reserve U1,U2,U3 for Universal_Algebra,
  m,n for Nat,
  a for set,
  A for non empty set,
  h for Function of U1,U2;

theorem Th13:
  for o be OperSymbol of MSSign U1 holds Den(o,MSAlg U1) is operation of U1
proof
  let o be OperSymbol of MSSign U1;
A1: dom signature U1 = dom the charact of U1 by Lm1;
  Den(o,MSAlg U1) = (the charact of U1).o & the carrier' of MSSign U1 =
  dom signature U1 by Th12,MSUALG_1:def 8;
  hence thesis by A1,FUNCT_1:def 3;
end;
