reserve I for set;
reserve S for non empty non void ManySortedSign,
  U0, U1 for non-empty MSAlgebra over S;

theorem Th18:
  for U0 being MSAlgebra over S, A being MSSubAlgebra of U0 for o
  being OperSymbol of S, x being set st x in Args(o,A) holds x in Args(o,U0)
proof
  let U0 be MSAlgebra over S, A be MSSubAlgebra of U0, o be OperSymbol of S, x
  be set such that
A1: x in Args(o,A);
  reconsider B0 = the Sorts of A as MSSubset of U0 by MSUALG_2:def 9;
  the MSAlgebra of U0 = the MSAlgebra of U0;
  then U0 is MSSubAlgebra of U0 by MSUALG_2:5;
  then reconsider B1 = the Sorts of U0 as MSSubset of U0 by MSUALG_2:def 9;
  B0 c= B1 by PBOOLE:def 18;
  then ((B0# * the Arity of S).o) c= ((B1# * the Arity of S).o) by MSUALG_2:2;
  hence thesis by A1;
end;
