reserve a, b, k, n, m for Nat,
  i for Integer,
  r for Real,
  p for Rational,
  c for Complex,
  x for object,
  f for Function;

theorem Th1:
  0 < r & r < 1 implies 1 < 1/r
proof
  assume that
A1: 0 < r and
A2: r < 1;
  1*r" > r*r" by A1,A2,XREAL_1:68;
  hence thesis by A1,XCMPLX_0:def 7;
end;
