
theorem
  for S being strict non empty ManySortedSign, A being non-empty
  MSAlgebra over S holds A+*A = the MSAlgebra of A
proof
  let S be strict non empty ManySortedSign, A be non-empty MSAlgebra over S;
  set A9 = the MSAlgebra of A;
  set SA = the Sorts of A9, CA = the Charact of A9;
  set SAA = the Sorts of A+*A, CAA = the Charact of A+*A;
  CA = CA+*CA;
  then
A1: CAA = CA by Def4;
  SA = SA+*SA;
  then SAA = SA by Def4;
  hence thesis by A1;
end;
