From a7d7542dc646a5fd124ef71e71ce260889f1701b Mon Sep 17 00:00:00 2001
From: Camil Staps
Date: Tue, 2 Feb 2016 19:24:50 +0100
Subject: Moved to 1415 directory

---
 1415/files/practicum/BewijsSubsEnMap.icl | 33 ++++++++++++++++++++++++++++++++
 1 file changed, 33 insertions(+)
 create mode 100644 1415/files/practicum/BewijsSubsEnMap.icl

(limited to '1415/files/practicum/BewijsSubsEnMap.icl')

diff --git a/1415/files/practicum/BewijsSubsEnMap.icl b/1415/files/practicum/BewijsSubsEnMap.icl
new file mode 100644
index 0000000..43329e3
--- /dev/null
+++ b/1415/files/practicum/BewijsSubsEnMap.icl
@@ -0,0 +1,33 @@
+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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