
theorem lemcontr1:
for r being Rational holds r|^3 >= 0 iff r >= 0
proof
let r be Rational;
r|^3 = r|^(2 + 1)
    .= r|^(1+1) * r by NEWTON:6
    .= (r|^1 * r) * r by NEWTON:6
    .= (r * r) * r;
hence thesis;
end;
