theorem
  for S be non void non empty ManySortedSign, X be non-empty
  ManySortedSet of the carrier of S holds FreeGen(X)is non-empty
proof
  let S be non void non empty ManySortedSign, X be non-empty ManySortedSet of
  the carrier of S;
  let x be object;
  assume x in the carrier of S;
  then reconsider s = x as SortSymbol of S;
  (FreeGen(X)).s = FreeGen(s,X) by Def16;
  hence thesis;
end;
