reserve X for set;
reserve S for Subset-Family of X;

theorem thmIL:
  for X be set st X is cap-closed cup-closed holds
  X is Ring_of_sets
  proof
    let X be set;
    assume X is cap-closed cup-closed;
    then for x,y be set st x in X & y in X holds x/\y in X & x\/y in X;
    hence thesis by COHSP_1:def 7,LATTICE7:def 8;
  end;
