# HG changeset patch
# User fahadausaf <fahad.ausaf@icloud.com>
# Date 1412599408 -3600
# Node ID a5427713eef44c85b503f1f81a805c1be5ede522
# Parent  a92c10af61bda2708a9efb6a817add10d3bd947a
multiply 2

diff -r a92c10af61bd -r a5427713eef4 thys/#MyFirst.thy#
--- a/thys/#MyFirst.thy#	Mon Oct 06 12:00:46 2014 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,113 +0,0 @@
-theory MyFirst
-imports Main
-begin
-
-datatype 'a list = Nil | Cons 'a "'a list"
-
-fun app :: "'a list \<Rightarrow> 'a list \<Rightarrow> 'a list" where
-"app Nil ys = ys" |
-"app (Cons x xs) ys = Cons x (app xs ys)"
-
-fun rev :: "'a list \<Rightarrow> 'a list" where
-"rev Nil = Nil" |
-"rev (Cons x xs) = app (rev xs) (Cons x Nil)"
-
-value "rev(Cons True (Cons False Nil))"
-
-value "1 + (2::nat)"
-value "1 + (2::int)"
-value "1 - (2::nat)"
-value "1 - (2::int)"
-
-lemma app_Nil2 [simp]: "app xs Nil = xs"
-apply(induction xs)
-apply(auto)
-done
-
-lemma app_assoc [simp]: "app (app xs ys) zs = app xs (app ys zs)"
-apply(induction xs)
-apply(auto)
-done
-
-lemma rev_app [simp]: "rev(app xs ys) = app (rev ys) (rev xs)"
-apply (induction xs)
-apply (auto)
-done
-
-theorem rev_rev [simp]: "rev(rev xs) = xs"
-apply (induction xs)
-apply (auto)
-done
-
-fun add :: "nat \<Rightarrow> nat \<Rightarrow> nat" where
-"add 0 n = n" |
-"add (Suc m) n = Suc(add m n)"
-
-lemma add_02: "add m 0 = m"
-apply(induction m)
-apply(auto)
-done
-
-value "add 2 3"
-
-(**commutative-associative**)
-lemma add_04: "add m (add n k) = add k (add m n)"
-apply(induct)
-apply(auto)
-oops
-
-fun dub :: "nat \<Rightarrow> nat" where
-"dub 0 = 0" |
-"dub m = add m m"
-
-lemma dub_01: "dub 0 = 0"
-apply(induct)
-apply(auto)
-done
-
-lemma dub_02: "dub m = add m m"
-apply(induction m)
-apply(auto)
-done
-
-value "dub 2"
-
-fun trip :: "nat \<Rightarrow> nat" where
-"trip 0 = 0" |
-"trip m = add m (add m m)"
-
-lemma trip_01: "trip 0 = 0"
-apply(induct)
-apply(auto)
-done
-
-lemma trip_02: "trip m = add m (add m m)"
-apply(induction m)
-apply(auto)
-done
-
-value "trip 1"
-value "trip 2"
-
-fun mull :: "nat \<Rightarrow> nat \<Rightarrow> nat" where
-"mull 0 0 = 0" |
-"mull m 0 = 0" |
-(**"mull m 1 = m" | **)
-"mull m n = m*n" 
-
-(**Define a function that counts the
-number of occurrences of an element in a list **)
-(**
-fun count :: "'a\<Rightarrow>'a list\<Rightarrow>nat" where
-"count  "
-**)
-
-
-
-
-
-
-
-
-
-
diff -r a92c10af61bd -r a5427713eef4 thys/MyFirst.thy
--- a/thys/MyFirst.thy	Mon Oct 06 12:00:46 2014 +0100
+++ b/thys/MyFirst.thy	Mon Oct 06 13:43:28 2014 +0100
@@ -93,8 +93,12 @@
 "mull 0 0 = 0" |
 "mull m 0 = 0" |
 (**"mull m 1 = m" | **)
-"mull m n = m*n" 
+(**"mull m (1::nat) = m" | **)
+(**"mull m (suc(0)) = m" | **)
+"mull m n = mull m (n-(1::nat))" 
 
+(**Define a function that counts the
+number of occurrences of an element in a list **)
 (**
 fun count :: "'a\<Rightarrow>'a list\<Rightarrow>nat" where
 "count  "