reserve T for non empty TopSpace;
reserve A for Subset of T;

theorem Th56:
  for A being with_non-empty_elements set, B being set st B c= A
  holds B is with_non-empty_elements
proof
  let A be with_non-empty_elements set, B be set;
  assume
A1: B c= A;
  assume {} in B;
  hence thesis by A1;
end;
