
theorem
  for K be Field, K1 be Subfield of K, x, y be Element of K,
  x1, y1 be Element of K1 st x = x1 & y = y1 & y <> 0.K
  holds x/y =x1/y1
  proof
    let K be Field,
    K1 be Subfield of K,
    x, y be Element of K,
    x1, y1 be Element of K1;
    set C = the carrier of K;
    set C1 = the carrier of K1;
    assume A1: x = x1 & y = y1 & y <> 0.K;
    then y" = y1" by Th21;
    hence thesis by A1,Th18;
  end;
