
theorem
  for S be Subset-Family of REAL
   st S = { I where I is Subset of REAL : I is left_open_interval }
  holds S is with_empty_element semi-diff-closed cap-closed
proof
   let S be Subset-Family of REAL;
   assume S = { I where I is Subset of REAL : I is left_open_interval }; then
S is cap-closed & S is diff-finite-partition-closed with_empty_element &
   S is with_countable_Cover by SRINGS_2:10;
   hence thesis by th10;
end;
