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
  for S1, S2, S3 being 1-sorted holds Carrier <* S1, S2, S3 *>
    = <* the carrier of S1, the carrier of S2, the carrier of S3 *>
proof
  let S1, S2, S3 be 1-sorted;
  set C = <* the carrier of S1, the carrier of S2 *>;
  thus Carrier <* S1, S2, S3 *> = Carrier(<* S1, S2 *>^<*S3*>) by FINSEQ_1:43
    .= Carrier<*S1,S2*> ^ Carrier<*S3*> by Th14
    .= C ^ Carrier<*S3*> by Th17
    .= C ^ <*the carrier of S3*> by Th16
    .= <* the carrier of S1, the carrier of S2, the carrier of S3 *>
    by FINSEQ_1:43;
end;
