reserve S,S9 for non void Signature,
  f,g for Function;

theorem Th60:
  for S1,S2 being non empty Signature for A being MSAlgebra over
S1 st A is MSAlgebra over S2 holds the carrier of S1 = the carrier of S2 & the
  carrier' of S1 = the carrier' of S2
proof
  let S1,S2 be non empty Signature;
  let A be MSAlgebra over S1;
  assume A is MSAlgebra over S2;
  then reconsider B = A as MSAlgebra over S2;
  the Sorts of A = the Sorts of B;
  then dom the Sorts of A = the carrier of S2 by PARTFUN1:def 2;
  hence the carrier of S1 = the carrier of S2 by PARTFUN1:def 2;
  the Charact of A = the Charact of B;
  then dom the Charact of A = the carrier' of S2 by PARTFUN1:def 2;
  hence thesis by PARTFUN1:def 2;
end;
