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diff --git a/files/practicum/BewijsSubsEnMap.icl b/files/practicum/BewijsSubsEnMap.icl
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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:

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