|- (subset 0 a)
|- (mem 0 (pow a))
|- (= (union a a) a)
((all x) (~ (mem x a))) |- (= a 0)
|- (subset (diff c (union a b)) 
           (inter (diff c a) (diff c b))) 
|- (= (diff c (union a b))  
      (inter (diff c a) (diff c b)))
|- (subset (diff c (inter a b))  
           (union (diff c a) (diff c b)))
|- (= (diff c (inter a b))  
      (union (diff c a) (diff c b)))
|- (= (union a (union b c)) (union (union a b) c))
(= U (compl 0)), (= a (inter a U)) |- (= a U)
|- (subset (inter a (union b c))
           (union (inter a b) (inter a c)))

