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 Th16:
  for S being 1-sorted
  holds Carrier <* S *> = <* the carrier of S *>
proof
  let S be 1-sorted;
  thus Carrier <* S *> = Carrier {[1,S]} by FINSEQ_1:def 5
    .= Carrier(1 .--> S) by FUNCT_4:82
    .= Carrier({1} --> S)
    .= {1} --> the carrier of S by Th15
    .= 1 .--> the carrier of S
    .= {[1,the carrier of S]} by FUNCT_4:82
    .= <* the carrier of S *> by FINSEQ_1:def 5;
end;
