reserve U1,U2,U3 for Universal_Algebra,
  n,m for Nat,
  x,y,z for object,
  A,B for non empty set,
  h1 for FinSequence of [:A,B:];
reserve h1 for homogeneous quasi_total non empty PartFunc of
    (the carrier of U1)*,the carrier of U1,
  h2 for homogeneous quasi_total non empty PartFunc of
    (the carrier of U2)*,the carrier of U2;

theorem Th17:
  for S1, S2 being 1-sorted holds
    Carrier <* S1, S2 *> = <* the carrier of S1, the carrier of S2 *>
proof
  let S1, S2 be 1-sorted;
  thus Carrier <* S1, S2 *> = Carrier(<*S1*>^<*S2*>) by FINSEQ_1:def 9
    .= Carrier<*S1*> ^ Carrier<*S2*> by Th14
    .= <*the carrier of S1*> ^ Carrier<*S2*> by Th16
    .= <* the carrier of S1 *> ^ <* the carrier of S2 *> by Th16
    .= <* the carrier of S1, the carrier of S2 *> by FINSEQ_1:def 9;
end;
