reserve x, y, z, r, s, t for Real;

theorem Th20:
  x <> 0 implies sgn x * sgn (1/x) = 1
proof
  assume x <> 0;
  then sgn ( x * (1/x) ) = sgn 1 by XCMPLX_1:106;
  then sgn ( x * (1/x) ) = 1 by Def2;
  hence thesis by Th18;
end;
