theorem Th90:
  abs -z = abs z
proof
  now
    let j be Nat;
    assume
A1: j in Seg n;
    then reconsider c = z.j, c9 = (-z).j as Element of COMPLEX by Th57;
    thus (abs -z).j = |.c9.| by A1,Th88
      .= |.-c.| by A1,Th60
      .= |.c.| by COMPLEX1:52
      .= (abs z).j by A1,Th88;
  end;
  hence thesis by FINSEQ_2:119;
end;
