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 Th14:
  for o be OperSymbol of MSSign U1 for y be Element of Args(o,
  MSAlg U1) holds y is FinSequence of the carrier of U1
proof
  let o be OperSymbol of MSSign U1;
  let y be Element of Args(o,MSAlg U1);
  set O1 = Den(o,MSAlg U1);
A1: O1 = (the charact of U1).o & the carrier' of MSSign U1 = dom signature
  U1 by Th12,MSUALG_1:def 8;
  dom signature U1 = dom the charact of U1 by Lm1;
  then reconsider O1 as operation of U1 by A1,FUNCT_1:def 3;
  Args(o,MSAlg U1) = dom O1 by FUNCT_2:def 1;
  then y in (the carrier of U1)* by TARSKI:def 3;
  hence thesis by FINSEQ_1:def 11;
end;
