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+Zij gegeven de volgende functie-definities:
+
+subs             :: [a] -> [[a]]
+subs []          = [[]]                              (1.)
+subs [x:xs]      = subs xs ++ map (cons x) (subs xs) (2.)
+
+map              :: (a -> b) [a] -> [b]
+map f []         = []                                (3.)
+map f [x:xs]     = [f x : map f xs]                  (4.)
+
+(++)             :: [a] [a] -> [a]
+(++) []     ys   = ys                                (5.)
+(++) [x:xs] ys   = [x : xs ++ ys]                    (6.)
+
+cons             :: a [a] -> [a]
+cons x xs        = [x : xs]                          (7.)
+
+
+Bewijs de volgende stelling voor alle functies f en eindige lijsten xs:
+
+    subs (map f xs) = map (map f) (subs xs).
+
+Je kunt gebruik maken van de volgende hulpstellingen (lemma's) die gelden voor alle
+functies f, g en eindige lijsten xs en ys:
+
+map f (xs ++ ys)       = map f xs ++ map f ys        (8.)
+map g (map f xs)       = map (g o f) xs              (9.)
+(cons (f a)) o (map f) = (map f) o (cons a)          (10.)
+(g o f) x              = g (f x)                     (11.)
+
+
+Bewijs:
+-------