reserve a,b,c,d for Real;
reserve z,z1,z2 for Complex;

theorem Th43:
  a >= 0 implies |.a.| = a
proof
  assume a >= 0;
  then Re a >= 0 by Def1;
  hence |.a.| = Re a by SQUARE_1:22
  .= a by Def1;
end;
