theorem Th9:
  for S be strict non void non empty ManySortedSign, A be non-empty
  strict MSAlgebra over S holds A = A Over S
proof
  let S be strict non void non empty ManySortedSign;
  let A be non-empty strict MSAlgebra over S;
A1: the Charact of A Over S = (the Charact of A)|the carrier' of S by Def2
    .= the Charact of A;
  the Sorts of A Over S = (the Sorts of A)|the carrier of S by Def2
    .= the Sorts of A;
  hence thesis by A1;
end;
