
theorem
  for a,b,c,d,a9,b9,c9,d9 being object st
    <* a, b, c, d *> = <* a9, b9, c9, d9 *> holds
      a = a9 & b = b9 & c = c9 & d = d9
  proof
    let a,b,c,d,a9,b9,c9,d9 be object;
    assume
A1: <* a, b, c, d *> = <* a9, b9, c9, d9 *>;
    set x = <* a,b,c,d *>, y = <*a9,b9,c9,d9 *>;
    x.1 = a & x.2 = b & x.3 = c & x.4 = d & y.1 = a9 & y.2 = b9 &
      y.3 = c9 & y.4 = d9;
    hence thesis by A1;
  end;
