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 Th6:
  frac(m/n) = (m mod n) / n
proof
  per cases;
  suppose
A1: n = 0;
    hence frac(m/n) = frac(0) .= (m mod n) / n by A1;
  end;
  suppose
A2: n > 0;
    then m = n * (m div n) + (m mod n) by NAT_D:2;
    then m/n + 0 = (m div n) + (m mod n) / n by A2,XCMPLX_1:113;
    hence thesis;
  end;
end;
