(COMPLEX) is_continuous_on COMPLEX
proof
A1: now
    let x be Complex;
    let r be Real;
    assume that
    x in COMPLEX and
A2: 0 < r;
    take s=r;
    thus 0 < s by A2;
    let y be Complex;
    assume that
  y in COMPLEX and
A3: |.y-x.| < s;
    reconsider xx=x, yy=y as Element of COMPLEX by XCMPLX_0:def 2;
    |.id(COMPLEX)/.yy - id(COMPLEX)/.xx.| < r by A3;
    hence |.id(COMPLEX)/.y - id(COMPLEX)/.x.| < r;
  end;
  dom id(COMPLEX) = COMPLEX by FUNCT_2:def 1;
  hence thesis by A1,CFCONT_1:39;
end;
