
theorem
  for x,y being set holds {x,y,x /\ y} is c=filtered
proof
  let x,y be set;
  let A be finite Subset of {x,y,x /\ y};
  take a = x /\ y;
  hereby
    let b be set;
    assume b in A;
    then b = x or b = y or b = x /\ y by ENUMSET1:def 1;
    hence a c= b by XBOOLE_1:17;
  end;
  thus thesis by ENUMSET1:def 1;
end;
