
theorem Th2:
  for H,K be non empty finite set holds
  card product (<* H, K *>) = card(H)*card(K)
  proof
    let H,K be non empty finite set;
    consider I be Function of [:H,K:], product <*H,K*> such that
    A1: I is one-to-one onto
    & for x,y be object st x in H & y in K
    holds I.(x,y) = <*x,y*> by PRVECT_3:5;
    A2: dom I = [:H,K:] by FUNCT_2:def 1;
    rng I = product <*H,K*> by FUNCT_2:def 3,A1;
    then card ([:H,K:]) = card(product <*H,K*>)
      by CARD_1:5,A1,A2,WELLORD2:def 4;
    hence thesis by CARD_2:46;
  end;
