--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Attic/CountSnoc.thy	Fri Feb 05 10:16:10 2016 +0000
@@ -0,0 +1,39 @@
+theory CountSnoc
+imports Main
+begin
+
+
+datatype 'a myList = Nil | Cons 'a "'a myList"
+
+fun app_list :: "'a myList \<Rightarrow> 'a myList \<Rightarrow> 'a myList" where
+"app_list Nil ys = ys" |
+"app_list (Cons x xs) ys = Cons x (app_list xs ys)"
+
+fun rev_list :: "'a myList \<Rightarrow> 'a myList" where
+"rev_list Nil = Nil" |
+"rev_list (Cons x xs) = app_list (rev_list xs) (Cons x Nil)"
+
+fun count_list :: "'a \<Rightarrow> 'a list \<Rightarrow> nat" where
+"count_list x [] = 0" |
+"count_list x (y#xs) = (
+  if x = y then Suc(count_list x xs) 
+  else count_list x xs)"
+
+value "count_list (1::nat) [1,1,1]"
+value "count_list (1::nat) [2,2,2]"
+value "count_list (2::nat) [2,2,1]"
+
+lemma count1: "count_list n (xs @ ys) = count_list n xs + count_list n ys"
+apply(induct xs)
+apply(auto)
+done
+ 
+thm count1
+thm refl
+thm conjI[OF refl[of "a"] refl[of "b"]]
+thm conjI[OF conjI]
+ 
+
+
+
+