theorem Th16:
  for d,d9 being BinOp of product a st
  for f,g being Element of product a, i being Element of dom a holds
    (d.(f,g)).i = (d9.(f,g)).i holds d = d9
proof
  let d,d9 be BinOp of product a such that
A1: for f,g be Element of product a, i be Element of dom a holds
    (d.(f,g)).i = (d9.(f,g)).i;
  now
    let f,g be Element of product a;
    dom (d.(f,g)) = dom a & dom (d9.(f,g)) = dom a by CARD_3:9;
    hence d.(f,g) = d9.(f,g) by A1;
  end;
  hence thesis;
end;
