
theorem Th3:
  for I be set,
      F be multMagma-Family of I,
      a be Element of product F
  holds dom a = I
  proof
    let I be set,
        F be multMagma-Family of I,
        a be Element of product F;
    a in product F; then
    a in product Carrier F by GROUP_7:def 2;
    hence thesis by PARTFUN1:def 2;
  end;
