hwsub draft
authorlammich <lammich@in.tum.de>
Mon, 23 Apr 2018 11:46:13 +0200
changeset 69920 994af7618cd7
parent 69919 db20be610639
child 69921 17c8fbbda477
hwsub
Ex_Fundus/Ex_Tree_Addressing.thy
SS18/Exercises/BST_Demo.thy
SS18/Exercises/hwsubm/hw01/a.kutafina@tum.de/msg-30498-1.txt
SS18/Exercises/hwsubm/hw01/a.kutafina@tum.de/sum.thy
SS18/Exercises/hwsubm/hw01/a.putwattana@tum.de/hw01.thy
SS18/Exercises/hwsubm/hw01/a.putwattana@tum.de/msg-30498-3.txt
SS18/Exercises/hwsubm/hw01/a.putwattana@tum.de/msg-30498-4.html
SS18/Exercises/hwsubm/hw01/alexejrotar@gmail.com/hw01.thy
SS18/Exercises/hwsubm/hw01/alexejrotar@gmail.com/msg-30498-2.txt
SS18/Exercises/hwsubm/hw01/daniel.kutasi@outlook.de/hw01.thy
SS18/Exercises/hwsubm/hw01/daniel.kutasi@outlook.de/msg-30498-5.txt
SS18/Exercises/hwsubm/hw01/daniel.kutasi@outlook.de/msg-30498-6.html
SS18/Exercises/hwsubm/hw01/eric.koepke@online.de/ex01.thy
SS18/Exercises/hwsubm/hw01/eric.koepke@online.de/msg-30498-7.txt
SS18/Exercises/hwsubm/hw01/explode_info
SS18/Exercises/hwsubm/hw01/extracted/a.kutafina@tum.de
SS18/Exercises/hwsubm/hw01/extracted/a.putwattana@tum.de
SS18/Exercises/hwsubm/hw01/extracted/alexejrotar@gmail.com
SS18/Exercises/hwsubm/hw01/extracted/daniel.kutasi@outlook.de
SS18/Exercises/hwsubm/hw01/extracted/eric.koepke@online.de
SS18/Exercises/hwsubm/hw01/extracted/felix.wielander@tum.de
SS18/Exercises/hwsubm/hw01/extracted/florian.stamer@tum.de
SS18/Exercises/hwsubm/hw01/extracted/g.bidlingmaier@tum.de
SS18/Exercises/hwsubm/hw01/extracted/ga53qud@mytum.de
SS18/Exercises/hwsubm/hw01/extracted/ge69kel@mytum.de
SS18/Exercises/hwsubm/hw01/extracted/ge72lic@mytum.de
SS18/Exercises/hwsubm/hw01/extracted/j.gottfriedsen@tum.de
SS18/Exercises/hwsubm/hw01/extracted/j.v.mutius@gmail.com
SS18/Exercises/hwsubm/hw01/extracted/jonatan.juhas@tum.de
SS18/Exercises/hwsubm/hw01/extracted/katharinaluise.schmitt@tum.de
SS18/Exercises/hwsubm/hw01/extracted/m.kirchmeier@tum.de
SS18/Exercises/hwsubm/hw01/extracted/markuswebel@gmail.com
SS18/Exercises/hwsubm/hw01/extracted/martin.rau@tum.de
SS18/Exercises/hwsubm/hw01/extracted/mitja.krebs@tum.de
SS18/Exercises/hwsubm/hw01/extracted/odnoshivkin@me.com
SS18/Exercises/hwsubm/hw01/extracted/omar.badramany@tum.de
SS18/Exercises/hwsubm/hw01/extracted/s.griebel@tum.de
SS18/Exercises/hwsubm/hw01/extracted/sabine.rieder@tum.de
SS18/Exercises/hwsubm/hw01/extracted/smith.nickh@gmail.com
SS18/Exercises/hwsubm/hw01/felix.wielander@tum.de/hw01.thy
SS18/Exercises/hwsubm/hw01/felix.wielander@tum.de/msg-30498-8.txt
SS18/Exercises/hwsubm/hw01/florian.stamer@tum.de/ex01.thy
SS18/Exercises/hwsubm/hw01/florian.stamer@tum.de/msg-30498-10.html
SS18/Exercises/hwsubm/hw01/florian.stamer@tum.de/msg-30498-9.txt
SS18/Exercises/hwsubm/hw01/g.bidlingmaier@tum.de/ex01.thy
SS18/Exercises/hwsubm/hw01/g.bidlingmaier@tum.de/msg-30498-13.txt
SS18/Exercises/hwsubm/hw01/ga53qud@mytum.de/hw01.thy
SS18/Exercises/hwsubm/hw01/ga53qud@mytum.de/msg-30498-11.txt
SS18/Exercises/hwsubm/hw01/ga53qud@mytum.de/msg-30498-12.html
SS18/Exercises/hwsubm/hw01/ge69kel@mytum.de/Homework01.thy
SS18/Exercises/hwsubm/hw01/ge69kel@mytum.de/msg-30498-14.txt
SS18/Exercises/hwsubm/hw01/ge69kel@mytum.de/msg-30498-15.html
SS18/Exercises/hwsubm/hw01/ge72lic@mytum.de/ex01.thy
SS18/Exercises/hwsubm/hw01/ge72lic@mytum.de/msg-30498-16.txt
SS18/Exercises/hwsubm/hw01/ge72lic@mytum.de/msg-30498-17.html
SS18/Exercises/hwsubm/hw01/j.gottfriedsen@tum.de/ex01.thy
SS18/Exercises/hwsubm/hw01/j.gottfriedsen@tum.de/msg-30498-18.txt
SS18/Exercises/hwsubm/hw01/j.gottfriedsen@tum.de/msg-30498-19.html
SS18/Exercises/hwsubm/hw01/j.v.mutius@gmail.com/hw01.thy
SS18/Exercises/hwsubm/hw01/j.v.mutius@gmail.com/msg-30498-22.txt
SS18/Exercises/hwsubm/hw01/jonatan.juhas@tum.de/ha01.thy
SS18/Exercises/hwsubm/hw01/jonatan.juhas@tum.de/msg-30498-20.txt
SS18/Exercises/hwsubm/hw01/jonatan.juhas@tum.de/msg-30498-21.html
SS18/Exercises/hwsubm/hw01/katharinaluise.schmitt@tum.de/ex01.thy
SS18/Exercises/hwsubm/hw01/katharinaluise.schmitt@tum.de/msg-30498-23.txt
SS18/Exercises/hwsubm/hw01/katharinaluise.schmitt@tum.de/msg-30498-24.html
SS18/Exercises/hwsubm/hw01/m.kirchmeier@tum.de/hw01.thy
SS18/Exercises/hwsubm/hw01/m.kirchmeier@tum.de/msg-30498-29.txt
SS18/Exercises/hwsubm/hw01/markuswebel@gmail.com/ex01.thy
SS18/Exercises/hwsubm/hw01/markuswebel@gmail.com/msg-30498-25.txt
SS18/Exercises/hwsubm/hw01/markuswebel@gmail.com/msg-30498-26.html
SS18/Exercises/hwsubm/hw01/martin.rau@tum.de/Home01.thy
SS18/Exercises/hwsubm/hw01/martin.rau@tum.de/msg-30498-27.txt
SS18/Exercises/hwsubm/hw01/mitja.krebs@tum.de/hw01.thy
SS18/Exercises/hwsubm/hw01/mitja.krebs@tum.de/msg-30498-28.txt
SS18/Exercises/hwsubm/hw01/odnoshivkin@me.com/hw1.thy
SS18/Exercises/hwsubm/hw01/odnoshivkin@me.com/msg-30498-30.txt
SS18/Exercises/hwsubm/hw01/omar.badramany@tum.de/hw01.thy
SS18/Exercises/hwsubm/hw01/omar.badramany@tum.de/msg-30498-31.txt
SS18/Exercises/hwsubm/hw01/omar.badramany@tum.de/msg-30498-32.html
SS18/Exercises/hwsubm/hw01/s.griebel@tum.de/homework_1.thy
SS18/Exercises/hwsubm/hw01/s.griebel@tum.de/msg-30498-35.txt
SS18/Exercises/hwsubm/hw01/s.griebel@tum.de/msg-30498-36.html
SS18/Exercises/hwsubm/hw01/sabine.rieder@tum.de/hw01.thy
SS18/Exercises/hwsubm/hw01/sabine.rieder@tum.de/msg-30498-33.txt
SS18/Exercises/hwsubm/hw01/sabine.rieder@tum.de/msg-30498-34.html
SS18/Exercises/hwsubm/hw01/smith.nickh@gmail.com/HW1.thy
SS18/Exercises/hwsubm/hw01/smith.nickh@gmail.com/msg-30498-37.txt
SS18/Exercises/hwsubm/hw01/smith.nickh@gmail.com/msg-30498-38.html
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Ex_Fundus/Ex_Tree_Addressing.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,155 @@
+theory Ex_Tree_Addressing
+imports Main
+begin
+
+  datatype tree = LEAF | NODE tree tree
+
+  type_synonym path = "bool list"
+
+  fun valid :: "tree \<Rightarrow> path \<Rightarrow> bool" where
+    "valid t [] \<longleftrightarrow> True"
+  | "valid (NODE l r) (p#ps) \<longleftrightarrow> (if p then valid r ps else valid l ps)"
+  | "valid _ _ \<longleftrightarrow> False"  
+  
+  fun get :: "tree \<Rightarrow> path \<Rightarrow> tree" where
+    "get t [] = t"
+  | "get (NODE l r) (p#ps) = (if p then get r ps else get l ps)"
+  | "get _ _ = undefined"    
+
+  fun put :: "tree \<Rightarrow> path \<Rightarrow> tree \<Rightarrow> tree" where
+    "put _ [] s = s"
+  | "put (NODE l r) (p#ps) s = (if p then NODE l (put r ps s) else NODE (put l ps s) r)"  
+  | "put t _ _ = t"
+
+  lemma put_invalid: "\<not>valid t p \<Longrightarrow> put t p s = t"
+    apply (induction t p rule: valid.induct) by auto
+    
+  (* Lens laws *)
+  lemma put_get: "valid t p \<Longrightarrow> put t p (get t p) = t"  
+    apply (induction t p rule: valid.induct) by auto
+    
+  lemma put_put: "valid t p \<Longrightarrow> put (put t p s) p s' = put t p s'"
+    apply (induction t p rule: valid.induct) by auto
+
+  lemma get_put: "valid t p \<Longrightarrow> get (put t p s) p = s"  
+    apply (induction t p rule: valid.induct) by auto
+
+  lemma valid_put: "valid t p \<Longrightarrow> valid (put t p s) p"  
+    apply (induction t p rule: valid.induct) by auto
+    
+  lemmas lens_laws = put_get put_put get_put valid_put     
+    
+  (* Append *)  
+  lemma valid_append: "valid t (p@q) \<longleftrightarrow> valid t p \<and> valid (get t p) q"
+    apply (induction t p rule: valid.induct) by auto
+    
+  lemma get_append: "valid t (p@q) \<Longrightarrow> get t (p@q) = get (get t p) q"
+    apply (induction t p rule: valid.induct) by auto
+    
+  lemma put_append: "valid t (p@q) \<Longrightarrow> put t (p@q) s = put t p (put (get t p) q s)"
+    apply (induction t p rule: valid.induct) by auto
+    
+    
+  lemma "valid t p \<Longrightarrow> valid s q \<Longrightarrow> valid (put t p s) (p@q)"
+    by (simp add: valid_append put_append lens_laws)
+  
+
+    
+  definition "path_le p q \<equiv> \<exists>p'. p@p' = q"
+  
+  lemma [simp]: "path_le [] q" unfolding path_le_def by auto
+  lemma [simp]: "path_le (d#p) (e#q) \<longleftrightarrow> d=e \<and> path_le p q"    
+    unfolding path_le_def by auto
+  lemma [simp]: "path_le p [] \<longleftrightarrow> p=[]"  
+    unfolding path_le_def by auto
+
+  lemma [simp]: "path_le ps (q#qs) \<longleftrightarrow> ps=[] \<or> (\<exists>ps'. ps=q#ps' \<and> path_le ps' qs)"  
+    by (cases ps) auto
+  lemma [simp]: "path_le (p#ps) qs \<longleftrightarrow> (\<exists>qs'. qs=p#qs' \<and> path_le ps qs')"  
+    by (cases qs) auto
+    
+        
+  (* Show that this is actually a pre-order *)
+  lemma path_le_refl[simp]: "path_le p p"  
+    unfolding path_le_def by auto
+      
+  lemma path_le_antisym: "\<lbrakk>path_le p q; path_le q p\<rbrakk> \<Longrightarrow> p=q"  
+    unfolding path_le_def by auto
+    
+  lemma path_le_trans[trans]: "\<lbrakk>path_le p q; path_le q r\<rbrakk> \<Longrightarrow> path_le p r"  
+    unfolding path_le_def by auto
+  
+  (* Incomparable positions are called independent *)    
+  definition "indep p q \<equiv> \<not>path_le p q \<and> \<not>path_le q p"
+  
+  lemma [simp]:
+    "\<not>indep ps []"
+    "\<not>indep [] qs"
+    "indep (p#ps) qs \<longleftrightarrow> (\<exists>q qs'. qs=q#qs' \<and> (p\<noteq>q \<or> indep ps qs'))"
+    "indep ps (q#qs) \<longleftrightarrow> (\<exists>p ps'. ps=p#ps' \<and> (p\<noteq>q \<or> indep ps' qs))"
+    unfolding indep_def 
+    apply simp
+    apply simp
+    apply (cases qs; auto)
+    apply (cases ps; auto)
+    done
+    
+  (* Show the following algebraic laws *)  
+  lemma indep_get_put: "\<lbrakk> valid t p; valid t q; indep p q \<rbrakk> 
+    \<Longrightarrow> get (put t p s) q = get t q"  
+    apply (induction t p arbitrary: q rule: get.induct)
+    apply (auto)
+    done  
+    
+  lemma par_replace_commute: "\<lbrakk> valid t p; valid t q; indep p q \<rbrakk>
+    \<Longrightarrow> put (put t p s) q r = put (put t q r) p s"  
+    apply (induction t p arbitrary: q rule: get.induct)
+    apply (auto)
+    done  
+    
+    
+    
+    
+    
+    
+    
+  fun indep' :: "path \<Rightarrow> path \<Rightarrow> bool" where
+    "indep' _ [] \<longleftrightarrow> False"
+  | "indep' [] _ \<longleftrightarrow> False"  
+  | "indep' (a#as) (b#bs) \<longleftrightarrow> a\<noteq>b \<or> indep' as bs"
+
+  lemma indep'_comm: "indep' p q \<Longrightarrow> indep' q p"
+    by (induction p q rule: indep'.induct) auto 
+    
+    
+  lemma indep'_valid: "valid t q \<Longrightarrow> indep' p q \<Longrightarrow> valid (put t p s) q \<longleftrightarrow> valid t q"
+    apply (cases "valid t p")
+    apply (simp_all add: put_invalid)
+    apply (induction p q arbitrary: t rule: indep'.induct)  
+    apply simp_all
+    subgoal for a as b bs t by (cases t; cases a; cases b; auto)
+    done    
+    
+  lemma indep'_put_swap: "valid t p \<Longrightarrow> valid t q \<Longrightarrow> indep' p q \<Longrightarrow> put (put t p s) q r = put (put t q r) p s"
+    apply (induction p q arbitrary: t rule: indep'.induct)  
+    apply simp_all
+    subgoal for a as b bs t by (cases t; cases a; cases b; auto)
+    done
+                        
+  lemma "valid t p \<Longrightarrow> indep' p q \<Longrightarrow> get (put t q s) p = get t p"  
+    apply (cases "valid t q")
+    apply (simp_all add: put_invalid)
+  proof -
+    assume [simp]: "valid t p" "valid t q" "indep' p q"
+    have "put t p (get t p) = t" by (simp add: lens_laws) 
+    
+    hence "get (put t q s) p = get (put (put t p (get t p)) q s) p"
+      by simp
+    also have "put (put t p (get t p)) q s = put (put t q s) p (get t p)"
+      by (simp add: indep'_put_swap)
+    finally show ?thesis 
+      by (simp add: lens_laws indep'_valid indep'_comm)  
+  qed
+
+end
+  
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/BST_Demo.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,196 @@
+theory BST_Demo
+imports "~~/src/HOL/Library/Tree"
+begin
+
+(* useful most of the time: *)
+declare Let_def [simp]
+
+section "Basic BST Functions"
+
+fun isin :: "('a::linorder) tree \<Rightarrow> 'a \<Rightarrow> bool" where
+"isin Leaf x = False" |
+"isin (Node l a r) x =
+  (if x < a then isin l x else
+   if x > a then isin r x
+   else True)"
+
+fun ins :: "'a::linorder \<Rightarrow> 'a tree \<Rightarrow> 'a tree" where
+"ins x Leaf = Node Leaf x Leaf" |
+"ins x (Node l a r) =
+  (if x < a then Node (ins x l) a r else
+   if x > a then Node l a (ins x r)
+   else Node l a r)"
+
+subsection "Functional Correctness"
+
+lemma set_tree_isin: "bst t \<Longrightarrow> isin t x = (x \<in> set_tree t)"
+apply(induction t)
+apply auto
+done
+
+lemma set_tree_ins: "set_tree (ins x t) = {x} \<union> set_tree t"
+apply(induction t)
+apply auto
+done
+
+subsection "Preservation of Invariant"
+
+lemma bst_ins: "bst t \<Longrightarrow> bst (ins x t)"
+apply(induction t)
+apply (auto simp: set_tree_ins)
+done
+
+
+section "Reducing the Number of Comparisons"
+
+text\<open>Idea: never test for \<open>=\<close> but remember the last value where you
+should have tested for \<open>=\<close> but did not. Compare with that value when
+you reach a leaf.\<close>
+
+fun isin2 :: "('a::linorder) tree \<Rightarrow> 'a option \<Rightarrow> 'a \<Rightarrow> bool" where
+"isin2 Leaf z x = (case z of None \<Rightarrow> False | Some y \<Rightarrow> x = y) " |
+"isin2 (Node l a r) z x =
+  (if x < a then isin2 l z x else isin2 r (Some a) x)"
+
+lemma isin2_Some:
+  "\<lbrakk> bst t;  \<forall>x \<in> set_tree t. y < x \<rbrakk>
+  \<Longrightarrow> isin2 t (Some y) x = (isin t x \<or> x=y)"
+apply(induction t arbitrary: y)
+apply auto
+done
+
+lemma isin2_None:
+  "bst t \<Longrightarrow> isin2 t None x = isin t x"
+apply(induction t)
+apply (auto simp: isin2_Some)
+done
+
+
+section "Trees with Size Info"
+
+type_synonym 'a tree_sz = "('a * nat) tree"
+
+fun inv_sz :: "('a::linorder) tree_sz \<Rightarrow> bool" where
+"inv_sz \<langle>\<rangle> = True" |
+"inv_sz \<langle>l, (a,s), r\<rangle> = (inv_sz l \<and> inv_sz r \<and> s = size l + size r + 1)"
+
+fun sz :: "'a tree_sz \<Rightarrow> nat" where
+"sz Leaf = 0" |
+"sz (Node _ (_,s) _) = s"
+
+abbreviation un_sz :: "'a tree_sz \<Rightarrow> 'a tree" where
+"un_sz t == map_tree fst t"
+
+fun ins_sz :: "'a::linorder \<Rightarrow> 'a tree_sz \<Rightarrow> 'a tree_sz" where
+"ins_sz x Leaf = Node Leaf (x,1) Leaf" |
+"ins_sz x (Node l (a,s) r) =
+  (if x < a then let l' = ins_sz x l in Node l' (a, sz l' + sz r + 1) r else
+   if x > a then let r' = ins_sz x r in Node l (a, sz l + sz r' + 1) r'
+   else Node l (a,s) r)"
+
+subsection "Functional Correctness"
+
+lemma un_sz_ins_sz: "un_sz (ins_sz x t) = ins x (un_sz t)"
+apply(induction t)
+apply auto
+done
+
+subsection "Preservation of Invariants"
+
+lemma "bst(un_sz t) \<Longrightarrow> bst(un_sz (ins_sz x t))"
+by(simp add: un_sz_ins_sz bst_ins)
+
+lemma sz_size[simp]: "inv_sz t \<Longrightarrow> sz t = size t"
+apply(induction t)
+apply auto
+done
+
+lemma "inv_sz t \<Longrightarrow> inv_sz (ins_sz x t)"
+apply(induction t)
+apply (auto)
+done
+
+(* nth smallest element: *)
+fun nth_min :: "('a::linorder) tree_sz \<Rightarrow> nat \<Rightarrow> 'a" where
+"nth_min \<langle>l, (a,s), r\<rangle> n =
+   (let sl = sz l in
+    if n = sl then a else
+    if n < sl then nth_min l n else nth_min r (n-sl-1))"
+
+lemma "\<lbrakk> bst(un_sz t);  inv_sz t;  n < size t \<rbrakk>
+ \<Longrightarrow> nth_min t n = nth (inorder(un_sz t)) n"
+apply(induction t arbitrary: n)
+apply (auto simp: nth_append)
+done
+
+(* First precond not necessary *)  
+lemma "\<lbrakk> (*bst(un_sz t);*)  inv_sz t;  n < size t \<rbrakk>
+ \<Longrightarrow> nth_min t n = nth (inorder(un_sz t)) n"
+apply(induction t arbitrary: n)
+apply (auto simp: nth_append)
+done
+
+section "Compressing the Height of BSTs"
+
+fun compress :: "'a tree \<Rightarrow> 'a tree" where
+"compress (Node Leaf a t) =
+  (case compress t of
+     Node Leaf b u \<Rightarrow> Node (Node Leaf a Leaf) b u |
+     u \<Rightarrow> Node Leaf a u)" |
+"compress (Node l a r) = Node (compress l) a (compress r)" |
+"compress Leaf = Leaf"
+
+(* Another way of saying that \<open>bst\<close> and \<open>set_tree\<close> are preserved: *)
+lemma "inorder(compress t) = inorder t"
+apply(induction t rule: compress.induct)
+apply (auto split: tree.split)
+done
+
+lemma "height (compress t) \<le> height t"
+apply(induction t rule: compress.induct)
+apply (auto split: tree.split)
+done
+
+(* What is the correct relationship? *)
+lemma "height t \<le> height (compress t)"
+oops
+
+
+section "BST Implementation of Maps"
+
+fun lookup :: "('a::linorder * 'b) tree \<Rightarrow> 'a \<Rightarrow> 'b option" where
+"lookup Leaf x = None" |
+"lookup (Node l (a,b) r) x =
+  (if x < a then lookup l x else
+   if x > a then lookup r x
+   else Some b)"
+
+fun update :: "'a \<Rightarrow> 'b \<Rightarrow> ('a::linorder * 'b) tree \<Rightarrow> ('a * 'b) tree" where
+"update x y Leaf = Node Leaf (x,y) Leaf" |
+"update x y (Node l (a,b) r) =
+  (if x < a then Node (update x y l) (a,b) r else
+   if x > a then Node l (a,b) (update x y r)
+   else Node l (x,y) r)"
+
+subsection "Functional Correctness"
+
+lemma "lookup (update x y t) a = (if x=a then Some y else lookup t a)"
+apply(induction t)
+apply auto
+done
+
+subsection "Preservation of Invariant"
+
+definition "bst1 t = bst (map_tree fst t)"
+
+lemma map_tree_update: "map_tree fst (update x y t) = ins x (map_tree fst t)"
+apply(induction t)
+apply auto
+done
+
+lemma "bst1 t \<Longrightarrow> bst1(update x y t)"
+apply(induction t)
+apply (auto simp: bst1_def map_tree_update set_tree_ins)
+done
+
+end
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/a.kutafina@tum.de/msg-30498-1.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,18 @@
+Dear Dr Lammich,
+
+sorry, I did not receive your email, so I tried to upload my homework at 
+nipkow3 portal. My Matrikelnummer is 03668266, if it's needed
+
+Best wishes
+Anastassiya Kutrafina
+
+-- 
+Mit freundlichen Grüßen
+
+Anastassiya Kutafina
+
+-- 
+Mit freundlichen Grüßen
+
+Anastassiya Kutafina
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/a.kutafina@tum.de/sum.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,32 @@
+(** Score: 7/10
+
+  Missing: Filter_pos, flatten
+*)
+
+theory sum
+  imports Main
+begin
+
+
+fun listsum :: "int list \<Rightarrow> int" where
+    "listsum [] = 0"
+  | "listsum (x#xs) = x + listsum xs"
+
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x. x \<noteq> 0 ) l ) = listsum l"
+  apply(induction l)
+  apply(auto)
+  done
+
+
+lemma aux_listsum_rev[simp] : "listsum (xs @ [a]) = a + listsum xs"
+  apply(induction xs)
+  apply(auto)
+  done
+
+lemma listsum_rev : "listsum (rev xs) = listsum xs"
+  apply(induction xs)
+  apply(auto)
+  done 
+
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/a.putwattana@tum.de/hw01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,48 @@
+(** Score: 10/10
+*)
+theory hw01
+imports Main
+begin
+  
+fun listsum :: "int list => int" where
+  "listsum [] = 0"
+| "listsum (x#xs) = x + listsum xs"
+
+  value "listsum [1,2,3] = 6"
+  value "listsum [] = 0"
+  value "listsum [1,-2,3] = 2"
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x. x \<noteq> 0) l) = listsum l" 
+  apply (induction l)
+   apply auto
+  done
+
+lemma listsum_aux[simp]: "listsum (xs @ ys) = listsum xs + listsum ys"
+  apply (induction xs)
+   apply auto
+  done
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+  apply (induction xs)
+   apply auto
+  done
+
+lemma "listsum (filter (\<lambda>x. \<not> x < 0) l) \<ge> listsum l"
+  apply (induction l)
+   apply auto
+  done
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+  "flatten [] = []"
+| "flatten (l # ls) = l @ flatten ls"
+
+value "flatten [[1, 2, 3], [2]] = [1, 2, 3, 2::int]"
+value "flatten [[1, 2, 3], [], [2]] = [1, 2, 3, 2:: int]"
+
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply (induction xs)
+   apply auto
+  done
+
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/a.putwattana@tum.de/msg-30498-3.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,14 @@
+Dear Dr. Peter Lammich,
+
+
+I could not find a way to submit the homework to submission system.  So, I attach it with this email.
+
+My matriculation number is 03693616.
+
+
+Thank you for your consideration.
+
+
+Best regards,
+
+Attakorn Putwattana
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/a.putwattana@tum.de/msg-30498-4.html	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,22 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" style="font-size:12pt;color:#000000;font-family:Calibri,Helvetica,sans-serif;" dir="ltr">
+<p>Dear Dr. Peter Lammich,</p>
+<p><br>
+</p>
+<p>I could not find a way to submit the homework to submission system.&nbsp; So, I attach it with this email.</p>
+<p>My m<span>atriculation number is 03693616.</span></p>
+<p><span><br>
+</span></p>
+<p>Thank you for your consideration.</p>
+<p><br>
+</p>
+<p>Best regards,</p>
+<p>Attakorn Putwattana</p>
+</div>
+</body>
+</html>
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/alexejrotar@gmail.com/hw01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,47 @@
+(** Score: 10/10
+*)
+theory hw01
+  imports Main
+begin
+
+fun listsum :: "int list \<Rightarrow> int" where
+"listsum [] = 0" |
+"listsum (x#xs) = x + listsum xs"
+
+value "listsum [1,2,3] = 6"
+value "listsum [] = 0"
+value "listsum [1,-2,3] = 2"
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x. x \<noteq> 0) xs) = listsum xs"
+  apply(induction xs)
+  apply(auto)
+  done
+
+lemma listsum_app: "listsum (xs @ ys) = listsum xs + listsum ys"
+  apply(induction xs)
+   apply(auto)
+  done
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+  apply(induction xs)
+   apply(auto simp: listsum_app)
+  done
+
+lemma listsum_filter_neg: "listsum (filter (op \<le> 0) xs) \<ge> listsum xs"
+  apply(induction xs)
+   apply(auto)
+  done
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+"flatten [] = []" |
+"flatten (x#xs) = x @ flatten xs"
+
+value "flatten [[1,2,3],[2]] = [1,2,3,2::int]"
+value "flatten [[1,2,3],[],[2]] = [1,2,3,2::int]"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply(induction xs)
+   apply(auto simp: listsum_app)
+  done
+
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/alexejrotar@gmail.com/msg-30498-2.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,3 @@
+Hello,
+sorry for the late submission. I've just read your mail. Hope it's
+still ok.
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/daniel.kutasi@outlook.de/hw01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,46 @@
+(** Score: 10/10
+*)
+theory hw01
+imports Main
+begin
+
+fun listsum :: "int list \<Rightarrow> int" where
+  "listsum [] = 0"
+| "listsum (x # xs) = x + listsum xs"
+
+value "listsum [1,2,3] = 6"
+value "listsum [] = 0"
+value "listsum [1,-2,3] = 2"
+
+lemma listsum_filter_z: "listsum (filter (%x. x \<noteq> 0) l) = listsum l"
+  apply (induction l)
+  by auto
+
+lemma listsum_rev_aux[simp]: "listsum (xs @ [a]) = a + listsum xs"
+  apply (induction xs)
+  by auto
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+  apply (induction xs)
+  by auto
+
+lemma listsum_positives: "listsum (filter (%x. x \<ge> 0) xs) \<ge> listsum xs"
+  apply (induction xs)
+  by auto
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+  "flatten [] = []"
+| "flatten (l#ls) = l @ flatten ls"
+
+value "flatten [[1,2,3],[2]] = [1,2,3,2::int]"
+value "flatten [[1,2,3],[],[2]] = [1,2,3,2::int]"
+
+lemma listsum_flatten_aux[simp]: "listsum (xs @ ys) = listsum xs + listsum ys"
+  apply (induction xs)
+  by auto
+
+lemma listsum_flatten: "listsum (flatten xs) = listsum (map listsum xs)"
+  apply (induction xs)
+  by auto
+
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/daniel.kutasi@outlook.de/msg-30498-5.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,7 @@
+Hi,
+here's my submission.
+Best regards
+
+
+Kennung: ga68zak
+Matr-Nr. 03623674
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/daniel.kutasi@outlook.de/msg-30498-6.html	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,17 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
+</head>
+<body>
+<div dir="ltr">Hi,
+<div>here's my submission.</div>
+<div>Best regards</div>
+<div><br>
+</div>
+<div><br>
+</div>
+<div>Kennung: ga68zak</div>
+<div>Matr-Nr. 03623674</div>
+</div>
+</body>
+</html>
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/eric.koepke@online.de/ex01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,49 @@
+(** Score: 10/10
+*)
+theory ex01
+imports Main
+begin
+fun listsum:: "int list \<Rightarrow> int" where
+ "listsum (b#a)  =(listsum a) + b"
+|"listsum [] = 0"
+
+
+value "listsum [1,2,3]"
+value "listsum []"
+value "listsum [1,-2,3]"
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x. x\<noteq>0) l) = listsum l"
+  apply (induction l)
+  apply auto
+  done
+
+lemma aux_app: "listsum (xs @ [a]) = listsum (a#xs)"
+  apply (induction xs)
+  apply auto
+  done
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+  apply (induction xs)
+  apply (auto simp: aux_app)
+  done
+
+lemma listsum_filter_n: "listsum (filter (\<lambda>x. x\<ge>0) l) \<ge> listsum l"
+  apply (induction l)
+  apply auto
+  done
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+  "flatten [] = []"
+| "flatten (l#ls) = l @ flatten ls"
+
+value "flatten [[1::int,2,3],[2]]"
+
+lemma aux_sum: "listsum (xs @ a) = listsum xs + listsum a"
+  apply (induction xs)
+  apply auto
+  done
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply (induction xs)
+  apply (auto simp: aux_sum)
+  done
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/eric.koepke@online.de/msg-30498-7.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,6 @@
+Hello,
+Matr.Nr.: 03665531
+Homework is attached.
+
+Greetings,
+Eric Koepke
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/explode_info	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,86 @@
+Message: msg0 (a.kutafina@tum.de)
+    Part: msg0/msg-30498-1.txt (text/plain)
+    Part: msg0/sum.thy (text/plain)
+Message: msg1 (alexejrotar@gmail.com)
+    Part: msg1/msg-30498-2.txt (text/plain)
+    Part: msg1/hw01.thy (text/plain)
+Message: msg2 (a.putwattana@tum.de)
+    Part: msg2/msg-30498-3.txt (text/plain)
+    Part: msg2/msg-30498-4.html (text/html)
+    Part: msg2/hw01.thy (application/octet-stream)
+Message: msg3 (daniel.kutasi@outlook.de)
+    Part: msg3/msg-30498-5.txt (text/plain)
+    Part: msg3/msg-30498-6.html (text/html)
+    Part: msg3/hw01.thy (application/octet-stream)
+Message: msg4 (eric.koepke@online.de)
+    Part: msg4/msg-30498-7.txt (text/plain)
+    Part: msg4/ex01.thy (application/octet-stream)
+Message: msg5 (felix.wielander@tum.de)
+    Part: msg5/msg-30498-8.txt (text/plain)
+    Part: msg5/hw01.thy (text/plain)
+Message: msg6 (florian.stamer@tum.de)
+    Part: msg6/msg-30498-9.txt (text/plain)
+    Part: msg6/msg-30498-10.html (text/html)
+    Part: msg6/ex01.thy (application/octet-stream)
+Message: msg7 (ga53qud@mytum.de)
+    Part: msg7/msg-30498-11.txt (text/plain)
+    Part: msg7/msg-30498-12.html (text/html)
+    Part: msg7/hw01.thy (application/octet-stream)
+Message: msg8 (g.bidlingmaier@tum.de)
+    Part: msg8/msg-30498-13.txt (text/plain)
+    Part: msg8/ex01.thy (text/plain)
+Message: msg9 (ge69kel@mytum.de)
+    Part: msg9/msg-30498-14.txt (text/plain)
+    Part: msg9/msg-30498-15.html (text/html)
+    Part: msg9/Homework01.thy (application/octet-stream)
+Message: msg10 (ge72lic@mytum.de)
+    Part: msg10/msg-30498-16.txt (text/plain)
+    Part: msg10/msg-30498-17.html (text/html)
+    Part: msg10/ex01.thy (application/octet-stream)
+Message: msg11 (j.gottfriedsen@tum.de)
+    Part: msg11/msg-30498-18.txt (text/plain)
+    Part: msg11/msg-30498-19.html (text/html)
+    Part: msg11/ex01.thy (application/octet-stream)
+Message: msg12 (jonatan.juhas@tum.de)
+    Part: msg12/msg-30498-20.txt (text/plain)
+    Part: msg12/msg-30498-21.html (text/html)
+    Part: msg12/ha01.thy (application/octet-stream)
+Message: msg13 (j.v.mutius@gmail.com)
+    Part: msg13/msg-30498-22.txt (text/plain)
+    Part: msg13/hw01.thy (text/plain)
+Message: msg14 (katharinaluise.schmitt@tum.de)
+    Part: msg14/msg-30498-23.txt (text/plain)
+    Part: msg14/msg-30498-24.html (text/html)
+    Part: msg14/ex01.thy (application/octet-stream)
+Message: msg15 (markuswebel@gmail.com)
+    Part: msg15/msg-30498-25.txt (text/plain)
+    Part: msg15/msg-30498-26.html (text/html)
+    Part: msg15/ex01.thy (application/octet-stream)
+Message: msg16 (martin.rau@tum.de)
+    Part: msg16/msg-30498-27.txt (text/plain)
+    Part: msg16/Home01.thy (text/plain)
+Message: msg17 (mitja.krebs@tum.de)
+    Part: msg17/msg-30498-28.txt (text/plain)
+    Part: msg17/hw01.thy (application/octet-stream)
+Message: msg18 (m.kirchmeier@tum.de)
+    Part: msg18/msg-30498-29.txt (text/plain)
+    Part: msg18/hw01.thy (text/plain)
+Message: msg19 (odnoshivkin@me.com)
+    Part: msg19/msg-30498-30.txt (text/plain)
+    Part: msg19/hw1.thy (application/octet-stream)
+Message: msg20 (omar.badramany@tum.de)
+    Part: msg20/msg-30498-31.txt (text/plain)
+    Part: msg20/msg-30498-32.html (text/html)
+    Part: msg20/hw01.thy (application/octet-stream)
+Message: msg21 (sabine.rieder@tum.de)
+    Part: msg21/msg-30498-33.txt (text/plain)
+    Part: msg21/msg-30498-34.html (text/html)
+    Part: msg21/hw01.thy (application/octet-stream)
+Message: msg22 (s.griebel@tum.de)
+    Part: msg22/msg-30498-35.txt (text/plain)
+    Part: msg22/msg-30498-36.html (text/html)
+    Part: msg22/homework_1.thy (application/octet-stream)
+Message: msg23 (smith.nickh@gmail.com)
+    Part: msg23/msg-30498-37.txt (text/plain)
+    Part: msg23/msg-30498-38.html (text/html)
+    Part: msg23/HW1.thy (application/octet-stream)
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/a.kutafina@tum.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,140 @@
+From a.kutafina@tum.de Fri Apr 20 11:59:31 2018
+Return-Path: <a.kutafina@tum.de>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ QY2gDue52Vq0BQAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Fri, 20 Apr 2018 11:59:31 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id D8DC11C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Fri, 20 Apr 2018
+ 11:59:31 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id CDBA11E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Fri, 20 Apr 2018 11:59:31
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ CADF61C0376; Fri, 20 Apr 2018 11:59:31 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id C84B51C038A; Fri, 20 Apr 2018 11:59:31 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id A5F681C0378 for <lammich@in.tum.de>; Fri, 20 Apr 2018 11:59:31 +0200
+ (CEST)
+Received: from vmmaildmz2.informatik.tu-muenchen.de
+ (vmmaildmz2.informatik.tu-muenchen.de [131.159.0.88]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id 9B90A1C0376
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 11:59:31 +0200 (CEST)
+Received: by vmmaildmz2.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 9A4B41C24B4; Fri, 20 Apr 2018 11:59:31 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz2.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-4.3 required=7.0 tests=BAYES_00,DKIM_SIGNED,
+ DKIM_VALID,DKIM_VALID_AU,RCVD_IN_DNSWL_MED autolearn=no autolearn_force=no
+ version=3.4.0-tuminfo_1
+Received: from vmmaildmz2.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz2.informatik.tu-muenchen.de (Postfix) with ESMTP id E5EAE1C24B8
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 11:59:28 +0200 (CEST)
+Received: from postout1.mail.lrz.de (postout1.mail.lrz.de
+ [129.187.255.137]) (using TLSv1.2 with cipher AECDH-AES256-SHA (256/256
+ bits)) (No client certificate requested) by
+ vmmaildmz2.informatik.tu-muenchen.de (Postfix) with ESMTPS id DADF31C24AD
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 11:59:28 +0200 (CEST)
+Received: from lxmhs51.srv.lrz.de (localhost [127.0.0.1]) by
+ postout1.mail.lrz.de (Postfix) with ESMTP id 40SBCh5wQqzyZj; Fri, 20 Apr
+ 2018 11:59:28 +0200 (CEST)
+Authentication-Results: postout.lrz.de (amavisd-new); dkim=pass (2048-bit
+ key) reason="pass (just generated, assumed good)" header.d=tum.de
+DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/simple; d=tum.de; h=
+ content-language:content-type:content-type:mime-version
+ :user-agent:date:date:message-id:subject:subject:from:from
+ :received:received; s=postout; t=1524218368; bh=0qI6x07+47mu5jPl
+ NeYrlZgJOd86voY+EN8BoMMFAbw=; b=g4eZHE53YScUIurfyE9EvMMhkbqsnpUy
+ RSu/kn2Ci5yQB2rMLkYD4b/yBf37WN97bxMWyVusAuJ4QSxREMRT/mCZaXBl51Et
+ 8ETvs1sC/hdf2XQasXFGU+K+dyStf+ir17sDYb8gAT4ajG8DT1YS7G5TLCUy02PA
+ QyaS0cjB2xcuAMTrJMaZcnoY79Hg8vPyBi4k8AsXyfEKUslxG3O+wJJEpdRJ71Dt
+ mV6hXI/nZD8Ba2uUP/GiSYEbGTuYjy5XkPFvhVCqfm0K567bQiubVR64BK/8wVrv
+ 7shfglsXOiXBwhZnhhSPW+BUKhN7aEahEQPQLKsgZOri2aO6MRNFJw==
+X-Virus-Scanned: by amavisd-new at lrz.de in lxmhs51.srv.lrz.de
+Received: from postout1.mail.lrz.de ([127.0.0.1]) by lxmhs51.srv.lrz.de
+ (lxmhs51.srv.lrz.de [127.0.0.1]) (amavisd-new, port 20024) with LMTP id
+ z5cmDwx2nn9l; Fri, 20 Apr 2018 11:59:28 +0200 (CEST)
+Received: from [131.159.205.196] (w205-5g-v4.eduroam.dynamic.rbg.tum.de
+ [131.159.205.196]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384
+ (256/256 bits)) (No client certificate requested) by postout1.mail.lrz.de
+ (Postfix) with ESMTPSA id 40SBCh1xm8zybj; Fri, 20 Apr 2018 11:59:28 +0200
+ (CEST)
+To: lammich@in.tum.de, peter.lammich@tum.de
+From: Anastassiya Kutafina <a.kutafina@tum.de>
+Subject: [DPS-Homework]
+Message-ID: <0bedb9d3-68b7-e03f-16f9-802c1c1175fa@tum.de>
+Date: Fri, 20 Apr 2018 11:59:27 +0200
+User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101
+ Thunderbird/52.7.0
+MIME-Version: 1.0
+Content-Type: multipart/mixed; boundary="------------B2E45BE1EC80189DA59AA889"
+Content-Language: de-DE
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+This is a multi-part message in MIME format.
+--------------B2E45BE1EC80189DA59AA889
+Content-Type: text/plain; charset=utf-8; format=flowed
+Content-Transfer-Encoding: 8bit
+
+Dear Dr Lammich,
+
+sorry, I did not receive your email, so I tried to upload my homework at 
+nipkow3 portal. My Matrikelnummer is 03668266, if it's needed
+
+Best wishes
+Anastassiya Kutrafina
+
+-- 
+Mit freundlichen Grüßen
+
+Anastassiya Kutafina
+
+-- 
+Mit freundlichen Grüßen
+
+Anastassiya Kutafina
+
+
+--------------B2E45BE1EC80189DA59AA889
+Content-Type: text/plain; charset=UTF-8; name="sum.thy"
+Content-Disposition: attachment; filename="sum.thy"
+Content-Transfer-Encoding: 8bit
+
+theory sum
+  imports Main
+begin
+
+
+fun listsum :: "int list \<Rightarrow> int" where
+    "listsum [] = 0"
+  | "listsum (x#xs) = x + listsum xs"
+
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x. x \<noteq> 0 ) l ) = listsum l"
+  apply(induction l)
+  apply(auto)
+  done
+
+
+lemma aux_listsum_rev[simp] : "listsum (xs @ [a]) = a + listsum xs"
+  apply(induction xs)
+  apply(auto)
+  done
+
+lemma listsum_rev : "listsum (rev xs) = listsum xs"
+  apply(induction xs)
+  apply(auto)
+  done 
+
+end
+--------------B2E45BE1EC80189DA59AA889--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/a.putwattana@tum.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,178 @@
+From a.putwattana@tum.de Thu Apr 19 21:52:39 2018
+Return-Path: <a.putwattana@tum.de>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ h0pfLIfz2FqIKAAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Thu, 19 Apr 2018 21:52:39 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id B483A1C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Thu, 19 Apr 2018
+ 21:52:39 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id B2BBC1E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Thu, 19 Apr 2018 21:52:39
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ B05201C0376; Thu, 19 Apr 2018 21:52:39 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id ADBF81C038A; Thu, 19 Apr 2018 21:52:39 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id 86C3E1C0378 for <lammich@in.tum.de>; Thu, 19 Apr 2018 21:52:39 +0200
+ (CEST)
+Received: from vmmaildmz1.informatik.tu-muenchen.de
+ (vmmaildmz1.informatik.tu-muenchen.de [131.159.0.87]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id 7CA8C1C0376
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 21:52:39 +0200 (CEST)
+Received: by vmmaildmz1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 7B4271C2DAA; Thu, 19 Apr 2018 21:52:39 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz1.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-4.3 required=7.0 tests=BAYES_00,DKIM_SIGNED,
+ DKIM_VALID,DKIM_VALID_AU,HTML_MESSAGE,RCVD_IN_DNSWL_MED autolearn=no
+ autolearn_force=no version=3.4.0-tuminfo_1
+Received: from vmmaildmz1.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTP id A7A301C2DA9
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 21:52:37 +0200 (CEST)
+Received: from postout2.mail.lrz.de (postout2.mail.lrz.de
+ [129.187.255.138]) (using TLSv1.2 with cipher AECDH-AES256-SHA (256/256
+ bits)) (No client certificate requested) by
+ vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTPS id 9CA471C2D8A
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 21:52:37 +0200 (CEST)
+Received: from lxmhs52.srv.lrz.de (localhost [127.0.0.1]) by
+ postout2.mail.lrz.de (Postfix) with ESMTP id 40RqQY4Qn4z11Z3 for
+ <lammich@in.tum.de>; Thu, 19 Apr 2018 21:52:37 +0200 (CEST)
+Authentication-Results: postout.lrz.de (amavisd-new); dkim=pass (2048-bit
+ key) reason="pass (just generated, assumed good)" header.d=tum.de
+DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/simple; d=tum.de; h=
+ mime-version:content-type:content-type:content-language
+ :accept-language:message-id:date:date:subject:subject:from:from
+ :received:received:received:received; s=postout; t=1524167557;
+ bh=QRUyqnlErSG2324X0o/n6MY02TYdhgo3iLC7JE0i4S0=; b=f5b9djAYNWsG
+ 4i5SlnrLsGVrlfKYCSxCcrtleTs32SRj2bMjBfaTdgwX/YKNQhlsdHq6ITgUSO/O
+ 2MUYFJVdgylqGtlsk8ytU9CeS+ZpgDvK7poVPXN0+C2Ck4aLI/+6PITX0YY+/nAI
+ Etd0qdGtznZLp0Xk5WcHm7ixrML0eeZBq4JHyZvnuQpML0lo+82d8X1920jrVY69
+ QrOyAKFawDSZkfau1s484NmttjAov2hF4sIxUDUc0gF6EYpVPKSpJAhF5G/osoD7
+ QzJgbDOMbY7+6qXXnvzTB453FPB9m2T3IsMdWB+2e4t/Hi+7AbxB8CjYYIleCLud
+ n33fTOSbHQ==
+X-Virus-Scanned: by amavisd-new at lrz.de in lxmhs52.srv.lrz.de
+Received: from postout2.mail.lrz.de ([127.0.0.1]) by lxmhs52.srv.lrz.de
+ (lxmhs52.srv.lrz.de [127.0.0.1]) (amavisd-new, port 20024) with LMTP id
+ 6WbecIePe3kI for <lammich@in.tum.de>; Thu, 19 Apr 2018 21:52:37 +0200 (CEST)
+Received: from BADWLRZ-SWMBX09.ads.mwn.de (BADWLRZ-SWMBX09.ads.mwn.de
+ [IPv6:2001:4ca0:0:108::165]) (using TLSv1.2 with cipher
+ ECDHE-RSA-AES256-SHA384 (256/256 bits)) (Client CN "BADWLRZ-SWMBX09",
+ Issuer "BADWLRZ-SWMBX09" (not verified)) by postout2.mail.lrz.de (Postfix)
+ with ESMTPS id 40RqQY2nQCz11Z1 for <lammich@in.tum.de>; Thu, 19 Apr 2018
+ 21:52:37 +0200 (CEST)
+Received: from BADWLRZ-SWMBX07.ads.mwn.de (2001:4ca0:0:108::163) by
+ BADWLRZ-SWMBX09.ads.mwn.de (2001:4ca0:0:108::165) with Microsoft SMTP
+ Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256)
+ id 15.1.1466.3; Thu, 19 Apr 2018 21:52:35 +0200
+Received: from BADWLRZ-SWMBX07.ads.mwn.de ([fe80::302d:9066:578c:4d70]) by
+ BADWLRZ-SWMBX07.ads.mwn.de ([fe80::302d:9066:578c:4d70%13]) with mapi id
+ 15.01.1466.003; Thu, 19 Apr 2018 21:52:36 +0200
+From: "Putwattana, Attakorn" <a.putwattana@tum.de>
+To: "lammich@in.tum.de" <lammich@in.tum.de>
+Subject: Functional Data Structures Homework 1
+Thread-Topic: Functional Data Structures Homework 1
+Thread-Index: AQHT2BbpRNjMmNwPq0ywryeNRdkDiw==
+Date: Thu, 19 Apr 2018 19:52:36 +0000
+Message-ID: <fcfe1fe4736d4009aca3f5aed647e3ea@tum.de>
+Accept-Language: en-US
+Content-Language: en-US
+X-MS-Exchange-Organization-AuthAs: Internal
+X-MS-Exchange-Organization-AuthMechanism: 04
+X-MS-Exchange-Organization-AuthSource: BADWLRZ-SWMBX07.ads.mwn.de
+X-MS-Has-Attach: yes
+X-MS-TNEF-Correlator: 
+x-originating-ip: [95.157.24.186]
+Content-Type: multipart/mixed; boundary="_004_fcfe1fe4736d4009aca3f5aed647e3eatumde_"
+MIME-Version: 1.0
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+--_004_fcfe1fe4736d4009aca3f5aed647e3eatumde_
+Content-Type: multipart/alternative; boundary="_000_fcfe1fe4736d4009aca3f5aed647e3eatumde_"
+
+
+--_000_fcfe1fe4736d4009aca3f5aed647e3eatumde_
+Content-Type: text/plain; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+Dear Dr. Peter Lammich,
+
+
+I could not find a way to submit the homework to submission system.  So, I attach it with this email.
+
+My matriculation number is 03693616.
+
+
+Thank you for your consideration.
+
+
+Best regards,
+
+Attakorn Putwattana
+
+--_000_fcfe1fe4736d4009aca3f5aed647e3eatumde_
+Content-Type: text/html; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" style="font-size:12pt;color:#000000;font-family:Calibri,Helvetica,sans-serif;" dir="ltr">
+<p>Dear Dr. Peter Lammich,</p>
+<p><br>
+</p>
+<p>I could not find a way to submit the homework to submission system.&nbsp; So, I attach it with this email.</p>
+<p>My m<span>atriculation number is 03693616.</span></p>
+<p><span><br>
+</span></p>
+<p>Thank you for your consideration.</p>
+<p><br>
+</p>
+<p>Best regards,</p>
+<p>Attakorn Putwattana</p>
+</div>
+</body>
+</html>
+
+--_000_fcfe1fe4736d4009aca3f5aed647e3eatumde_--
+
+--_004_fcfe1fe4736d4009aca3f5aed647e3eatumde_
+Content-Type: application/octet-stream; name="hw01.thy"
+Content-Description: hw01.thy
+Content-Disposition: attachment; filename="hw01.thy"; size=1005; creation-date="Thu, 19 Apr 2018 19:48:36 GMT"; modification-date="Thu, 19 Apr 2018 19:48:36 GMT"
+Content-Transfer-Encoding: base64
+
+dGhlb3J5IGh3MDEKaW1wb3J0cyBNYWluCmJlZ2luCiAgCmZ1biBsaXN0c3VtIDo6ICJpbnQgbGlz
+dCA9PiBpbnQiIHdoZXJlCiAgImxpc3RzdW0gW10gPSAwIgp8ICJsaXN0c3VtICh4I3hzKSA9IHgg
+KyBsaXN0c3VtIHhzIgoKICB2YWx1ZSAibGlzdHN1bSBbMSwyLDNdID0gNiIKICB2YWx1ZSAibGlz
+dHN1bSBbXSA9IDAiCiAgdmFsdWUgImxpc3RzdW0gWzEsLTIsM10gPSAyIgoKbGVtbWEgbGlzdHN1
+bV9maWx0ZXJfejogImxpc3RzdW0gKGZpbHRlciAoXDxsYW1iZGE+eC4geCBcPG5vdGVxPiAwKSBs
+KSA9IGxpc3RzdW0gbCIgCiAgYXBwbHkgKGluZHVjdGlvbiBsKQogICBhcHBseSBhdXRvCiAgZG9u
+ZQoKbGVtbWEgbGlzdHN1bV9hdXhbc2ltcF06ICJsaXN0c3VtICh4cyBAIHlzKSA9IGxpc3RzdW0g
+eHMgKyBsaXN0c3VtIHlzIgogIGFwcGx5IChpbmR1Y3Rpb24geHMpCiAgIGFwcGx5IGF1dG8KICBk
+b25lCgpsZW1tYSBsaXN0c3VtX3JldjogImxpc3RzdW0gKHJldiB4cykgPSBsaXN0c3VtIHhzIgog
+IGFwcGx5IChpbmR1Y3Rpb24geHMpCiAgIGFwcGx5IGF1dG8KICBkb25lCgpsZW1tYSAibGlzdHN1
+bSAoZmlsdGVyIChcPGxhbWJkYT54LiBcPG5vdD4geCA8IDApIGwpIFw8Z2U+IGxpc3RzdW0gbCIK
+ICBhcHBseSAoaW5kdWN0aW9uIGwpCiAgIGFwcGx5IGF1dG8KICBkb25lCgpmdW4gZmxhdHRlbiA6
+OiAiJ2EgbGlzdCBsaXN0IFw8UmlnaHRhcnJvdz4gJ2EgbGlzdCIgd2hlcmUKICAiZmxhdHRlbiBb
+XSA9IFtdIgp8ICJmbGF0dGVuIChsICMgbHMpID0gbCBAIGZsYXR0ZW4gbHMiCgp2YWx1ZSAiZmxh
+dHRlbiBbWzEsIDIsIDNdLCBbMl1dID0gWzEsIDIsIDMsIDI6OmludF0iCnZhbHVlICJmbGF0dGVu
+IFtbMSwgMiwgM10sIFtdLCBbMl1dID0gWzEsIDIsIDMsIDI6OiBpbnRdIgoKCmxlbW1hICJsaXN0
+c3VtIChmbGF0dGVuIHhzKSA9IGxpc3RzdW0gKG1hcCBsaXN0c3VtIHhzKSIKICBhcHBseSAoaW5k
+dWN0aW9uIHhzKQogICBhcHBseSBhdXRvCiAgZG9uZQoKZW5k
+
+--_004_fcfe1fe4736d4009aca3f5aed647e3eatumde_--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/alexejrotar@gmail.com	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,149 @@
+From alexejrotar@gmail.com Fri Apr 20 12:04:36 2018
+Return-Path: <alexejrotar@gmail.com>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ 93byBKu62VpWEgAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Fri, 20 Apr 2018 12:04:36 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id AC3C01C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Fri, 20 Apr 2018
+ 12:04:36 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id A99041E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Fri, 20 Apr 2018 12:04:36
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ A56CF1C038F; Fri, 20 Apr 2018 12:04:36 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id A1FB21C038B; Fri, 20 Apr 2018 12:04:36 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id 7EEF41C038A for <lammich@in.tum.de>; Fri, 20 Apr 2018 12:04:36 +0200
+ (CEST)
+Received: from vmmaildmz1.informatik.tu-muenchen.de
+ (vmmaildmz1.informatik.tu-muenchen.de [131.159.0.87]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id 741411C0376
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 12:04:36 +0200 (CEST)
+Received: by vmmaildmz1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 72A101C2DAA; Fri, 20 Apr 2018 12:04:36 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz1.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-2.4 required=7.0 tests=AWL,BAYES_00,DKIM_SIGNED,
+ DKIM_VALID,DKIM_VALID_AU,FREEMAIL_FROM,RCVD_IN_DNSWL_NONE,RCVD_IN_MSPIKE_H2
+ autolearn=no autolearn_force=no version=3.4.0-tuminfo_1
+Received: from vmmaildmz1.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTP id C5F1C1C2DA9
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 12:04:34 +0200 (CEST)
+Received: from mail-wr0-f175.google.com (mail-wr0-f175.google.com
+ [209.85.128.175]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256
+ (128/128 bits)) (No client certificate requested) by
+ vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTPS id AA8321C2D9F
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 12:04:34 +0200 (CEST)
+Received: by mail-wr0-f175.google.com with SMTP id v24-v6so21416416wra.8
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 03:04:34 -0700 (PDT)
+DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com;
+ s=20161025; h=message-id:subject:from:to:date:mime-version;
+ bh=Y/uduS+VXpr4Ygquf2eD8Caju6fEPF4Ftf28HsgRpNM=;
+ b=h+sl189cK4qIuWoC66JXcmceFxZDlbFsoZ1Q99T+upjo2QMqUJ/vxONnP0oeqtL2zP
+ xA9njvB1B2J4YOSPxrQU5i1Y5JfBiMDtC47u3YVWGefk09GgnKRaBpZfssJ0nrYnDVwQ
+ Nb2ILiXXft0dSMvjxVq1FaMVj7d15hWW0C3bg2WR9S6juYo3yJNIq7soqguBq8w8pBeK
+ Wn6q3NJyKWXqXFTtld6/vOl3Eph64KMLZhMJApfZr8ELundApZKPCVBRUik1NOcva3dn
+ YZ6fgdqksSU9JXbguCL33tSd3u499x5XlvCizdsi9T5pyXQKA9OvYxqImfKBlyLsyRoc nbkA==
+X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net;
+ s=20161025;
+ h=x-gm-message-state:message-id:subject:from:to:date:mime-version;
+ bh=Y/uduS+VXpr4Ygquf2eD8Caju6fEPF4Ftf28HsgRpNM=;
+ b=mn81ZRH7D6q+6GVFMG/xy6DAEy0CLKAfKFTEsFiRXGRyW5qE3k10WVQF56PmFAo5+w
+ g20EaH7ZFQChJBCCoF59TFEoVsdBkWGbIeNajLw/fycx31ddm78Sh6p7T41aW+xv7L9z
+ N6/FzuwJRCZ9SvI1onVzKMLJXviyHy/KLs82eR9CYkqPAW4OyrptT50OpcZqxn2olGTP
+ 4iT30T+0m9YZ5PauqDJmp7ybue8IEojIOHZMPfW0r3BrVqvjGd7iUtBSqW5pm571dmF+
+ L4ZpD9xwKLy8s5Kzd30hpEaxmC/KawaP7rYNiiOGFypuPDodfWqu3kmSlobfRLxamMIr TdKQ==
+X-Gm-Message-State:
+ ALQs6tD6JkKD39364sMYXKVROWms/mojha9uNPzTku2DWUC8shwj5GO6
+ vtg7uP3XaVIPo5DojD0Wiynp+Le8
+X-Google-Smtp-Source:
+ AIpwx4+u6Odh9kHSp0UyuWgq/voWM+wGp7w3ScZQnbIHvFKZxka8WQfkmycUE66mHjA4LX2lnE+X7Q==
+X-Received: by 2002:adf:b004:: with SMTP id
+ f4-v6mr7486464wra.75.1524218674185; Fri, 20 Apr 2018 03:04:34 -0700 (PDT)
+Received: from w195-43-v4.eduroam.dynamic.rbg.tum.de
+ (w195-43-v4.eduroam.dynamic.rbg.tum.de. [131.159.195.147]) by
+ smtp.googlemail.com with ESMTPSA id
+ q7-v6sm5034353wrf.92.2018.04.20.03.04.32 for <lammich@in.tum.de>
+ (version=TLS1_2 cipher=ECDHE-RSA-CHACHA20-POLY1305 bits=256/256); Fri, 20
+ Apr 2018 03:04:33 -0700 (PDT)
+Message-ID: <1524218671.4609.2.camel@gmail.com>
+Subject: [FDS Homework] Rotar 01
+From: Alexej Rotar <alexejrotar@gmail.com>
+To: lammich@in.tum.de
+Date: Fri, 20 Apr 2018 12:04:31 +0200
+Content-Type: multipart/mixed; boundary="=-gJtuVecpztSWmXCPRu3q"
+X-Mailer: Evolution 3.26.6 (3.26.6-1.fc27) 
+Mime-Version: 1.0
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+--=-gJtuVecpztSWmXCPRu3q
+Content-Type: text/plain; charset="UTF-8"
+Content-Transfer-Encoding: 8bit
+
+Hello,
+sorry for the late submission. I've just read your mail. Hope it's
+still ok.
+--=-gJtuVecpztSWmXCPRu3q
+Content-Disposition: attachment; filename="hw01.thy"
+Content-Type: text/plain; name="hw01.thy"; charset="UTF-8"
+Content-Transfer-Encoding: 8bit
+
+theory hw01
+  imports Main
+begin
+
+fun listsum :: "int list \<Rightarrow> int" where
+"listsum [] = 0" |
+"listsum (x#xs) = x + listsum xs"
+
+value "listsum [1,2,3] = 6"
+value "listsum [] = 0"
+value "listsum [1,-2,3] = 2"
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x. x \<noteq> 0) xs) = listsum xs"
+  apply(induction xs)
+  apply(auto)
+  done
+
+lemma listsum_app: "listsum (xs @ ys) = listsum xs + listsum ys"
+  apply(induction xs)
+   apply(auto)
+  done
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+  apply(induction xs)
+   apply(auto simp: listsum_app)
+  done
+
+lemma listsum_filter_neg: "listsum (filter (op \<le> 0) xs) \<ge> listsum xs"
+  apply(induction xs)
+   apply(auto)
+  done
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+"flatten [] = []" |
+"flatten (x#xs) = x @ flatten xs"
+
+value "flatten [[1,2,3],[2]] = [1,2,3,2::int]"
+value "flatten [[1,2,3],[],[2]] = [1,2,3,2::int]"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply(induction xs)
+   apply(auto simp: listsum_app)
+  done
+
+end
+--=-gJtuVecpztSWmXCPRu3q--
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/daniel.kutasi@outlook.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,181 @@
+From daniel.kutasi@outlook.de Fri Apr 20 08:28:59 2018
+Return-Path: <daniel.kutasi@outlook.de>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ i15DCb+H2VpFEAAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Fri, 20 Apr 2018 08:28:59 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id D7C751C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Fri, 20 Apr 2018
+ 08:28:59 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id D5DC61E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Fri, 20 Apr 2018 08:28:59
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ D37641C0376; Fri, 20 Apr 2018 08:28:59 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id D03DB1C038A; Fri, 20 Apr 2018 08:28:59 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id ABDF61C0378 for <lammich@in.tum.de>; Fri, 20 Apr 2018 08:28:59 +0200
+ (CEST)
+Received: from vmmaildmz1.informatik.tu-muenchen.de
+ (vmmaildmz1.informatik.tu-muenchen.de [131.159.0.87]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id A1BE81C0376
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 08:28:59 +0200 (CEST)
+Received: by vmmaildmz1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id A00C01C2DAA; Fri, 20 Apr 2018 08:28:59 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz1.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-2.6 required=7.0
+ tests=AWL,BAYES_00,FREEMAIL_FROM,
+ HTML_MESSAGE,RCVD_IN_DNSWL_NONE,RCVD_IN_MSPIKE_H2,SPF_HELO_PASS
+ autolearn=no autolearn_force=no version=3.4.0-tuminfo_1
+Received: from vmmaildmz1.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTP id 72E931C2DA9
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 08:28:54 +0200 (CEST)
+Received: from EUR02-VE1-obe.outbound.protection.outlook.com
+ (mail-oln040092069024.outbound.protection.outlook.com [40.92.69.24]) (using
+ TLSv1.2 with cipher ECDHE-RSA-AES256-SHA384 (256/256 bits)) (No client
+ certificate requested) by vmmaildmz1.informatik.tu-muenchen.de (Postfix)
+ with ESMTPS id 52B471C2D9F for <lammich@in.tum.de>; Fri, 20 Apr 2018
+ 08:28:54 +0200 (CEST)
+Received: from VE1EUR02FT060.eop-EUR02.prod.protection.outlook.com
+ (10.152.12.57) by VE1EUR02HT156.eop-EUR02.prod.protection.outlook.com
+ (10.152.13.155) with Microsoft SMTP Server (version=TLS1_2,
+ cipher=TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA384_P384) id 15.20.675.14; Fri, 20
+ Apr 2018 06:28:53 +0000
+Received: from AM5PR1001MB0995.EURPRD10.PROD.OUTLOOK.COM (10.152.12.55) by
+ VE1EUR02FT060.mail.protection.outlook.com (10.152.13.140) with Microsoft
+ SMTP Server (version=TLS1_2,
+ cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256) id 15.20.675.14 via
+ Frontend Transport; Fri, 20 Apr 2018 06:28:53 +0000
+Received: from AM5PR1001MB0995.EURPRD10.PROD.OUTLOOK.COM
+ ([fe80::8ded:4e2a:e5d0:c0c3]) by AM5PR1001MB0995.EURPRD10.PROD.OUTLOOK.COM
+ ([fe80::8ded:4e2a:e5d0:c0c3%2]) with mapi id 15.20.0696.013; Fri, 20 Apr
+ 2018 06:28:53 +0000
+From: Daniel Kutasi <daniel.kutasi@outlook.de>
+To: Peter Lammich <lammich@in.tum.de>
+Subject: FDS Homework 1
+Thread-Topic: FDS Homework 1
+Thread-Index: AQHT2HDa7YsdWWeei0CnWjjCX2A00w==
+Date: Fri, 20 Apr 2018 06:28:53 +0000
+Message-ID: <AM5PR1001MB0995E8B57B6F6E08E9BD47FB88B40@AM5PR1001MB0995.EURPRD10.PROD.OUTLOOK.COM>
+Accept-Language: de-DE, en-US
+Content-Language: en-US
+X-MS-Has-Attach: yes
+X-MS-TNEF-Correlator: 
+x-incomingtopheadermarker:
+ OriginalChecksum:4123542FBA11F4B093B77761AB7597637C2AD47ED5204A3534876A3EAFAB74D8;UpperCasedChecksum:65DE71D5A77714A58AF52169EFC3D6DAC2E077BB040E6A501B5010D44BFA5A57;SizeAsReceived:6856;Count:44
+x-ms-exchange-messagesentrepresentingtype: 1
+x-tmn: [c3IxpqMarNPzdJCuDIx9m7h7GD1Mspy2]
+x-ms-publictraffictype: Email
+x-microsoft-exchange-diagnostics:
+ 1;VE1EUR02HT156;7:LG+KxgnpfrR2jkv1G4EPI1+4v8YPAr+bnFBdRzN8f1TO6hQlyXU9PO5vqo1UJrIIdHfH9T7orWy2Ts9YirunYuU4wzTxwwUUwlDag8NkJmjbVf8pVJBpoxB9pxcfkUfNshmd6590BIkgvEEUSNYMOzMYUtPD4+SfM3xnmxQG3eqnbTfImYu84qDbh6iGeTA05pi9NvW0aoTD1+6MgjZU8C1qfqgDxeTv5mjiJ9OUrfHSunVdKHkhrLNvKEwKj7RL
+x-incomingheadercount: 44
+x-eopattributedmessage: 0
+x-microsoft-antispam:
+ UriScan:;BCL:0;PCL:0;RULEID:(7020095)(201702061078)(5061506573)(5061507331)(1603103135)(2017031320274)(2017031324274)(2017031323274)(2017031322404)(1603101448)(1601125374)(1701031045);SRVR:VE1EUR02HT156;
+x-ms-traffictypediagnostic: VE1EUR02HT156:
+x-exchange-antispam-report-cfa-test:
+ BCL:0;PCL:0;RULEID:(444000031);SRVR:VE1EUR02HT156;BCL:0;PCL:0;RULEID:;SRVR:VE1EUR02HT156;
+x-forefront-prvs: 0648FCFFA8
+x-forefront-antispam-report:
+ SFV:NSPM;SFS:(7070007)(98901004);DIR:OUT;SFP:1901;SCL:1;SRVR:VE1EUR02HT156;H:AM5PR1001MB0995.EURPRD10.PROD.OUTLOOK.COM;FPR:;SPF:None;LANG:;
+x-microsoft-antispam-message-info:
+ JcRJiFsF6FoTgnsHm1gLX+gqG0i1qs2e7v7Mi7DPqHG4tZqIKupxG05oahO02/pN1lQaSMuxrMX/sQ8kCgIiD3gcRjJ2h5hqeaFkGI7guVjFoJxm+u6UDDpMPKLNx4x6qnhdmZvpBSRMiw38n9epgdgkR38q6pwpJHdSYCOAoQpUyAU0NLyihngNGXYpPYNX
+Content-Type: multipart/mixed; boundary="_004_AM5PR1001MB0995E8B57B6F6E08E9BD47FB88B40AM5PR1001MB0995_"
+MIME-Version: 1.0
+X-MS-Office365-Filtering-Correlation-Id:
+ 2525fb2e-9031-48c8-643c-08d5a687fbaf
+X-OriginatorOrg: outlook.com
+X-MS-Exchange-CrossTenant-RMS-PersistedConsumerOrg:
+ 9bd8b953-1c55-4da7-b616-8bcad099ae8b
+X-MS-Exchange-CrossTenant-Network-Message-Id:
+ 2525fb2e-9031-48c8-643c-08d5a687fbaf
+X-MS-Exchange-CrossTenant-rms-persistedconsumerorg:
+ 9bd8b953-1c55-4da7-b616-8bcad099ae8b
+X-MS-Exchange-CrossTenant-originalarrivaltime: 20 Apr 2018 06:28:53.2958
+ (UTC)
+X-MS-Exchange-CrossTenant-fromentityheader: Internet
+X-MS-Exchange-CrossTenant-id: 84df9e7f-e9f6-40af-b435-aaaaaaaaaaaa
+X-MS-Exchange-Transport-CrossTenantHeadersStamped: VE1EUR02HT156
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+--_004_AM5PR1001MB0995E8B57B6F6E08E9BD47FB88B40AM5PR1001MB0995_
+Content-Type: multipart/alternative; boundary="_000_AM5PR1001MB0995E8B57B6F6E08E9BD47FB88B40AM5PR1001MB0995_"
+
+
+--_000_AM5PR1001MB0995E8B57B6F6E08E9BD47FB88B40AM5PR1001MB0995_
+Content-Type: text/plain; charset="utf-8"
+Content-Transfer-Encoding: 8bit
+
+Hi,
+here's my submission.
+Best regards
+
+
+Kennung: ga68zak
+Matr-Nr. 03623674
+
+--_000_AM5PR1001MB0995E8B57B6F6E08E9BD47FB88B40AM5PR1001MB0995_
+Content-Type: text/html; charset="utf-8"
+Content-ID: <14ACC7AAE4966E4E86D40289B91D1A96@EURPRD10.PROD.OUTLOOK.COM>
+Content-Transfer-Encoding: 8bit
+
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
+</head>
+<body>
+<div dir="ltr">Hi,
+<div>here's my submission.</div>
+<div>Best regards</div>
+<div><br>
+</div>
+<div><br>
+</div>
+<div>Kennung: ga68zak</div>
+<div>Matr-Nr. 03623674</div>
+</div>
+</body>
+</html>
+
+--_000_AM5PR1001MB0995E8B57B6F6E08E9BD47FB88B40AM5PR1001MB0995_--
+
+--_004_AM5PR1001MB0995E8B57B6F6E08E9BD47FB88B40AM5PR1001MB0995_
+Content-Type: application/octet-stream; name="hw01.thy"
+Content-Description: hw01.thy
+Content-Disposition: attachment; filename="hw01.thy"; size=1066; creation-date="Fri, 20 Apr 2018 06:28:51 GMT"; modification-date="Fri, 20 Apr 2018 06:28:51 GMT"
+Content-ID: <162e1bd50d31f318ce71>
+Content-Transfer-Encoding: base64
+
+dGhlb3J5IGh3MDEKaW1wb3J0cyBNYWluCmJlZ2luCgpmdW4gbGlzdHN1bSA6OiAiaW50IGxpc3Qg
+XDxSaWdodGFycm93PiBpbnQiIHdoZXJlCiAgImxpc3RzdW0gW10gPSAwIgp8ICJsaXN0c3VtICh4
+ICMgeHMpID0geCArIGxpc3RzdW0geHMiCgp2YWx1ZSAibGlzdHN1bSBbMSwyLDNdID0gNiIKdmFs
+dWUgImxpc3RzdW0gW10gPSAwIgp2YWx1ZSAibGlzdHN1bSBbMSwtMiwzXSA9IDIiCgpsZW1tYSBs
+aXN0c3VtX2ZpbHRlcl96OiAibGlzdHN1bSAoZmlsdGVyICgleC4geCBcPG5vdGVxPiAwKSBsKSA9
+IGxpc3RzdW0gbCIKICBhcHBseSAoaW5kdWN0aW9uIGwpCiAgYnkgYXV0bwoKbGVtbWEgbGlzdHN1
+bV9yZXZfYXV4W3NpbXBdOiAibGlzdHN1bSAoeHMgQCBbYV0pID0gYSArIGxpc3RzdW0geHMiCiAg
+YXBwbHkgKGluZHVjdGlvbiB4cykKICBieSBhdXRvCgpsZW1tYSBsaXN0c3VtX3JldjogImxpc3Rz
+dW0gKHJldiB4cykgPSBsaXN0c3VtIHhzIgogIGFwcGx5IChpbmR1Y3Rpb24geHMpCiAgYnkgYXV0
+bwoKbGVtbWEgbGlzdHN1bV9wb3NpdGl2ZXM6ICJsaXN0c3VtIChmaWx0ZXIgKCV4LiB4IFw8Z2U+
+IDApIHhzKSBcPGdlPiBsaXN0c3VtIHhzIgogIGFwcGx5IChpbmR1Y3Rpb24geHMpCiAgYnkgYXV0
+bwoKZnVuIGZsYXR0ZW4gOjogIidhIGxpc3QgbGlzdCBcPFJpZ2h0YXJyb3c+ICdhIGxpc3QiIHdo
+ZXJlCiAgImZsYXR0ZW4gW10gPSBbXSIKfCAiZmxhdHRlbiAobCNscykgPSBsIEAgZmxhdHRlbiBs
+cyIKCnZhbHVlICJmbGF0dGVuIFtbMSwyLDNdLFsyXV0gPSBbMSwyLDMsMjo6aW50XSIKdmFsdWUg
+ImZsYXR0ZW4gW1sxLDIsM10sW10sWzJdXSA9IFsxLDIsMywyOjppbnRdIgoKbGVtbWEgbGlzdHN1
+bV9mbGF0dGVuX2F1eFtzaW1wXTogImxpc3RzdW0gKHhzIEAgeXMpID0gbGlzdHN1bSB4cyArIGxp
+c3RzdW0geXMiCiAgYXBwbHkgKGluZHVjdGlvbiB4cykKICBieSBhdXRvCgpsZW1tYSBsaXN0c3Vt
+X2ZsYXR0ZW46ICJsaXN0c3VtIChmbGF0dGVuIHhzKSA9IGxpc3RzdW0gKG1hcCBsaXN0c3VtIHhz
+KSIKICBhcHBseSAoaW5kdWN0aW9uIHhzKQogIGJ5IGF1dG8KCmVuZA==
+
+--_004_AM5PR1001MB0995E8B57B6F6E08E9BD47FB88B40AM5PR1001MB0995_--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/eric.koepke@online.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,117 @@
+From eric.koepke@online.de Fri Apr 20 12:28:52 2018
+Return-Path: <eric.koepke@online.de>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ XnWRMNbA2VokbgAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Fri, 20 Apr 2018 12:28:52 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id F256C1C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Fri, 20 Apr 2018
+ 12:28:52 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id E7CC01E0126
+ for <lammich@mail.informatik.tu-muenchen.de>; Fri, 20 Apr 2018 12:28:52
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ E53921C0376; Fri, 20 Apr 2018 12:28:52 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id E23851C038B; Fri, 20 Apr 2018 12:28:52 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id BE7101C038A for <lammich@in.tum.de>; Fri, 20 Apr 2018 12:28:52 +0200
+ (CEST)
+Received: from vmmaildmz2.informatik.tu-muenchen.de
+ (vmmaildmz2.informatik.tu-muenchen.de [131.159.0.88]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id AA79D1C0376
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 12:28:52 +0200 (CEST)
+Received: by vmmaildmz2.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id A8EB81C24B7; Fri, 20 Apr 2018 12:28:52 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz2.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-1.9 required=7.0
+ tests=BAYES_00,RCVD_IN_DNSWL_NONE autolearn=no autolearn_force=no
+ version=3.4.0-tuminfo_1
+Received: from vmmaildmz2.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz2.informatik.tu-muenchen.de (Postfix) with ESMTP id D451F1C24B4
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 12:28:50 +0200 (CEST)
+Received: from mout.kundenserver.de (mout.kundenserver.de
+ [212.227.126.133]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256
+ (128/128 bits)) (No client certificate requested) by
+ vmmaildmz2.informatik.tu-muenchen.de (Postfix) with ESMTPS id B79241C24AD
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 12:28:50 +0200 (CEST)
+Received: from [192.168.2.102] ([93.202.59.237]) by
+ mrelayeu.kundenserver.de (mreue003 [212.227.15.167]) with ESMTPSA (Nemesis)
+ id 0LodTi-1eU77w1bXG-00gYmG for <lammich@in.tum.de>; Fri, 20 Apr 2018
+ 12:28:50 +0200
+Date: Fri, 20 Apr 2018 12:28:47 +0200
+Subject: [FDS-Homework]
+X-Priority: 3
+Message-ID: <5oab9cqyp5co-o2kyug-51k2zw-e9djqc-lr8sbr-c8ejaf-480arm-pioq80tapf6c-dg4g7yi021u6-nogxww-ab9hgtj2rlwu-jr0jmpdc0wci2fspk1-xdbk4lk2kmjz-8dbbsv7y5odd-brnby4k92oo1.1524220128359@email.android.com>
+From: "eric.koepke@online.de" <eric.koepke@online.de>
+To: lammich@in.tum.de
+MIME-Version: 1.0
+Content-Type: multipart/mixed; boundary="--_com.android.email_1092777471577910"
+X-Provags-ID: V03:K1:mW8K95drQcW44nRwPDKxxw+dPYRS+E+GaggmiKLLDUBEHvJxrVn
+ IQmjmMrfcTKPa23OmaVvGQCPJB7WGMsJ8ISezohsl8Ims/XiUyfa9g0Oyc2LWN/Y9RlMaMb
+ 8mQONt9GCswQqroWzAggtSYe3usZ9V1htrFt03tTbpPVYQ2T9a8QeXyaKG91o4Ovxi+sspB
+ OpZFuJGXoNIeuF8bp4a+A==
+X-UI-Out-Filterresults:
+ notjunk:1;V01:K0:9jaUt64z9+Q=:gtMQP2Scf1uIEBY3i5ldiG
+ 30+wQOdTy1MZaGeV9+43VjjfP2Rre8wUm04CMWhWgMp3eqXLv74IFbjfb/p7ukWdKPgj/SD4e
+ YUzYmnQ4U00+bBomo6yiq34Pebfu+Tt83/JKWRpScYK972wPtf7+d5JCNJzXwse7HnqzVV1Kj
+ aJezvfqKdrcwE8cQHSnm0eCNHncc/MVXIt90D55ks9z85jsp2oLJKIpuy0NVDhjKluQiDZ4Q4
+ Riqi3a+wG8UEC7a7XXVgbEGao5Z3/3dO6O8NduINLyiqdTckfPTA6+faIFiKW1idsanJcgvac
+ z9FWHdzzVnOEsACU784bNRF+kp3rJTvvkJZdMD2vlddMNRW1q7TBBiW8oAHr3NoQADvQzhCd8
+ ICxcjAXJjXYnJ04h1JH5Al27/ZFNdaW/Rm53uzbwIadqe9dLa04I2hn1AJKkwjDykse2zok0r
+ POps/jumB5fZu5tZ/VQeRXLQ8toPIYGt/W/nalqwkcSNcWw0r44sA/bmX6hjWcwssY4qwBHnZ
+ CRxJlaS+8lUMugVJNXJ4IyulpBYD3MZG1EcxXh/S6M5irZEETeseLQEMfVZI8fLYjlkL6iAB6
+ FFVqpz7sZSFVkEizmPIbnRRhvWrxC+vOq4FEm3jA4pKHX0Z2o0C1LnlppK3LQVEDGMNaNRQ37
+ VzqK25YxrMPMbBXFQEjhOwo01RT49M1cxo6z721cJpcaQiXAzKe1Twmlh4K8lzLCNR+H88Yzd
+ GpAbwhePGyLCTlaf5WJpsokafi+whUDJNoJ16Q==
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+----_com.android.email_1092777471577910
+Content-Type: text/plain; charset=utf-8
+Content-Transfer-Encoding: 8bit
+
+Hello,
+Matr.Nr.: 03665531
+Homework is attached.
+
+Greetings,
+Eric Koepke
+----_com.android.email_1092777471577910
+Content-Type: application/octet-stream; name="ex01.thy"
+Content-Transfer-Encoding: base64
+Content-Disposition: attachment; filename="ex01.thy"; size=1031
+
+dGhlb3J5IGV4MDEKaW1wb3J0cyBNYWluCmJlZ2luCmZ1biBsaXN0c3VtOjogImludCBsaXN0IFw8
+UmlnaHRhcnJvdz4gaW50IiB3aGVyZQogImxpc3RzdW0gKGIjYSkgID0obGlzdHN1bSBhKSArIGIi
+CnwibGlzdHN1bSBbXSA9IDAiCgoKdmFsdWUgImxpc3RzdW0gWzEsMiwzXSIKdmFsdWUgImxpc3Rz
+dW0gW10iCnZhbHVlICJsaXN0c3VtIFsxLC0yLDNdIgoKbGVtbWEgbGlzdHN1bV9maWx0ZXJfejog
+Imxpc3RzdW0gKGZpbHRlciAoXDxsYW1iZGE+eC4geFw8bm90ZXE+MCkgbCkgPSBsaXN0c3VtIGwi
+CiAgYXBwbHkgKGluZHVjdGlvbiBsKQogIGFwcGx5IGF1dG8KICBkb25lCgpsZW1tYSBhdXhfYXBw
+OiAibGlzdHN1bSAoeHMgQCBbYV0pID0gbGlzdHN1bSAoYSN4cykiCiAgYXBwbHkgKGluZHVjdGlv
+biB4cykKICBhcHBseSBhdXRvCiAgZG9uZQoKbGVtbWEgbGlzdHN1bV9yZXY6ICJsaXN0c3VtIChy
+ZXYgeHMpID0gbGlzdHN1bSB4cyIKICBhcHBseSAoaW5kdWN0aW9uIHhzKQogIGFwcGx5IChhdXRv
+IHNpbXA6IGF1eF9hcHApCiAgZG9uZQoKbGVtbWEgbGlzdHN1bV9maWx0ZXJfbjogImxpc3RzdW0g
+KGZpbHRlciAoXDxsYW1iZGE+eC4geFw8Z2U+MCkgbCkgXDxnZT4gbGlzdHN1bSBsIgogIGFwcGx5
+IChpbmR1Y3Rpb24gbCkKICBhcHBseSBhdXRvCiAgZG9uZQoKZnVuIGZsYXR0ZW4gOjogIidhIGxp
+c3QgbGlzdCBcPFJpZ2h0YXJyb3c+ICdhIGxpc3QiIHdoZXJlCiAgImZsYXR0ZW4gW10gPSBbXSIK
+fCAiZmxhdHRlbiAobCNscykgPSBsIEAgZmxhdHRlbiBscyIKCnZhbHVlICJmbGF0dGVuIFtbMTo6
+aW50LDIsM10sWzJdXSIKCmxlbW1hIGF1eF9zdW06ICJsaXN0c3VtICh4cyBAIGEpID0gbGlzdHN1
+bSB4cyArIGxpc3RzdW0gYSIKICBhcHBseSAoaW5kdWN0aW9uIHhzKQogIGFwcGx5IGF1dG8KICBk
+b25lCgpsZW1tYSAibGlzdHN1bSAoZmxhdHRlbiB4cykgPSBsaXN0c3VtIChtYXAgbGlzdHN1bSB4
+cykiCiAgYXBwbHkgKGluZHVjdGlvbiB4cykKICBhcHBseSAoYXV0byBzaW1wOiBhdXhfc3VtKQog
+IGRvbmU=
+
+
+----_com.android.email_1092777471577910--
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/felix.wielander@tum.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,153 @@
+From felix.wielander@tum.de Thu Apr 19 10:41:25 2018
+Return-Path: <felix.wielander@tum.de>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ YQEIOStW2FqQRAAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Thu, 19 Apr 2018 10:41:25 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id F0ACA1C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Thu, 19 Apr 2018
+ 10:41:25 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id EF31B1E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Thu, 19 Apr 2018 10:41:25
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ EC8AE1C0376; Thu, 19 Apr 2018 10:41:25 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id E95C91C03A1; Thu, 19 Apr 2018 10:41:25 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id C55291C038F for <lammich@in.tum.de>; Thu, 19 Apr 2018 10:41:25 +0200
+ (CEST)
+Received: from vmmaildmz1.informatik.tu-muenchen.de
+ (vmmaildmz1.informatik.tu-muenchen.de [131.159.0.87]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id B0B3C1C0376
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 10:41:25 +0200 (CEST)
+Received: by vmmaildmz1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id AE4DB1C2DAC; Thu, 19 Apr 2018 10:41:25 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz1.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-4.3 required=7.0 tests=BAYES_00,DKIM_SIGNED,
+ DKIM_VALID,DKIM_VALID_AU,RCVD_IN_DNSWL_MED autolearn=no autolearn_force=no
+ version=3.4.0-tuminfo_1
+Received: from vmmaildmz1.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTP id EFEA91C2DAA
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 10:41:23 +0200 (CEST)
+Received: from postout2.mail.lrz.de (postout2.mail.lrz.de
+ [129.187.255.138]) (using TLSv1.2 with cipher AECDH-AES256-SHA (256/256
+ bits)) (No client certificate requested) by
+ vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTPS id E50681C2D8A
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 10:41:19 +0200 (CEST)
+Received: from lxmhs52.srv.lrz.de (localhost [127.0.0.1]) by
+ postout2.mail.lrz.de (Postfix) with ESMTP id 40RXWz6GRpz11Z2 for
+ <lammich@in.tum.de>; Thu, 19 Apr 2018 10:41:19 +0200 (CEST)
+Authentication-Results: postout.lrz.de (amavisd-new); dkim=pass (2048-bit
+ key) reason="pass (just generated, assumed good)" header.d=tum.de
+DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/simple; d=tum.de; h=
+ content-language:content-type:content-type:mime-version
+ :user-agent:date:date:message-id:subject:subject:from:from
+ :received:received; s=postout; t=1524127279; bh=G3PrXrr3qWhNuMVt
+ vE9t8CDAwzrx8YlxzT0N2Kp5bZY=; b=LvF6Zua7B4CC/QPljnVxNqRKof3A54I4
+ rhs5ls4+j8RWrNHCsNx+UTyJsE36MJ3SAjpajvpJp67czriZN3n8quH/bqTqQUmX
+ tdc8/cYHz1j25R6vAKWOcWyMHbBt/HmVaeryyVV4D3b2OyajpDQsLspF3Z6EOxY/
+ 9SGIZArBJggEFqOKhtFMXU7oEJ+zwVBj2g4NdZQPUaHlqia+xccfrAV0SD+K8CBk
+ i39AAZ6vK8gkRCTN4hmImm8QLtbTOZWFmyXmu8wJgIFPvsyfCBQPcuNfrcP4sdQd
+ hXSuYwW7EOn/qPpfI0dLO/hUla7vjnRCFKtcTs3YssrclY8hNo/y8g==
+X-Virus-Scanned: by amavisd-new at lrz.de in lxmhs52.srv.lrz.de
+Received: from postout2.mail.lrz.de ([127.0.0.1]) by lxmhs52.srv.lrz.de
+ (lxmhs52.srv.lrz.de [127.0.0.1]) (amavisd-new, port 20024) with LMTP id
+ bshguiwXRMCy for <lammich@in.tum.de>; Thu, 19 Apr 2018 10:41:19 +0200 (CEST)
+Received: from [IPv6:2001:a61:4801:7801:d7d6:ce52:8a2d:e4d8] (unknown
+ [IPv6:2001:a61:4801:7801:d7d6:ce52:8a2d:e4d8]) (using TLSv1.2 with cipher
+ ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (No client certificate
+ requested) by postout2.mail.lrz.de (Postfix) with ESMTPSA id 40RXWz2HKWzytJ
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 10:41:19 +0200 (CEST)
+To: lammich@in.tum.de
+From: Felix Wielander <felix.wielander@tum.de>
+Subject: [Functional Data Structures] Homework 1
+Message-ID: <f6307e8a-f91c-373c-2016-8dc7633a3d0b@tum.de>
+Date: Thu, 19 Apr 2018 10:41:18 +0200
+User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101
+ Thunderbird/52.6.0
+MIME-Version: 1.0
+Content-Type: multipart/mixed; boundary="------------7F3426ACDB92C73DEE938794"
+Content-Language: en-US
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+This is a multi-part message in MIME format.
+--------------7F3426ACDB92C73DEE938794
+Content-Type: text/plain; charset=utf-8; format=flowed
+Content-Transfer-Encoding: 8bit
+
+Hallo Herr Lammich,
+
+im Anhang finden Sie meine Homework1.
+
+Viele Grüße,
+Felix Wielander
+
+
+--------------7F3426ACDB92C73DEE938794
+Content-Type: text/plain; charset=UTF-8; name="hw01.thy"
+Content-Disposition: attachment; filename="hw01.thy"
+Content-Transfer-Encoding: 8bit
+
+theory hw01
+imports Main
+begin
+
+(* 1 *)
+fun listsum :: "int list \<Rightarrow> int" where
+  "listsum []    = 0" |
+  "listsum (x#xs)  = x + listsum xs"
+
+value "listsum [1,2,3] = 6"
+value "listsum [] = 0"
+value "listsum [1,-2,3] = 2"
+
+(* 2 *)
+lemma listsum_filter_z : "listsum (filter (\<lambda>x . x \<noteq> 0) l) = listsum l"
+  apply(induction l)
+  apply(auto)
+  done
+
+(* 3 *)
+lemma listsum_rev_aux[simp]: "listsum (xs @ ys) = listsum xs + listsum ys"
+  apply(induction xs)
+  apply(auto)
+  done
+
+lemma listsum_rev : "listsum (rev xs) = listsum xs"
+  apply(induction xs)
+  apply(auto)
+  done
+
+(* 4 *)
+lemma listsum_filter_neg : "listsum (filter (\<lambda>x . x \<ge> 0) xs) \<ge> listsum xs"
+  apply(induction xs)
+  apply(auto)
+  done
+
+(* 5 *)
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+  "flatten [] = []" |
+  "flatten (l #ls) = l @ flatten ls"
+
+value "flatten [[1 ,2 ,3 ],[2]] = [1 ,2 ,3 ,2 ::int]"
+value "flatten [[1 ,2 ,3 ],[],[2]] = [1 ,2 ,3 ,2 ::int]"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply(induction xs)
+  apply(auto)
+  done
+
+
+end
+--------------7F3426ACDB92C73DEE938794--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/florian.stamer@tum.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,167 @@
+From florian.stamer@tum.de Fri Apr 20 10:23:56 2018
+Return-Path: <florian.stamer@tum.de>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ H3xFB5Oj2Vo0LwAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Fri, 20 Apr 2018 10:23:56 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id 2C6731C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Fri, 20 Apr 2018
+ 10:23:56 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id 2AA8C1E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Fri, 20 Apr 2018 10:23:56
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ 278F41C0378; Fri, 20 Apr 2018 10:23:56 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 24BBA1C038A; Fri, 20 Apr 2018 10:23:56 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id 000231C0378 for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:23:55 +0200
+ (CEST)
+Received: from vmmaildmz1.informatik.tu-muenchen.de
+ (vmmaildmz1.informatik.tu-muenchen.de [131.159.0.87]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id E98DC1C0376
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:23:55 +0200 (CEST)
+Received: by vmmaildmz1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id E66D41C2DA9; Fri, 20 Apr 2018 10:23:55 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz1.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-4.3 required=7.0 tests=BAYES_00,DKIM_SIGNED,
+ DKIM_VALID,DKIM_VALID_AU,HTML_MESSAGE,RCVD_IN_DNSWL_MED autolearn=no
+ autolearn_force=no version=3.4.0-tuminfo_1
+Received: from vmmaildmz1.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTP id CBBC81C2DAA
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:23:53 +0200 (CEST)
+Received: from postout2.mail.lrz.de (postout2.mail.lrz.de
+ [129.187.255.138]) (using TLSv1.2 with cipher AECDH-AES256-SHA (256/256
+ bits)) (No client certificate requested) by
+ vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTPS id C13A01C2D9F
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:23:53 +0200 (CEST)
+Received: from lxmhs52.srv.lrz.de (localhost [127.0.0.1]) by
+ postout2.mail.lrz.de (Postfix) with ESMTP id 40S85P5Chxz11Vd for
+ <lammich@in.tum.de>; Fri, 20 Apr 2018 10:23:53 +0200 (CEST)
+Authentication-Results: postout.lrz.de (amavisd-new); dkim=pass (2048-bit
+ key) reason="pass (just generated, assumed good)" header.d=tum.de
+DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/simple; d=tum.de; h=
+ mime-version:content-type:content-type:content-language
+ :accept-language:message-id:date:date:subject:subject:from:from
+ :received:received:received:received; s=postout; t=1524212633;
+ bh=QiwpzHud0FUZXc31JwMr7XADYs8uKOpGthDgcN7QFEM=; b=10HhxCDBeyuD
+ XzExRFkYbVGMhg3sS9M6S4UxG7stHYUcdA4iy5e8koUdH3iZXU9tMUV8idwKV7UH
+ /MLgrxzn+KbnDdZo/5QqaxK9hP4g1yzFhGh3O6VAAjgJ38wOp9qYI+xXjtzD29rp
+ ffFOWVPmAIOyscsXyP6Ptd46IoPe1Yebage32eFQ6REPAP/VUNeZJSDE0op+7mos
+ TkDDGqOCQ0FE1NgdhgUPH+c2AfQ8LpPwFqbcXcSGLCxTYO+LbgomZuT/Y3pBzjI2
+ 76RIKLOmDIelhqUuW5InPRqfBN6KRaHbI6Vty+2VmbfDpxTJe+1lH2HQQ/GqQcut
+ 4xzUr/8M1A==
+X-Virus-Scanned: by amavisd-new at lrz.de in lxmhs52.srv.lrz.de
+Received: from postout2.mail.lrz.de ([127.0.0.1]) by lxmhs52.srv.lrz.de
+ (lxmhs52.srv.lrz.de [127.0.0.1]) (amavisd-new, port 20024) with LMTP id
+ pQvEBo4UjmKu for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:23:53 +0200 (CEST)
+Received: from BADWLRZ-SWMBX01.ads.mwn.de (BADWLRZ-SWMBX01.ads.mwn.de
+ [IPv6:2001:4ca0:0:108::157]) (using TLSv1.2 with cipher
+ ECDHE-RSA-AES256-SHA384 (256/256 bits)) (Client CN "BADWLRZ-SWMBX01",
+ Issuer "BADWLRZ-SWMBX01" (not verified)) by postout2.mail.lrz.de (Postfix)
+ with ESMTPS id 40S85P3DXfz11VS for <lammich@in.tum.de>; Fri, 20 Apr 2018
+ 10:23:53 +0200 (CEST)
+Received: from BADWLRZ-SWMBX09.ads.mwn.de (2001:4ca0:0:108::165) by
+ BADWLRZ-SWMBX01.ads.mwn.de (2001:4ca0:0:108::157) with Microsoft SMTP
+ Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256)
+ id 15.1.1466.3; Fri, 20 Apr 2018 10:23:52 +0200
+Received: from BADWLRZ-SWMBX09.ads.mwn.de ([fe80::28c9:20b8:a4d6:473c]) by
+ BADWLRZ-SWMBX09.ads.mwn.de ([fe80::28c9:20b8:a4d6:473c%12]) with mapi id
+ 15.01.1466.003; Fri, 20 Apr 2018 10:23:52 +0200
+From: "Stamer, Florian" <florian.stamer@tum.de>
+To: "lammich@in.tum.de" <lammich@in.tum.de>
+Subject: [FDS-Homework]
+Thread-Topic: [FDS-Homework]
+Thread-Index: AQHT2IC42jNPJeAssE2ubCbM5+p15g==
+Date: Fri, 20 Apr 2018 08:23:52 +0000
+Message-ID: <ca055b8148064a95b7e1191d661a898e@tum.de>
+Accept-Language: de-DE, en-US
+Content-Language: de-DE
+X-MS-Exchange-Organization-AuthAs: Internal
+X-MS-Exchange-Organization-AuthMechanism: 04
+X-MS-Exchange-Organization-AuthSource: BADWLRZ-SWMBX09.ads.mwn.de
+X-MS-Has-Attach: yes
+X-MS-TNEF-Correlator: 
+x-originating-ip: [88.72.224.111]
+Content-Type: multipart/mixed; boundary="_004_ca055b8148064a95b7e1191d661a898etumde_"
+MIME-Version: 1.0
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+--_004_ca055b8148064a95b7e1191d661a898etumde_
+Content-Type: multipart/alternative; boundary="_000_ca055b8148064a95b7e1191d661a898etumde_"
+
+
+--_000_ca055b8148064a95b7e1191d661a898etumde_
+Content-Type: text/plain; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+Dear Mr. Lammich,
+
+
+the file is in the attachment.
+
+
+Best regards
+
+Florian Stamer [03664701]
+
+--_000_ca055b8148064a95b7e1191d661a898etumde_
+Content-Type: text/html; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" style="font-size:12pt;color:#000000;font-family:Calibri,Helvetica,sans-serif;" dir="ltr">
+<p>Dear Mr. Lammich,</p>
+<p><br>
+</p>
+<p>the file is in the attachment.</p>
+<p><br>
+</p>
+<p>Best regards</p>
+<p>Florian Stamer [03664701]</p>
+</div>
+</body>
+</html>
+
+--_000_ca055b8148064a95b7e1191d661a898etumde_--
+
+--_004_ca055b8148064a95b7e1191d661a898etumde_
+Content-Type: application/octet-stream; name="ex01.thy"
+Content-Description: ex01.thy
+Content-Disposition: attachment; filename="ex01.thy"; size=897; creation-date="Fri, 20 Apr 2018 08:23:13 GMT"; modification-date="Fri, 20 Apr 2018 08:23:13 GMT"
+Content-Transfer-Encoding: base64
+
+dGhlb3J5IGV4MDEKaW1wb3J0cyBNYWluCmJlZ2luCiAgKCpoMSAqKQogIGZ1biBsaXN0c3VtIDo6
+ICJpbnQgbGlzdCBcPFJpZ2h0YXJyb3c+IGludCIgd2hlcmUKICAgICJsaXN0c3VtIFtdID0gMCIK
+ICB8ICJsaXN0c3VtICh4I3hzKSA9IHggKyBsaXN0c3VtIHhzIgoKICBsZW1tYSBsaXN0c3VtX2Zp
+bHRlcl96OiAibGlzdHN1bSAoZmlsdGVyIChcPGxhbWJkYT54LiB4XDxub3RlcT4wKSBsKSA9IGxp
+c3RzdW0gbCIKICBhcHBseSAoaW5kdWN0aW9uIGwpCiAgYXBwbHkgKGF1dG8pCiAgZG9uZQoKICBs
+ZW1tYSBsaXN0c3VtX2FwcDogImxpc3RzdW0gKHhzIEAgeXMpID0gbGlzdHN1bSB4cyArIGxpc3Rz
+dW0geXMiCiAgYXBwbHkgKGluZHVjdGlvbiB4cykKICBhcHBseSAoYXV0bykKICBkb25lCgogIGxl
+bW1hIGxpc3RzdW1fcmV2OiAibGlzdHN1bSAocmV2IHhzKSA9IGxpc3RzdW0geHMiCiAgYXBwbHkg
+KGluZHVjdGlvbiB4cykKICBhcHBseSAoYXV0byBzaW1wIGFkZDogbGlzdHN1bV9hcHApCiAgZG9u
+ZQoKICBsZW1tYSBsaXN0c3VtX2ZpbHRlcl9wb3M6ICJsaXN0c3VtIChmaWx0ZXIgKFw8bGFtYmRh
+PnguIHhcPGdlPjApIGwpIFw8Z2U+IGxpc3RzdW0gbCIKICBhcHBseSAoaW5kdWN0aW9uIGwpCiAg
+YXBwbHkgKGF1dG8pCiAgZG9uZQoKICBmdW4gZmxhdHRlbiA6OiAiJ2EgbGlzdCBsaXN0IFw8Umln
+aHRhcnJvdz4gJ2EgbGlzdCIgd2hlcmUKICAgICJmbGF0dGVuIFtdID0gW10iCiAgfCAiZmxhdHRl
+biAobCNscykgPSBsIEAgZmxhdHRlbiBscyIKCiAgbGVtbWEgImxpc3RzdW0gKGZsYXR0ZW4geHMp
+ID0gbGlzdHN1bSAobWFwIGxpc3RzdW0geHMpIgogIGFwcGx5IChpbmR1Y3Rpb24geHMpCiAgYXBw
+bHkgKGF1dG8gc2ltcCBhZGQ6IGxpc3RzdW1fYXBwKQogIGRvbmUKZW5k
+
+--_004_ca055b8148064a95b7e1191d661a898etumde_--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/g.bidlingmaier@tum.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,147 @@
+From g.bidlingmaier@tum.de Fri Apr 20 09:52:47 2018
+Return-Path: <g.bidlingmaier@tum.de>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ ipTbODWc2VqXOwAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Fri, 20 Apr 2018 09:52:47 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id 098E31C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Fri, 20 Apr 2018
+ 09:52:47 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id 07DC01E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Fri, 20 Apr 2018 09:52:47
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ 052F21C0376; Fri, 20 Apr 2018 09:52:47 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 026991C038A; Fri, 20 Apr 2018 09:52:47 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id D2F0A1C0378 for <lammich@in.tum.de>; Fri, 20 Apr 2018 09:52:46 +0200
+ (CEST)
+Received: from vmmaildmz1.informatik.tu-muenchen.de
+ (vmmaildmz1.informatik.tu-muenchen.de [131.159.0.87]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id BEF961C0376
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 09:52:46 +0200 (CEST)
+Received: by vmmaildmz1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id BD4D51C2DAB; Fri, 20 Apr 2018 09:52:46 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz1.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-4.3 required=7.0 tests=BAYES_00,DKIM_SIGNED,
+ DKIM_VALID,DKIM_VALID_AU,RCVD_IN_DNSWL_MED autolearn=no autolearn_force=no
+ version=3.4.0-tuminfo_1
+Received: from vmmaildmz1.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTP id 152181C2DA9
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 09:52:45 +0200 (CEST)
+Received: from postout1.mail.lrz.de (postout1.mail.lrz.de
+ [129.187.255.137]) (using TLSv1.2 with cipher AECDH-AES256-SHA (256/256
+ bits)) (No client certificate requested) by
+ vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTPS id 0A9F81C2D9F
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 09:52:45 +0200 (CEST)
+Received: from lxmhs51.srv.lrz.de (localhost [127.0.0.1]) by
+ postout1.mail.lrz.de (Postfix) with ESMTP id 40S7PS71r1zypb for
+ <lammich@in.tum.de>; Fri, 20 Apr 2018 09:52:44 +0200 (CEST)
+Authentication-Results: postout.lrz.de (amavisd-new); dkim=pass (2048-bit
+ key) reason="pass (just generated, assumed good)" header.d=tum.de
+DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/simple; d=tum.de; h=
+ content-language:content-type:content-type:mime-version
+ :user-agent:date:date:message-id:subject:subject:from:from
+ :received:received; s=postout; t=1524210764; bh=u8XlUi9pvZ3wMLZE
+ HeepeS/QO2gIz2BRB3dsROZAtHE=; b=Nl2fFJa9Zs/RdqEJPCgS6on0gxFQdo80
+ tAHt2HVpeSUVeeMkkg5gnHeBzOjpSauPnnECOq80WPIgJLqzpSMe3OQJkzWivNY0
+ 4h2YZVosP6xzYOnrukWsBIx+G7kLzBRUX1hl+97DymGhGu2DuaWu6Hyx5ZFssurR
+ tm5BlIE238cb0XGZYBxn4ftvN+NtgfRe8Qcvz1kDJdusWdjXHDSNNwCM/mUycsTx
+ spZyyU93CNl7d72aGGvA9ibZclp/I6pYV6iEFCYIHhmNlip0nOK3Kz0B/RAFsQfx
+ j0eFRGjI5gM41ZVsfNGTtOuWtRaLjGbN6WKaeyFPG4/bWBUUrYRmJA==
+X-Virus-Scanned: by amavisd-new at lrz.de in lxmhs51.srv.lrz.de
+Received: from postout1.mail.lrz.de ([127.0.0.1]) by lxmhs51.srv.lrz.de
+ (lxmhs51.srv.lrz.de [127.0.0.1]) (amavisd-new, port 20024) with LMTP id
+ g1H2eGNO-Z5x for <lammich@in.tum.de>; Fri, 20 Apr 2018 09:52:44 +0200 (CEST)
+Received: from [IPv6:2001:4ca0:2003:1920:6b90:2f1d:3641:aceb]
+ (w1mvwyf4vjjh7u-v6.eduroam.dynamic.rbg.tum.de
+ [IPv6:2001:4ca0:2003:1920:6b90:2f1d:3641:aceb]) (using TLSv1.2 with cipher
+ ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (No client certificate
+ requested) by postout1.mail.lrz.de (Postfix) with ESMTPSA id 40S7PS4J30zypV
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 09:52:44 +0200 (CEST)
+To: lammich@in.tum.de
+From: Gunther Bidlingmaier <g.bidlingmaier@tum.de>
+Subject: FDS-Homework 1
+Message-ID: <a5cad69e-0d0a-aea1-f69c-e7eced720bcb@tum.de>
+Date: Fri, 20 Apr 2018 09:52:43 +0200
+User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101
+ Thunderbird/52.7.0
+MIME-Version: 1.0
+Content-Type: multipart/mixed; boundary="------------89AC7CA573FA6F22E70AFC2F"
+Content-Language: en-US
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+This is a multi-part message in MIME format.
+--------------89AC7CA573FA6F22E70AFC2F
+Content-Type: text/plain; charset=utf-8; format=flowed
+Content-Transfer-Encoding: 8bit
+
+Gunther Bidlingmaier
+
+03663324
+
+
+--------------89AC7CA573FA6F22E70AFC2F
+Content-Type: text/plain; charset=UTF-8; name="ex01.thy"
+Content-Disposition: attachment; filename="ex01.thy"
+Content-Transfer-Encoding: 8bit
+
+theory ex01
+imports Main
+begin
+
+fun listsum :: "int list \<Rightarrow> int" where
+    "listsum [] = 0"
+  | "listsum (x#xs) = x + listsum xs"
+
+value "listsum [1 ,2 ,3 ] = 6"
+value "listsum [] = 0"
+value "listsum [1 ,-2 ,3 ] = 2"
+
+lemma listsum_filter_z:
+"listsum (filter (\<lambda>x. x \<noteq> 0 ) l ) = listsum l"
+  apply (induction l)
+  apply auto
+  done
+
+lemma listsum_app: "listsum (xs @ ys) = listsum xs + listsum ys"
+  apply (induction xs)
+   apply auto
+  done
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+  apply (induction xs)
+  apply (auto simp: listsum_app)
+  done
+
+lemma "listsum (filter (\<lambda>x. x \<ge> 0) l) \<ge> listsum l"
+  apply (induction l)
+  apply auto
+  done
+
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+    "flatten [] = []"
+  | "flatten (l#ls) = l @ flatten ls"
+
+value "flatten [[1 ,2 ,3 ],[2 ]] = [1 ,2 ,3 ,2 ::int]"
+value "flatten [[1 ,2 ,3 ],[],[2 ]] = [1 ,2 ,3 ,2 ::int]"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply (induction xs)
+  apply (auto simp: listsum_app)
+  done
+
+end
+--------------89AC7CA573FA6F22E70AFC2F--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/ga53qud@mytum.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,162 @@
+From ga53qud@mytum.de Thu Apr 19 22:27:04 2018
+Return-Path: <ga53qud@mytum.de>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ DTrSKIr72FqUCAAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Thu, 19 Apr 2018 22:27:04 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id 7D2E51C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Thu, 19 Apr 2018
+ 22:27:04 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id 7B1D81E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Thu, 19 Apr 2018 22:27:04
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ 76DAB1C0378; Thu, 19 Apr 2018 22:27:04 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 7228E1C038B; Thu, 19 Apr 2018 22:27:04 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id 4A37A1C038A for <lammich@in.tum.de>; Thu, 19 Apr 2018 22:27:04 +0200
+ (CEST)
+Received: from vmmaildmz2.informatik.tu-muenchen.de
+ (vmmaildmz2.informatik.tu-muenchen.de [131.159.0.88]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id 3F5DA1C0376
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 22:27:04 +0200 (CEST)
+Received: by vmmaildmz2.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 3DB1D1C24B4; Thu, 19 Apr 2018 22:27:04 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz2.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-2.2 required=7.0 tests=BAYES_00,DEAR_SOMETHING,
+ HTML_MESSAGE,RCVD_IN_DNSWL_MED autolearn=no autolearn_force=no
+ version=3.4.0-tuminfo_1
+Received: from vmmaildmz2.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz2.informatik.tu-muenchen.de (Postfix) with ESMTP id 72AE21C24B7
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 22:27:02 +0200 (CEST)
+Received: from postout1.mail.lrz.de (postout1.mail.lrz.de
+ [129.187.255.137]) (using TLSv1.2 with cipher AECDH-AES256-SHA (256/256
+ bits)) (No client certificate requested) by
+ vmmaildmz2.informatik.tu-muenchen.de (Postfix) with ESMTPS id 67C791C03AC
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 22:27:02 +0200 (CEST)
+Received: from lxmhs51.srv.lrz.de (localhost [127.0.0.1]) by
+ postout1.mail.lrz.de (Postfix) with ESMTP id 40RrBG2dHGzykj for
+ <lammich@in.tum.de>; Thu, 19 Apr 2018 22:27:02 +0200 (CEST)
+X-Virus-Scanned: by amavisd-new at lrz.de in lxmhs51.srv.lrz.de
+Received: from postout1.mail.lrz.de ([127.0.0.1]) by lxmhs51.srv.lrz.de
+ (lxmhs51.srv.lrz.de [127.0.0.1]) (amavisd-new, port 20024) with LMTP id
+ BBFqwy4AnQrn for <lammich@in.tum.de>; Thu, 19 Apr 2018 22:27:02 +0200 (CEST)
+Received: from BADWLRZ-SWMBX09.ads.mwn.de (BADWLRZ-SWMBX09.ads.mwn.de
+ [IPv6:2001:4ca0:0:108::165]) (using TLSv1.2 with cipher
+ ECDHE-RSA-AES256-SHA384 (256/256 bits)) (Client CN "BADWLRZ-SWMBX09",
+ Issuer "BADWLRZ-SWMBX09" (not verified)) by postout1.mail.lrz.de (Postfix)
+ with ESMTPS id 40RrBG0gJmzykh for <lammich@in.tum.de>; Thu, 19 Apr 2018
+ 22:27:02 +0200 (CEST)
+Received: from BADWLRZ-SWMBX01.ads.mwn.de (2001:4ca0:0:108::157) by
+ BADWLRZ-SWMBX09.ads.mwn.de (2001:4ca0:0:108::165) with Microsoft SMTP
+ Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256)
+ id 15.1.1466.3; Thu, 19 Apr 2018 22:27:00 +0200
+Received: from BADWLRZ-SWMBX01.ads.mwn.de ([fe80::7d02:f283:edbd:b19c]) by
+ BADWLRZ-SWMBX01.ads.mwn.de ([fe80::7d02:f283:edbd:b19c%12]) with mapi id
+ 15.01.1466.003; Thu, 19 Apr 2018 22:27:00 +0200
+From: "Das Sharma, Amartya" <ga53qud@mytum.de>
+To: "lammich@in.tum.de" <lammich@in.tum.de>
+Subject: Functional Data Structures homework week 1
+Thread-Topic: Functional Data Structures homework week 1
+Thread-Index: AQHT2Bvbzf0qr04hu0urOmWMUpCiCQ==
+Date: Thu, 19 Apr 2018 20:27:00 +0000
+Message-ID: <fa0e0cad130b4d39aa3e57c2bc0745e9@mytum.de>
+Accept-Language: en-US
+Content-Language: en-US
+X-MS-Exchange-Organization-AuthAs: Internal
+X-MS-Exchange-Organization-AuthMechanism: 04
+X-MS-Exchange-Organization-AuthSource: BADWLRZ-SWMBX01.ads.mwn.de
+X-MS-Has-Attach: yes
+X-MS-TNEF-Correlator: 
+x-originating-ip: [212.204.102.86]
+Content-Type: multipart/mixed; boundary="_004_fa0e0cad130b4d39aa3e57c2bc0745e9mytumde_"
+MIME-Version: 1.0
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+--_004_fa0e0cad130b4d39aa3e57c2bc0745e9mytumde_
+Content-Type: multipart/alternative; boundary="_000_fa0e0cad130b4d39aa3e57c2bc0745e9mytumde_"
+
+
+--_000_fa0e0cad130b4d39aa3e57c2bc0745e9mytumde_
+Content-Type: text/plain; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+Dear Sir,
+
+
+Please find attached my homework for week 1 of Functional Data Structures.
+
+
+Thanking you,
+
+Amartya Das Sharma
+
+Enrollment 03694265
+
+--_000_fa0e0cad130b4d39aa3e57c2bc0745e9mytumde_
+Content-Type: text/html; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" style="font-size:12pt;color:#000000;font-family:Calibri,Helvetica,sans-serif;" dir="ltr">
+<p>Dear Sir,</p>
+<p><br>
+</p>
+<p>Please find attached my homework for week 1 of Functional Data Structures.</p>
+<p><br>
+</p>
+<p>Thanking you, <br>
+</p>
+<p>Amartya Das Sharma</p>
+<p>Enrollment 03694265<br>
+</p>
+</div>
+</body>
+</html>
+
+--_000_fa0e0cad130b4d39aa3e57c2bc0745e9mytumde_--
+
+--_004_fa0e0cad130b4d39aa3e57c2bc0745e9mytumde_
+Content-Type: application/octet-stream; name="hw01.thy"
+Content-Description: hw01.thy
+Content-Disposition: attachment; filename="hw01.thy"; size=1032; creation-date="Thu, 19 Apr 2018 20:26:44 GMT"; modification-date="Thu, 19 Apr 2018 20:26:44 GMT"
+Content-Transfer-Encoding: base64
+
+dGhlb3J5IGh3MDEKICBpbXBvcnRzIE1haW4KYmVnaW4KCmZ1biBsaXN0c3VtOjogImludCBsaXN0
+IFw8UmlnaHRhcnJvdz4gaW50IiB3aGVyZQogICJsaXN0c3VtIFtdID0gMCIKfCAibGlzdHN1bSAo
+eCAjIHhzKSA9ICBsaXN0c3VtIHhzICsgeCIKCnZhbHVlICJsaXN0c3VtIFsxLDIsM10gPSA2Igp2
+YWx1ZSAibGlzdHN1bSBbXSA9IDAiCnZhbHVlICJsaXN0c3VtIFsxLC0yLDNdID0gMiIKCmxlbW1h
+IGxpc3RzdW1fZmlsdGVyX3g6ICJsaXN0c3VtIChmaWx0ZXIgKFw8bGFtYmRhPnguIHhcPG5vdGVx
+PjApIGwpID0gbGlzdHN1bSBsIgogIGFwcGx5KGluZHVjdGlvbiBsKQogIGFwcGx5KGF1dG8pCiAg
+ZG9uZQoKbGVtbWEgbGlzdHN1bV9hcHBlbmQ6ICJsaXN0c3VtICh4cyBAIHlzKSA9IGxpc3RzdW0g
+eHMgKyBsaXN0c3VtIHlzIgogIGFwcGx5KGluZHVjdGlvbiB4cykKICAgYXBwbHkoYXV0bykKICBk
+b25lCgpsZW1tYSBsaXN0c3VtX3JldjogImxpc3RzdW0gKHJldiB4cykgPSBsaXN0c3VtIHhzIgog
+IGFwcGx5KGluZHVjdGlvbiB4cykKICAgYXBwbHkoYXV0byBzaW1wOmxpc3RzdW1fYXBwZW5kKQog
+IGRvbmUKCmxlbW1hIGxpc3RzdW1fbm9uZWc6ICJsaXN0c3VtIChmaWx0ZXIgKFw8bGFtYmRhPngu
+IHg+MCkgbCkgXDxnZT4gbGlzdHN1bSBsIgogIGFwcGx5KGluZHVjdGlvbiBsKQogICBhcHBseShh
+dXRvKQogIGRvbmUKCmZ1biBmbGF0dGVuIDo6ICInYSBsaXN0IGxpc3QgXDxSaWdodGFycm93PiAn
+YSBsaXN0IiB3aGVyZQogICJmbGF0dGVuIFtdID0gW10iCnwgImZsYXR0ZW4gKGwjbHMpID0gbCBA
+IGZsYXR0ZW4gbHMiCgp2YWx1ZSAiZmxhdHRlbiBbWzEsMiwzXSxbMl1dID0gWzEsMiwzLDI6Omlu
+dF0iCnZhbHVlICJmbGF0dGVuIFtbMSwyLDNdLFtdLFsyXV0gPSBbMSwyLDMsMjo6aW50XSIKCmxl
+bW1hICJsaXN0c3VtIChmbGF0dGVuIHhzKSA9IGxpc3RzdW0obWFwIGxpc3RzdW0geHMpIgogIGFw
+cGx5KGluZHVjdGlvbiB4cykKICBhcHBseShhdXRvIHNpbXA6bGlzdHN1bV9hcHBlbmQpCiAgZG9u
+ZQoKZW5k
+
+--_004_fa0e0cad130b4d39aa3e57c2bc0745e9mytumde_--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/ge69kel@mytum.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,154 @@
+From ge69kel@mytum.de Thu Apr 19 22:35:28 2018
+Return-Path: <ge69kel@mytum.de>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ hvZNDHX82FpNGAAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Thu, 19 Apr 2018 22:35:28 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id A8F321C202A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Thu, 19 Apr 2018
+ 22:35:28 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id A75F71E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Thu, 19 Apr 2018 22:35:28
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ A426F1C0376; Thu, 19 Apr 2018 22:35:28 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id A1BA91C038A; Thu, 19 Apr 2018 22:35:28 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id 7D0151C0378 for <lammich@in.tum.de>; Thu, 19 Apr 2018 22:35:28 +0200
+ (CEST)
+Received: from vmmaildmz1.informatik.tu-muenchen.de
+ (vmmaildmz1.informatik.tu-muenchen.de [131.159.0.87]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id 716141C0376
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 22:35:28 +0200 (CEST)
+Received: by vmmaildmz1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 6FE6D1C2DAA; Thu, 19 Apr 2018 22:35:28 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz1.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-4.2 required=7.0 tests=BAYES_00,HTML_MESSAGE,
+ RCVD_IN_DNSWL_MED autolearn=no autolearn_force=no version=3.4.0-tuminfo_1
+Received: from vmmaildmz1.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTP id D59731C2DA9
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 22:35:26 +0200 (CEST)
+Received: from postout1.mail.lrz.de (postout1.mail.lrz.de
+ [129.187.255.137]) (using TLSv1.2 with cipher AECDH-AES256-SHA (256/256
+ bits)) (No client certificate requested) by
+ vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTPS id C97421C2D8A
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 22:35:26 +0200 (CEST)
+Received: from lxmhs51.srv.lrz.de (localhost [127.0.0.1]) by
+ postout1.mail.lrz.de (Postfix) with ESMTP id 40RrMy4dvPzyV4 for
+ <lammich@in.tum.de>; Thu, 19 Apr 2018 22:35:26 +0200 (CEST)
+X-Virus-Scanned: by amavisd-new at lrz.de in lxmhs51.srv.lrz.de
+Received: from postout1.mail.lrz.de ([127.0.0.1]) by lxmhs51.srv.lrz.de
+ (lxmhs51.srv.lrz.de [127.0.0.1]) (amavisd-new, port 20024) with LMTP id
+ VuHYVKVABw61 for <lammich@in.tum.de>; Thu, 19 Apr 2018 22:35:26 +0200 (CEST)
+Received: from BADWLRZ-SWMBX10.ads.mwn.de (BADWLRZ-SWMBX10.ads.mwn.de
+ [10.156.54.166]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-SHA384
+ (256/256 bits)) (Client CN "BADWLRZ-SWMBX10", Issuer "BADWLRZ-SWMBX10" (not
+ verified)) by postout1.mail.lrz.de (Postfix) with ESMTPS id 40RrMy2XvlzyTg
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 22:35:26 +0200 (CEST)
+Received: from BADWLRZ-SWMBX01.ads.mwn.de (2001:4ca0:0:108::157) by
+ BADWLRZ-SWMBX10.ads.mwn.de (2001:4ca0:0:108::166) with Microsoft SMTP
+ Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256)
+ id 15.1.1466.3; Thu, 19 Apr 2018 22:35:24 +0200
+Received: from BADWLRZ-SWMBX01.ads.mwn.de ([fe80::7d02:f283:edbd:b19c]) by
+ BADWLRZ-SWMBX01.ads.mwn.de ([fe80::7d02:f283:edbd:b19c%12]) with mapi id
+ 15.01.1466.003; Thu, 19 Apr 2018 22:35:24 +0200
+From: "Somasundaram, Arun" <ge69kel@mytum.de>
+To: "lammich@in.tum.de" <lammich@in.tum.de>
+Subject: Functional Data Structures Week 1 Homework Submission
+Thread-Topic: Functional Data Structures Week 1 Homework Submission
+Thread-Index: AQHT2B0IxM11IYfDd0Kr6Mpo4MVzjA==
+Date: Thu, 19 Apr 2018 20:35:24 +0000
+Message-ID: <38a9442c19504df6bc6aa45082d4a38a@mytum.de>
+Accept-Language: en-US
+Content-Language: en-US
+X-MS-Exchange-Organization-AuthAs: Internal
+X-MS-Exchange-Organization-AuthMechanism: 04
+X-MS-Exchange-Organization-AuthSource: BADWLRZ-SWMBX01.ads.mwn.de
+X-MS-Has-Attach: yes
+X-MS-TNEF-Correlator: 
+x-originating-ip: [10.149.235.88]
+Content-Type: multipart/mixed; boundary="_004_38a9442c19504df6bc6aa45082d4a38amytumde_"
+MIME-Version: 1.0
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+--_004_38a9442c19504df6bc6aa45082d4a38amytumde_
+Content-Type: multipart/alternative; boundary="_000_38a9442c19504df6bc6aa45082d4a38amytumde_"
+
+
+--_000_38a9442c19504df6bc6aa45082d4a38amytumde_
+Content-Type: text/plain; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+Dear Dr. Lammich
+
+
+Please find attached my .thy file for the week 1 homework for Functional Data Structures.
+
+
+Thank You
+
+Arun S
+
+--_000_38a9442c19504df6bc6aa45082d4a38amytumde_
+Content-Type: text/html; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" style="font-size: 12pt; color: rgb(0, 0, 0); font-family: Calibri, Helvetica, sans-serif, EmojiFont, &quot;Apple Color Emoji&quot;, &quot;Segoe UI Emoji&quot;, NotoColorEmoji, &quot;Segoe UI Symbol&quot;, &quot;Android Emoji&quot;, EmojiSymbols;" dir="ltr">
+<p>Dear Dr. Lammich</p>
+<p><br>
+</p>
+<p>Please find attached my .thy file for the week 1 homework for Functional Data Structures.</p>
+<p><br>
+</p>
+<p>Thank You</p>
+<p>Arun S</p>
+</div>
+</body>
+</html>
+
+--_000_38a9442c19504df6bc6aa45082d4a38amytumde_--
+
+--_004_38a9442c19504df6bc6aa45082d4a38amytumde_
+Content-Type: application/octet-stream; name="Homework01.thy"
+Content-Description: Homework01.thy
+Content-Disposition: attachment; filename="Homework01.thy"; size=1023; creation-date="Thu, 19 Apr 2018 20:32:02 GMT"; modification-date="Thu, 19 Apr 2018 20:32:02 GMT"
+Content-Transfer-Encoding: base64
+
+dGhlb3J5IEhvbWV3b3JrMDEKICBpbXBvcnRzIE1haW4KYmVnaW4KZnVuIGxpc3RzdW0gOjogImlu
+dCBsaXN0IFw8UmlnaHRhcnJvdz4gaW50IiB3aGVyZQogICJsaXN0c3VtIFtdID0gMCIKfCAibGlz
+dHN1bSAoeCN4cykgPSB4ICsgbGlzdHN1bSB4cyIKCnZhbHVlICJsaXN0c3VtIFsxLDIsM10gPSA2
+Igp2YWx1ZSAibGlzdHN1bSBbXSA9IDAiCnZhbHVlICJsaXN0c3VtIFsxLC0yLDNdID0gMiIKCmxl
+bW1hIGxpc3RzdW1maWx0ZXJfejogImxpc3RzdW0gKGZpbHRlciAoXDxsYW1iZGE+eC4geFw8bm90
+ZXE+MCkgbCkgPSBsaXN0c3VtIGwiCiAgYXBwbHkgKGluZHVjdGlvbiBsKQogICBhcHBseSBhdXRv
+CiAgZG9uZQpsZW1tYSBsaXN0c3VtbGlzdDogImxpc3RzdW0gKHhzQHlzKSA9KGxpc3RzdW0geHMp
+ICsgKGxpc3RzdW0geXMpIgogIGFwcGx5IChpbmR1Y3Rpb24geHMpCiAgIGFwcGx5IGF1dG8KICBk
+b25lCgpsZW1tYSBsaXN0c3VtX3JldjogImxpc3RzdW0gKHJldiB4cykgPSBsaXN0c3VtIHhzIgog
+IGFwcGx5IChpbmR1Y3Rpb24geHMpCiAgIGFwcGx5IChhdXRvIHNpbXA6IGxpc3RzdW1saXN0KQog
+IGRvbmUKCmxlbW1hIGxpc3RzdW1maWx0ZXJfbjogImxpc3RzdW0gKGZpbHRlcihcPGxhbWJkYT54
+LiB4PjApIGwpIFw8Z2U+IGxpc3RzdW0gbCIKICBhcHBseShpbmR1Y3Rpb24gbCkKICAgYXBwbHkg
+YXV0bwogIGRvbmUKCmZ1biBmbGF0dGVuIDo6ICInYSBsaXN0IGxpc3QgXDxSaWdodGFycm93Pidh
+IGxpc3QiIHdoZXJlCiAgImZsYXR0ZW4gW10gPSBbXSIKfCAiZmxhdHRlbiAobCNscykgPSBsQGZs
+YXR0ZW4gbHMiCgp2YWx1ZSAiZmxhdHRlbiBbWzEsMiwzXSxbMl1dID0gWzEsMiwzLDI6OmludF0i
+CnZhbHVlICJmbGF0dGVuIFtbMSwyLDNdLFtdLFsyXV0gPSBbMSwyLDMsMjo6aW50XSIKCmxlbW1h
+ICJsaXN0c3VtIChmbGF0dGVuIHhzKSA9IGxpc3RzdW0gKG1hcCBsaXN0c3VtIHhzKSIKICBhcHBs
+eShpbmR1Y3Rpb24geHMpCiAgYXBwbHkgKGF1dG8gc2ltcDpsaXN0c3VtbGlzdCkKICAgCiAg
+
+--_004_38a9442c19504df6bc6aa45082d4a38amytumde_--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/ge72lic@mytum.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,141 @@
+From ge72lic@mytum.de Fri Apr 20 10:19:49 2018
+Return-Path: <ge72lic@mytum.de>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ KsjvL5yi2VqyHwAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Fri, 20 Apr 2018 10:19:49 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id 4D7FE1C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Fri, 20 Apr 2018
+ 10:19:49 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id 4BB251E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Fri, 20 Apr 2018 10:19:49
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ 48D0E1C0376; Fri, 20 Apr 2018 10:19:49 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 462DA1C038B; Fri, 20 Apr 2018 10:19:49 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id 232611C038A for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:19:49 +0200
+ (CEST)
+Received: from vmmaildmz2.informatik.tu-muenchen.de
+ (vmmaildmz2.informatik.tu-muenchen.de [131.159.0.88]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id 187F31C0376
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:19:49 +0200 (CEST)
+Received: by vmmaildmz2.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 16B031C24B7; Fri, 20 Apr 2018 10:19:49 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz2.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-3.8 required=7.0 tests=BAYES_00,HTML_MESSAGE,
+ MIME_HTML_MOSTLY,RCVD_IN_DNSWL_MED,TVD_SPACE_RATIO autolearn=no
+ autolearn_force=no version=3.4.0-tuminfo_1
+Received: from vmmaildmz2.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz2.informatik.tu-muenchen.de (Postfix) with ESMTP id 6404C1C24B4
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:19:47 +0200 (CEST)
+Received: from postout1.mail.lrz.de (postout1.mail.lrz.de
+ [129.187.255.137]) (using TLSv1.2 with cipher AECDH-AES256-SHA (256/256
+ bits)) (No client certificate requested) by
+ vmmaildmz2.informatik.tu-muenchen.de (Postfix) with ESMTPS id 593B01C24AD
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:19:47 +0200 (CEST)
+Received: from lxmhs51.srv.lrz.de (localhost [127.0.0.1]) by
+ postout1.mail.lrz.de (Postfix) with ESMTP id 40S80g2BTTzybn for
+ <lammich@in.tum.de>; Fri, 20 Apr 2018 10:19:47 +0200 (CEST)
+X-Virus-Scanned: by amavisd-new at lrz.de in lxmhs51.srv.lrz.de
+Received: from postout1.mail.lrz.de ([127.0.0.1]) by lxmhs51.srv.lrz.de
+ (lxmhs51.srv.lrz.de [127.0.0.1]) (amavisd-new, port 20024) with LMTP id
+ 6XE3a7JCk62w for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:19:47 +0200 (CEST)
+Received: from BADWLRZ-SWMBX09.ads.mwn.de (BADWLRZ-SWMBX09.ads.mwn.de
+ [IPv6:2001:4ca0:0:108::165]) (using TLSv1.2 with cipher
+ ECDHE-RSA-AES256-SHA384 (256/256 bits)) (Client CN "BADWLRZ-SWMBX09",
+ Issuer "BADWLRZ-SWMBX09" (not verified)) by postout1.mail.lrz.de (Postfix)
+ with ESMTPS id 40S80g0kZXzySZ for <lammich@in.tum.de>; Fri, 20 Apr 2018
+ 10:19:47 +0200 (CEST)
+Received: from BADWLRZ-SWMBX01.ads.mwn.de (2001:4ca0:0:108::157) by
+ BADWLRZ-SWMBX09.ads.mwn.de (2001:4ca0:0:108::165) with Microsoft SMTP
+ Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256)
+ id 15.1.1466.3; Fri, 20 Apr 2018 10:19:45 +0200
+Received: from BADWLRZ-SWMBX01.ads.mwn.de ([fe80::7d02:f283:edbd:b19c]) by
+ BADWLRZ-SWMBX01.ads.mwn.de ([fe80::7d02:f283:edbd:b19c%12]) with mapi id
+ 15.01.1466.003; Fri, 20 Apr 2018 10:19:45 +0200
+From: "Pfeiffer, Marcus" <ge72lic@mytum.de>
+To: "lammich@in.tum.de" <lammich@in.tum.de>
+Subject: [FDS-Homework] Marcus Pfeiffer (03703095)
+Thread-Topic: [FDS-Homework] Marcus Pfeiffer (03703095)
+Thread-Index: AQHT2IBFcYZYlLnmT0WvHBXsgEOX6A==
+Date: Fri, 20 Apr 2018 08:19:45 +0000
+Message-ID: <dd315048b776433c93cb876eb9fe2e92@mytum.de>
+Accept-Language: de-DE, en-US
+Content-Language: de-DE
+X-MS-Exchange-Organization-AuthAs: Internal
+X-MS-Exchange-Organization-AuthMechanism: 04
+X-MS-Exchange-Organization-AuthSource: BADWLRZ-SWMBX01.ads.mwn.de
+X-MS-Has-Attach: yes
+X-MS-TNEF-Correlator: 
+x-originating-ip: [131.159.76.55]
+Content-Type: multipart/mixed; boundary="_004_dd315048b776433c93cb876eb9fe2e92mytumde_"
+MIME-Version: 1.0
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+--_004_dd315048b776433c93cb876eb9fe2e92mytumde_
+Content-Type: multipart/alternative; boundary="_000_dd315048b776433c93cb876eb9fe2e92mytumde_"
+
+
+--_000_dd315048b776433c93cb876eb9fe2e92mytumde_
+Content-Type: text/plain; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+
+
+--_000_dd315048b776433c93cb876eb9fe2e92mytumde_
+Content-Type: text/html; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" style="font-size:12pt;color:#000000;font-family:Calibri,Helvetica,sans-serif;" dir="ltr">
+</div>
+</body>
+</html>
+
+--_000_dd315048b776433c93cb876eb9fe2e92mytumde_--
+
+--_004_dd315048b776433c93cb876eb9fe2e92mytumde_
+Content-Type: application/octet-stream; name="ex01.thy"
+Content-Description: ex01.thy
+Content-Disposition: attachment; filename="ex01.thy"; size=1029; creation-date="Fri, 20 Apr 2018 08:15:52 GMT"; modification-date="Fri, 20 Apr 2018 08:15:52 GMT"
+Content-Transfer-Encoding: base64
+
+dGhlb3J5IGV4MDEKaW1wb3J0cyBNYWluCmJlZ2luCiBmdW4gbGlzdHN1bSA6OiAiaW50IGxpc3Qg
+XDxSaWdodGFycm93PiBpbnQiIHdoZXJlCiAgICAibGlzdHN1bSBbXSA9IDAiCiAgfCAibGlzdHN1
+bSAoeCN4cykgPSB4ICsgbGlzdHN1bSB4cyIKCiB2YWx1ZSAiKGxpc3RzdW0gWzEgLDIgLDMgXSkg
+PSA2IgogdmFsdWUgImxpc3RzdW0gW10gPSAwIgogdmFsdWUgImxpc3RzdW0gWzEgLC0yICwzIF0g
+PSAyIgogdmFsdWUgImxlbihbMSwgMiwgM10pIgoKbGVtbWEgbGlzdHN1bV9maWx0ZXJfejogImxp
+c3RzdW0gKGZpbHRlciAoXDxsYW1iZGE+eCAuIHggXDxub3RlcT4gMCApIGwgKSA9IGxpc3RzdW0g
+bCIKICBhcHBseShpbmR1Y3Rpb24gbCkgYnkgYXV0bwoKbGVtbWEgYXV4IDogImxpc3RzdW0oeHNA
+eXMpID0gbGlzdHN1bSB4cyArIGxpc3RzdW0geXMiCiAgYXBwbHkoaW5kdWN0aW9uIHhzKSBieSBh
+dXRvCgoKbGVtbWEgbGlzdHN1bV9yZXY6ICJsaXN0c3VtIChyZXYgeHMpID0gbGlzdHN1bSB4cyIK
+ICBhcHBseShpbmR1Y3Rpb24geHMpCiAgIGFwcGx5KGF1dG8gc2ltcDogYXV4KQogIGRvbmUKCmxl
+bW1hIGxpc3RzdW1fbm9uX2RlY3I6ICJsaXN0c3VtIChmaWx0ZXIgKFw8bGFtYmRhPnggLiB4IFw8
+Z2U+IDApIGwpIFw8Z2U+IGxpc3RzdW0gbCIKICBhcHBseShpbmR1Y3Rpb24gbCkgYnkgYXV0bwoK
+CmZ1biBmbGF0dGVuIDo6ICInYSBsaXN0IGxpc3QgXDxSaWdodGFycm93PiAnYSBsaXN0IiB3aGVy
+ZQogICJmbGF0dGVuIFtdID0gW10iCnwgImZsYXR0ZW4gKGwjbHMpID0gbEAgZmxhdHRlbiBscyAi
+Cgp2YWx1ZSAiZmxhdHRlbiBbWzEgLDIgLDMgXSxbMiBdXSA9IFsxICwyICwzICwyIDo6aW50XSIK
+dmFsdWUgImZsYXR0ZW4gW1sxICwyICwzIF0sW10sWzIgXV0gPSBbMSAsMiAsMyAsMiA6OmludF0i
+CgoKCmxlbW1hICJsaXN0c3VtIChmbGF0dGVuIHhzKSA9IGxpc3RzdW0gKG1hcCBsaXN0c3VtIHhz
+KSIKICBhcHBseShpbmR1Y3Rpb24geHMpCiAgYXBwbHkoYXV0byBzaW1wOiBhdXgpCiAgZG9uZQoK
+ZW5k
+
+--_004_dd315048b776433c93cb876eb9fe2e92mytumde_--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/j.gottfriedsen@tum.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,149 @@
+From j.gottfriedsen@tum.de Thu Apr 19 19:10:15 2018
+Return-Path: <j.gottfriedsen@tum.de>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ Gk3cBnDN2FovKAAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Thu, 19 Apr 2018 19:10:15 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id 9A7291C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Thu, 19 Apr 2018
+ 19:10:15 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id 98C391E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Thu, 19 Apr 2018 19:10:15
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ 951361C0376; Thu, 19 Apr 2018 19:10:15 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 924791C038A; Thu, 19 Apr 2018 19:10:15 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id 6E5851C0378 for <lammich@in.tum.de>; Thu, 19 Apr 2018 19:10:15 +0200
+ (CEST)
+Received: from vmmaildmz1.informatik.tu-muenchen.de
+ (vmmaildmz1.informatik.tu-muenchen.de [131.159.0.87]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id 63B001C0376
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 19:10:15 +0200 (CEST)
+Received: by vmmaildmz1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 6178D1C2DB7; Thu, 19 Apr 2018 19:10:15 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz1.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-4.2 required=7.0 tests=AWL,BAYES_00,HTML_MESSAGE,
+ RCVD_IN_DNSWL_MED autolearn=no autolearn_force=no version=3.4.0-tuminfo_1
+Received: from vmmaildmz1.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTP id 4AD771C2DBA
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 19:10:07 +0200 (CEST)
+Received: from forwout1.mail.lrz.de (forwout1.mail.lrz.de
+ [129.187.255.130]) (using TLSv1.2 with cipher AECDH-AES256-SHA (256/256
+ bits)) (No client certificate requested) by
+ vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTPS id 3FE1E1C2DBC
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 19:10:07 +0200 (CEST)
+Received: from postforw2.mail.lrz.de (postforw.mail.lrz.de
+ [IPv6:2001:4ca0:0:116::a9c:63e]) by forwout1.mail.lrz.de (Postfix) with
+ ESMTP id 40Rlq30rj9zQ3 for <lammich@in.tum.de>; Thu, 19 Apr 2018 19:10:07
+ +0200 (CEST)
+Received: from BADWLRZ-SWMBX01.ads.mwn.de (BADWLRZ-SWMBX01.ads.mwn.de
+ [10.156.54.157]) by postforw2.mail.lrz.de (Postfix) with ESMTP id
+ 40Rlq30ggvzySN for <ga57nid@exchwl.mytum.de>; Thu, 19 Apr 2018 19:10:07
+ +0200 (CEST)
+Received: from BADWLRZ-SWMBX07.ads.mwn.de (2001:4ca0:0:108::163) by
+ BADWLRZ-SWMBX01.ads.mwn.de (2001:4ca0:0:108::157) with Microsoft SMTP
+ Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256)
+ id 15.1.1466.3; Thu, 19 Apr 2018 19:10:05 +0200
+Received: from BADWLRZ-SWMBX07.ads.mwn.de ([fe80::302d:9066:578c:4d70]) by
+ BADWLRZ-SWMBX07.ads.mwn.de ([fe80::302d:9066:578c:4d70%13]) with mapi id
+ 15.01.1466.003; Thu, 19 Apr 2018 19:10:05 +0200
+From: Jakob Gottfriedsen <j.gottfriedsen@tum.de>
+To: "Lammich, Peter" <peter.lammich@tum.de>
+Subject: Submission of FDS Homework Sheet 1
+Thread-Topic: Submission of FDS Homework Sheet 1
+Thread-Index: AQHT2AEtWOXEl2wHbESbhXEE+gKG5Q==
+Date: Thu, 19 Apr 2018 17:10:05 +0000
+Message-ID: <ba5a70acc7e1465cb8fb73137475b8cb@tum.de>
+Accept-Language: de-DE, en-US
+Content-Language: de-DE
+X-MS-Exchange-Organization-AuthAs: Internal
+X-MS-Has-Attach: yes
+X-MS-TNEF-Correlator: 
+x-originating-ip: [188.193.150.59]
+Content-Type: multipart/mixed; boundary="_004_ba5a70acc7e1465cb8fb73137475b8cbtumde_"
+MIME-Version: 1.0
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+--_004_ba5a70acc7e1465cb8fb73137475b8cbtumde_
+Content-Type: multipart/alternative; boundary="_000_ba5a70acc7e1465cb8fb73137475b8cbtumde_"
+
+
+--_000_ba5a70acc7e1465cb8fb73137475b8cbtumde_
+Content-Type: text/plain; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+Hello,
+
+
+As the submission system is still not available, my solution to sheet 1 is attached to this mail.
+
+
+Name:
+
+Jakob Gottfriedsen
+
+--_000_ba5a70acc7e1465cb8fb73137475b8cbtumde_
+Content-Type: text/html; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" dir="ltr" style="font-size: 12pt; color: rgb(0, 0, 0); font-family: Calibri, Helvetica, sans-serif, &quot;EmojiFont&quot;, &quot;Apple Color Emoji&quot;, &quot;Segoe UI Emoji&quot;, NotoColorEmoji, &quot;Segoe UI Symbol&quot;, &quot;Android Emoji&quot;, EmojiSymbols;">
+<p>Hello,</p>
+<p><br>
+</p>
+<p>As the submission system is still not available, my solution to sheet 1 is attached to this mail.</p>
+<p><br>
+</p>
+<p>Name:</p>
+<p>Jakob Gottfriedsen<br>
+</p>
+</div>
+</body>
+</html>
+
+--_000_ba5a70acc7e1465cb8fb73137475b8cbtumde_--
+
+--_004_ba5a70acc7e1465cb8fb73137475b8cbtumde_
+Content-Type: application/octet-stream; name="ex01.thy"
+Content-Description: ex01.thy
+Content-Disposition: attachment; filename="ex01.thy"; size=979; creation-date="Thu, 19 Apr 2018 17:06:34 GMT"; modification-date="Thu, 19 Apr 2018 17:06:34 GMT"
+Content-Transfer-Encoding: base64
+
+dGhlb3J5IGV4MDEKICBpbXBvcnRzIE1haW4KYmVnaW4KCmZ1biBsaXN0c3VtIDo6ICJpbnQgbGlz
+dCBcPFJpZ2h0YXJyb3c+IGludCIgd2hlcmUKICAibGlzdHN1bSBbXSA9IDAiIHwKICAibGlzdHN1
+bSAoeCAjIHhzKSA9IHggKyBsaXN0c3VtIHhzIgoKdmFsdWUgImxpc3RzdW1bMSwgMiwgM10gPSA2
+Igp2YWx1ZSAibGlzdHN1bVtdID0gMCIKdmFsdWUgImxpc3RzdW1bMSwgLTIsIDNdID0gMiIKCmxl
+bW1hIGxpc3RzdW1fZmlsdGVyX3o6ICJsaXN0c3VtIChmaWx0ZXIgKFw8bGFtYmRhPnguIHggXDxu
+b3RlcT4gMCkgbCkgPSBsaXN0c3VtIGwiCiAgYnkgKGluZHVjdGlvbiBsKSBhdXRvCgpsZW1tYSBs
+aXN0c3VtX2FwcDogImxpc3RzdW0gKHhzIEAgeXMpID0gbGlzdHN1bSB4cyArIGxpc3RzdW0geXMi
+CiAgYnkgKGluZHVjdGlvbiB4cykgYXV0bwoKbGVtbWEgbGlzdHN1bV9yZXY6ICJsaXN0c3VtIChy
+ZXYgeHMpID0gbGlzdHN1bSB4cyIKICBieSAoaW5kdWN0aW9uIHhzKSAoYXV0byBzaW1wIGFkZDog
+bGlzdHN1bV9hcHApCgpsZW1tYSBsaXN0c3VtX2ZpbHRlcl9uZWc6ICJsaXN0c3VtIGwgXDxsZT4g
+bGlzdHN1bSAoZmlsdGVyIChcPGxhbWJkYT54LiB4IFw8Z2U+IDApIGwpIgogIGJ5IChpbmR1Y3Rp
+b24gbCkgYXV0bwoKZnVuIGZsYXR0ZW4gOjogIidhIGxpc3QgbGlzdCBcPFJpZ2h0YXJyb3c+ICdh
+IGxpc3QiIHdoZXJlCiAgImZsYXR0ZW4gW10gPSBbXSIgfAogICJmbGF0dGVuIChsICMgbHMpID0g
+bCBAIGZsYXR0ZW4gbHMiCgp2YWx1ZSAiZmxhdHRlbiBbWzEsIDIsIDNdLCBbMl1dID0gWzEsIDIs
+IDMsIDI6OmludF0iCnZhbHVlICJmbGF0dGVuIFtbMSwgMiwgM10sIFtdLCBbMl1dID0gWzEsIDIs
+IDMsIDI6OmludF0iCgpsZW1tYSAibGlzdHN1bSAoZmxhdHRlbiB4cykgPSBsaXN0c3VtIChtYXAg
+bGlzdHN1bSB4cykiCiAgYnkgKGluZHVjdGlvbiB4cykgKGF1dG8gc2ltcCBhZGQ6IGxpc3RzdW1f
+YXBwKQoKZW5kCg==
+
+--_004_ba5a70acc7e1465cb8fb73137475b8cbtumde_--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/j.v.mutius@gmail.com	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,139 @@
+From j.v.mutius@gmail.com Fri Apr 20 10:28:04 2018
+Return-Path: <j.v.mutius@gmail.com>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ v6z8Nlik2Vp9OgAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Fri, 20 Apr 2018 10:28:04 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id 736AA1C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Fri, 20 Apr 2018
+ 10:28:04 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id 720291E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Fri, 20 Apr 2018 10:28:04
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ 6FA701C0376; Fri, 20 Apr 2018 10:28:04 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 6D1FB1C038F; Fri, 20 Apr 2018 10:28:04 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id 4A36B1C038A for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:28:04 +0200
+ (CEST)
+Received: from vmmaildmz1.informatik.tu-muenchen.de
+ (vmmaildmz1.informatik.tu-muenchen.de [131.159.0.87]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id 358201C0376
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:28:04 +0200 (CEST)
+Received: by vmmaildmz1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 340411C2DA9; Fri, 20 Apr 2018 10:28:04 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz1.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-2.0 required=7.0 tests=BAYES_00,DKIM_SIGNED,
+ DKIM_VALID,DKIM_VALID_AU,FREEMAIL_FROM,RCVD_IN_DNSWL_NONE,RCVD_IN_MSPIKE_H2
+ autolearn=no autolearn_force=no version=3.4.0-tuminfo_1
+Received: from vmmaildmz1.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTP id 317C51C2DAB
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:27:56 +0200 (CEST)
+Received: from mail-wr0-f172.google.com (mail-wr0-f172.google.com
+ [209.85.128.172]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256
+ (128/128 bits)) (No client certificate requested) by
+ vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTPS id 1F8891C2D9F
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:27:51 +0200 (CEST)
+Received: by mail-wr0-f172.google.com with SMTP id v15-v6so2576427wrm.10
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 01:27:51 -0700 (PDT)
+DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com;
+ s=20161025; h=message-id:subject:from:to:date:mime-version;
+ bh=jAEPPkGWtJM/5KvSpakog6L+0z9nRvzML1PIorUVKMI=;
+ b=tTt9KUeDimhUYPC8/qcawT8/it0Eguu83oQrwfOIwOMQp2Keko85IrOw4rsNedtCe+
+ Lx5wjEQ0kKC2e98pRC7/sTSdkktpM39n+6J90RuST962ISe0svuR3JPWTsErLPGO/dgd
+ bIDGgw3HS3C5nnH4FKTK6QG4zROrAvnrV7whL7uifQq800h4jLEnM7QMTDZtn8fs0SOa
+ zfRlL85ks+AzuPI7b1CgFk2W+6U903rSOlKstfavQvNNqNmPtVqO3fn6exn9gz+CHm3H
+ WWB0N5lMPZq34bJelDRCpEsagdfLb8Fqcrbi8kp3Yo0Us7cNRabLaqV+LXiMZ48sckrA ovpw==
+X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net;
+ s=20161025;
+ h=x-gm-message-state:message-id:subject:from:to:date:mime-version;
+ bh=jAEPPkGWtJM/5KvSpakog6L+0z9nRvzML1PIorUVKMI=;
+ b=T5AIpDj2RNEuAOL8kVgp3kdOhmFxM9ch7Kaq5K7WFk+zEtVGAmltmbPVoMtLXtWVAR
+ 2lC53Jld1GparIygt+1Zt7yhobhoHHrLna8qh0uxfPhLk8zkoaC6bmL8MOrk0pynLiup
+ bedmAR3neHKwLuPmFpaLjHkmVEnrYiGMjsF3awQIFbH1RU9jYHCyGrEJAFOqEYO7LyS0
+ JM7gR8r9OOrJ9dg3zMObuPcY6Acy/T4T5pd7qe5UVsHTIrbaxvmILM92bXD0IWhDI17A
+ HjbXXbIt8Hn6wzKIIldN0heEAYyOqtSiVee1CpCmP2z3vMkaatE4MUSgBuiLmUMymP6g       
+ 9fWg==
+X-Gm-Message-State:
+ ALQs6tCNkWe9e83FBEVgQDx1y6p9o6D5f0fn+NHDlO0uT5pd1mIbohzh
+ glxAY0Sfu/5fZ1raWGYs6XNhke5h
+X-Google-Smtp-Source:
+ AIpwx49olfu1GwDw2wgBySQwfBZlCMsxFrnKL09io43TxJ0NcMEDSxagf9J2XUqleoeyYw6/vlCbwQ==
+X-Received: by 2002:adf:e38e:: with SMTP id
+ e14-v6mr1129541wrm.198.1524212870634; Fri, 20 Apr 2018 01:27:50 -0700 (PDT)
+Received: from x200arch (w3mcopupx55fiv-v6.eduroam.dynamic.rbg.tum.de.
+ [2001:4ca0:2003:1920:ee1a:a3c0:db1f:36d8]) by smtp.googlemail.com with
+ ESMTPSA id u5sm2137657wmd.40.2018.04.20.01.27.49 for <lammich@in.tum.de>
+ (version=TLS1_2 cipher=ECDHE-RSA-CHACHA20-POLY1305 bits=256/256); Fri, 20
+ Apr 2018 01:27:49 -0700 (PDT)
+Message-ID: <d6cfee84ae0ed8abcd3f28808e75618207522af6.camel@gmail.com>
+Subject: [FDS-Homework]
+From: Joshua von Mutius <j.v.mutius@gmail.com>
+To: Peter Lammich <lammich@in.tum.de>
+Date: Fri, 20 Apr 2018 10:25:18 +0200
+Content-Type: multipart/mixed; boundary="=-9jZk6IzviEKaXdlzCTxS"
+X-Mailer: Evolution 3.28.1 
+Mime-Version: 1.0
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+--=-9jZk6IzviEKaXdlzCTxS
+Content-Type: text/plain; charset="UTF-8"
+Content-Transfer-Encoding: 8bit
+
+Hello Mr. Lammich,
+
+attached to this email one can find my theory file for 
+the homework.
+
+Joshua von Mutius
+--=-9jZk6IzviEKaXdlzCTxS
+Content-Disposition: attachment; filename="hw01.thy"
+Content-Type: text/plain; name="hw01.thy"; charset="UTF-8"
+Content-Transfer-Encoding: 8bit
+
+theory hw01
+  imports Main
+begin
+
+fun listsum :: "int list \<Rightarrow> int" where
+"listsum [] = 0" |
+"listsum (x#xs) = x + listsum xs"
+
+value "listsum [1,2,3] = 6"
+value "listsum [] = 0"
+value "listsum [1,-2,3] = 2"
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x. x \<noteq>  0) l) = listsum l"
+  apply(induction l) by auto
+
+lemma listsum_app: "listsum (xs @ ys) = listsum xs + listsum ys"
+  apply(induction xs) by auto
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+  apply(induction xs) by (auto simp: listsum_app)
+
+lemma listsum_filt_neg_smalleq: "listsum (filter (\<lambda>x. x \<ge> 0) xs) \<ge> listsum xs"
+  apply(induction xs) by auto
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+"flatten [] = []" |
+"flatten (l#ls) = l @ flatten ls"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply(induction xs) by (auto simp: listsum_app)
+
+end
+--=-9jZk6IzviEKaXdlzCTxS--
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/jonatan.juhas@tum.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,143 @@
+From jonatan.juhas@tum.de Fri Apr 20 22:47:29 2018
+Return-Path: <jonatan.juhas@gmail.com>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ yuwIMdpR2lqNRQAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Fri, 20 Apr 2018 22:47:29 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id 33E9F1C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Fri, 20 Apr 2018
+ 22:47:29 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id 2E8741E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Fri, 20 Apr 2018 22:47:29
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ 2BDF61C0376; Fri, 20 Apr 2018 22:47:29 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 28BBE1C037C; Fri, 20 Apr 2018 22:47:29 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id 02F101C0378 for <lammich@in.tum.de>; Fri, 20 Apr 2018 22:47:29 +0200
+ (CEST)
+Received: from vmmaildmz2.informatik.tu-muenchen.de
+ (vmmaildmz2.informatik.tu-muenchen.de [131.159.0.88]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id EC6E01C0376
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 22:47:28 +0200 (CEST)
+Received: by vmmaildmz2.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id EA43C1C24B7; Fri, 20 Apr 2018 22:47:28 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz2.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-0.2 required=7.0
+ tests=BAYES_00,HTML_IMAGE_ONLY_08,
+ HTML_IMAGE_RATIO_08,HTML_MESSAGE,RCVD_IN_DNSWL_NONE,RCVD_IN_MSPIKE_H2,
+ T_REMOTE_IMAGE autolearn=no autolearn_force=no version=3.4.0-tuminfo_1
+Received: from vmmaildmz2.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz2.informatik.tu-muenchen.de (Postfix) with ESMTP id C89B81C24B4
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 22:47:26 +0200 (CEST)
+Received: from mail-wr0-f172.google.com (mail-wr0-f172.google.com
+ [209.85.128.172]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256
+ (128/128 bits)) (No client certificate requested) by
+ vmmaildmz2.informatik.tu-muenchen.de (Postfix) with ESMTPS id B509A1C24AD
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 22:47:26 +0200 (CEST)
+Received: by mail-wr0-f172.google.com with SMTP id f14-v6so26100993wre.4
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 13:47:26 -0700 (PDT)
+X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net;
+ s=20161025;
+ h=x-gm-message-state:date:from:to:message-id:subject:mime-version;
+ bh=uJw0VNCfCBWu8RlBkgMResd4VedqNZ4Kxj4p2rKQYHw=;
+ b=F7VOXmRzGB7kiy6lD56pF3WCL833JHZKnOBEXmBLZVz4NqWgJfeU4VvSE1BqxNRdM3
+ R6vCDN+ElL9BCl+5OpneZOh4eRcIimx+8/D8xW9oKSOubfVgbDAQ72isJnD19DlsQ6T2
+ cdt/23x6j4TiYyeStDJAs2UtlDOAT1FX6qs7+BC+XCux0CWq+hKI7Sq9Tgg7uEYWGeFv
+ UMeEm9ERkNjgnA+gJAE0MnMFBfXqwYJ2Y12LhuaYbBhtUM7cLxJRVsYyrReGm/f2cHhL
+ GaEez/+4W73j2asaPxqfKEIrfjaDKPUE5wBpdU10HQmQaDyn6bF5MIjC+fYnDw72m7LX eFSg==
+X-Gm-Message-State:
+ ALQs6tAgWH0gjXQtK1sR/S+FtVwgFPAtiN4L1ZVQNavQ3M9SEeP5iqKi
+ JbePy2TmxT2fweBxPAoj1PUq8KDD
+X-Google-Smtp-Source:
+ AIpwx49/udh/58yunEXJtmd0X4hf+36QrOOqjYyvnVEMGPCG7QL2f9Ls+hTxzRswZxui9cZAnpp/3A==
+X-Received: by 10.80.138.138 with SMTP id
+ j10mr15553804edj.36.1524257246074; Fri, 20 Apr 2018 13:47:26 -0700 (PDT)
+Received: from DisMyLaptop ([195.242.213.115]) by smtp.gmail.com with
+ ESMTPSA id f13sm3978826edl.67.2018.04.20.13.47.24 for <lammich@in.tum.de>
+ (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128);     Fri,
+ 20 Apr 2018 13:47:24 -0700 (PDT)
+Date: Fri, 20 Apr 2018 22:47:23 +0200
+From: "J. Juhas" <jonatan.juhas@tum.de>
+To: "=?utf-8?Q?lammich=40in.tum.de?=" <lammich@in.tum.de>
+Message-ID: <1524256873.local-ecd65737-76e1-v1.2.1-7e7447b6@getmailspring.com>
+Subject: [FDS-Homework]
+X-Mailer: Mailspring
+MIME-Version: 1.0
+Content-Type: multipart/mixed; boundary="5ada51db_7d63dc4_8fe"
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+--5ada51db_7d63dc4_8fe
+Content-Type: multipart/alternative; boundary="5ada51db_5e22cec9_8fe"
+
+
+--5ada51db_5e22cec9_8fe
+Content-Type: text/plain; charset="utf-8"
+Content-Disposition: inline
+Content-Transfer-Encoding: 8bit
+
+Dear Peter,
+
+I was unable to attend classes today nor the last week. I presume the submission via E-Mail deadline was the same as the one for the submission system.
+Since I don't know if you discussed the solutions during today's lecture I wanted to try and submit my solution anyways - if for nothing else than for the sake of feedback.
+
+Thanks and have a nice weekend,
+Jonatan Juhas
+
+--5ada51db_5e22cec9_8fe
+Content-Type: text/html; charset="utf-8"
+Content-Disposition: inline
+Content-Transfer-Encoding: 8bit
+
+<div>Dear Peter,</div><br><div>I was unable to attend classes today nor the last week. I presume the submission via E-Mail deadline was the same as the one for the submission system.</div><div>Since I don't know if you discussed the solutions during today's lecture I wanted to try and submit my solution anyways - if for nothing else than for the sake of feedback.</div><br><div>Thanks and have a nice weekend,</div><div>Jonatan Juhas</div><div><signature id="local-2d702942-d407"></signature></div><img class="mailspring-open" alt="Open Tracking" width="0" height="0" style="border:0; width:0; height:0;" src="https://link.getmailspring.com/open/1524256873.local-ecd65737-76e1-v1.2.1-7e7447b6@getmailspring.com?recipient=bGFtbWljaEBpbi50dW0uZGU%3D">
+--5ada51db_5e22cec9_8fe--
+
+--5ada51db_7d63dc4_8fe
+Content-Type: application/octet-stream
+Content-Transfer-Encoding: base64
+Content-Disposition: attachment; filename="ha01.thy"
+
+dGhlb3J5IGhhMDEKICBpbXBvcnRzIE1haW4KYmVnaW4KCigqIEltcGxlbWVudGF0aW9uICopCmZ1
+biBsaXN0c3VtIDo6ICJpbnQgbGlzdCBcPFJpZ2h0YXJyb3c+IGludCIgd2hlcmUKICAibGlzdHN1
+bSBbXSA9IDAiIHwKICAibGlzdHN1bSAoeCN4cykgPSB4ICsgbGlzdHN1bSB4cyIKCigqIEJydXRl
+IHRlc3RpbmcgKikKKCogSSdtIG5vdCBzdXJlIHlldCB3aGF0J3MgdGhlIGRpZmZlcmVuY2UgYmV0
+d2VlbiB2YWx1ZSBidXQgSSB0aGluayBsZW1tYSBpcyBiZXR0ZXIgaGVyZSAqKQpsZW1tYSAibGlz
+dHN1bSBbMSwyLDNdID0gNiIgYnkgYXV0bwpsZW1tYSAibGlzdHN1bSBbXSA9IDAiIGJ5IGF1dG8K
+bGVtbWEgImxpc3RzdW0gWzEsLTIsM10gPSAyIiBieSBhdXRvCgooKiBGaXJzdCBjb25kaXRpb246
+IEZpbHRlcmluZyB6ZXJvZXMgZG9lc24ndCBjaGFuZ2UgcmVzdWx0ICopCmxlbW1hIGxpc3RzdW1f
+ZmlsdGVyX3plcm86ICJsaXN0c3VtIChmaWx0ZXIgKFw8bGFtYmRhPnguIHggXDxub3RlcT4gMCkg
+bCkgPSBsaXN0c3VtIGwiCiAgYXBwbHkgKGluZHVjdGlvbiBsKQogIGFwcGx5IGF1dG8KICBkb25l
+CgooKiBTZWNvbmQgY29uZGl0aW9uOiBSZXZlcnNpbmcgbGlzdCBkb2Vzbid0IGNoYW5nZSByZXN1
+bHQgKikKbGVtbWEgYXV4OiAibGlzdHN1bSAoeHNAeXMpID0gbGlzdHN1bSB4cyArICBsaXN0c3Vt
+IHlzIiAKICBhcHBseSAoaW5kdWN0aW9uIHhzKSBieSBhdXRvCgpsZW1tYSBsaXN0c3VtX3JldmVy
+c2U6ICJsaXN0c3VtIChyZXYgbCkgPSBsaXN0c3VtIGwiCiAgYXBwbHkgKGluZHVjdGlvbiBsKQog
+IGFwcGx5IChhdXRvIHNpbXA6IGF1eCkKICBkb25lCgooKiBUaGlyZCBjb25kaXRpb246IEZpbHRl
+cmluZyBvdXQgbmVnYXRpdmUgbnVtYmVycyByZXN1bHRzIGluIGEgcmVzdWx0IGVxdWFsIG9yIGdy
+ZWF0ZXIgdGhhbiBvcmlnaW5hbCAqKQpsZW1tYSBsaXN0c3VtX2ZpbHRlcl9uZWdhdGl2ZTogImxp
+c3RzdW0gbCBcPGdlPiBsaXN0c3VtIChmaWx0ZXIgKFw8bGFtYmRhPnguIHggPCAwKSBsKSIKICBh
+cHBseSAoaW5kdWN0aW9uIGwpCiAgYXBwbHkgKGF1dG8gc2ltcDogYXV4KQogIGRvbmUKKCogTm90
+ZTogVG9vayBhIHdoaWxlIHVudGlsIEkgZmlndXJlZCBpdCBjYW4gYWN0dWFsbHkgYmUgZ3JlYXRl
+ciAqKQoKZnVuIGZsYXR0ZW4gOjogIidhIGxpc3QgbGlzdCBcPFJpZ2h0YXJyb3c+ICdhIGxpc3Qi
+IHdoZXJlCiAgImZsYXR0ZW4gW10gPSBbXSIgfAogICJmbGF0dGVuIChsI2xzKSA9IGwgQCBmbGF0
+dGVuIGxzIgoKKCogQnJ1dGUgdGVzdGluZyAqKQpsZW1tYSAiZmxhdHRlbiBbWzEsMiwzXSwgWzJd
+XSA9IFsxLDIsMywyOjppbnRdIiBieSBhdXRvCmxlbW1hICJmbGF0dGVuIFtbMSwyLDNdLFtdLFsy
+XV0gPSBbMSwyLDMsMjo6aW50XSIgYnkgYXV0bwoKKCogRmlyc3QgY29uZGl0aW9uOiBTdW0gb2Yg
+dGhlIGZsYXR0ZW5lZCBsaXN0IGlzIGVxdWFsIHRvIHRoZSBzdW0gb2YgYWxsIGl0J3MgZWxlbWVu
+dHMgKikKbGVtbWEgImxpc3RzdW0gKGZsYXR0ZW4geHMpID0gbGlzdHN1bSAobWFwIGxpc3RzdW0g
+eHMpIgogIGFwcGx5IChpbmR1Y3Rpb24geHMpCiAgYXBwbHkgKGF1dG8gc2ltcDogYXV4KQogIGRv
+bmUKCmVuZA==
+
+--5ada51db_7d63dc4_8fe--
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/katharinaluise.schmitt@tum.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,188 @@
+From katharinaluise.schmitt@tum.de Fri Apr 20 17:11:49 2018
+Return-Path: <katharinaluise.schmitt@tum.de>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ 6RlwF+kC2lqxTQAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Fri, 20 Apr 2018 17:11:49 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id C37C61C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Fri, 20 Apr 2018
+ 17:11:49 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id C200A1E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Fri, 20 Apr 2018 17:11:49
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ BECAE1C038A; Fri, 20 Apr 2018 17:11:49 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id BB5501C037C; Fri, 20 Apr 2018 17:11:49 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id 957661C0378 for <lammich@in.tum.de>; Fri, 20 Apr 2018 17:11:49 +0200
+ (CEST)
+Received: from vmmaildmz1.informatik.tu-muenchen.de
+ (vmmaildmz1.informatik.tu-muenchen.de [131.159.0.87]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id 8B14E1C0376
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 17:11:49 +0200 (CEST)
+Received: by vmmaildmz1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 89B661C2DA9; Fri, 20 Apr 2018 17:11:49 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz1.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-4.3 required=7.0 tests=BAYES_00,DKIM_SIGNED,
+ DKIM_VALID,DKIM_VALID_AU,HTML_MESSAGE,RCVD_IN_DNSWL_MED autolearn=no
+ autolearn_force=no version=3.4.0-tuminfo_1
+Received: from vmmaildmz1.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTP id D1A2C1C2DAA
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 17:11:47 +0200 (CEST)
+Received: from postout1.mail.lrz.de (postout1.mail.lrz.de
+ [129.187.255.137]) (using TLSv1.2 with cipher AECDH-AES256-SHA (256/256
+ bits)) (No client certificate requested) by
+ vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTPS id C6B201C2D9F
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 17:11:47 +0200 (CEST)
+Received: from lxmhs51.srv.lrz.de (localhost [127.0.0.1]) by
+ postout1.mail.lrz.de (Postfix) with ESMTP id 40SK835PL2z1042 for
+ <lammich@in.tum.de>; Fri, 20 Apr 2018 17:11:47 +0200 (CEST)
+Authentication-Results: postout.lrz.de (amavisd-new); dkim=pass (2048-bit
+ key) reason="pass (just generated, assumed good)" header.d=tum.de
+DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/simple; d=tum.de; h=
+ mime-version:content-type:content-type:content-language
+ :accept-language:message-id:date:date:subject:subject:from:from
+ :received:received:received:received; s=postout; t=1524237107;
+ bh=F0EtooP59VEjDWwWHVwnxax46XkTmLqvfx22XJx848I=; b=yo955fzUrrFB
+ tp4GABHSiSTfpV4pvQS+h+VtedE+HR2eH0aS9mBfZj3j9DqKCmQVhGIrM6KrpusY
+ 67Q7seC5oHtc5IJrLtN3CL6zM9fhy2dYioI4UCk1/YX9xNNGn1G/hy0fMWll9R1/
+ VSqgqmyAv1qY/DB8fIYXDGwmAsgLCWDOwa2i/HacaWqwCWapLqxQCC5Ob3q6vdRE
+ fPlBx5tsKRyljSLSa6F97pmEDvk/Pbg/QlHSCpVCDgMUXBOOaCb35XU4iO1naJQt
+ 0DWsL8d55Wmq1JjnCzg3HwVuf8/6TZOCXz70yMh1xPd+hpEIFGm5srujJ/nbT3O5
+ FSviH8ID1w==
+X-Virus-Scanned: by amavisd-new at lrz.de in lxmhs51.srv.lrz.de
+Received: from postout1.mail.lrz.de ([127.0.0.1]) by lxmhs51.srv.lrz.de
+ (lxmhs51.srv.lrz.de [127.0.0.1]) (amavisd-new, port 20024) with LMTP id
+ vunE5DgiYdQB for <lammich@in.tum.de>; Fri, 20 Apr 2018 17:11:47 +0200 (CEST)
+Received: from BADWLRZ-SWMBX08.ads.mwn.de (BADWLRZ-SWMBX08.ads.mwn.de
+ [IPv6:2001:4ca0:0:108::164]) (using TLSv1.2 with cipher
+ ECDHE-RSA-AES256-SHA384 (256/256 bits)) (Client CN "BADWLRZ-SWMBX08",
+ Issuer "BADWLRZ-SWMBX08" (not verified)) by postout1.mail.lrz.de (Postfix)
+ with ESMTPS id 40SK8318jtz103t for <lammich@in.tum.de>; Fri, 20 Apr 2018
+ 17:11:47 +0200 (CEST)
+Received: from BADWLRZ-SWMBX09.ads.mwn.de (2001:4ca0:0:108::165) by
+ BADWLRZ-SWMBX08.ads.mwn.de (2001:4ca0:0:108::164) with Microsoft SMTP
+ Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256)
+ id 15.1.1466.3; Fri, 20 Apr 2018 17:11:36 +0200
+Received: from BADWLRZ-SWMBX09.ads.mwn.de ([fe80::28c9:20b8:a4d6:473c]) by
+ BADWLRZ-SWMBX09.ads.mwn.de ([fe80::28c9:20b8:a4d6:473c%12]) with mapi id
+ 15.01.1466.003; Fri, 20 Apr 2018 17:11:36 +0200
+From: "Schmitt, Katharina" <katharinaluise.schmitt@tum.de>
+To: "lammich@in.tum.de" <lammich@in.tum.de>
+Subject: [FDS-Homework] Submission for Exercise Sheet 1
+Thread-Topic: [FDS-Homework] Submission for Exercise Sheet 1
+Thread-Index: AQHT2LkuXBQHIxdttUaVTtTsJyGXIQ==
+Date: Fri, 20 Apr 2018 15:11:35 +0000
+Message-ID: <e99ef75ca2b04729a131c0996a060342@tum.de>
+Accept-Language: de-DE, en-US
+Content-Language: de-DE
+X-MS-Exchange-Organization-AuthAs: Internal
+X-MS-Exchange-Organization-AuthMechanism: 04
+X-MS-Exchange-Organization-AuthSource: BADWLRZ-SWMBX09.ads.mwn.de
+X-MS-Has-Attach: yes
+X-MS-TNEF-Correlator: 
+x-originating-ip: [188.174.55.139]
+Content-Type: multipart/mixed; boundary="_004_e99ef75ca2b04729a131c0996a060342tumde_"
+MIME-Version: 1.0
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+--_004_e99ef75ca2b04729a131c0996a060342tumde_
+Content-Type: multipart/alternative; boundary="_000_e99ef75ca2b04729a131c0996a060342tumde_"
+
+
+--_000_e99ef75ca2b04729a131c0996a060342tumde_
+Content-Type: text/plain; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+Dear Dr. Lammich,
+
+
+attached please find my homework submission for the first exercise sheet.
+
+My administrative data is the following:
+
+
+Name: Katharina Schmitt
+
+Enrollment Number: 03630761
+
+TUM User ID: ga49ceq
+
+
+Best regards,
+
+Katharina Schmitt
+
+--_000_e99ef75ca2b04729a131c0996a060342tumde_
+Content-Type: text/html; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" dir="ltr" style="font-size:12pt; color:rgb(0,0,0); font-family:Calibri,Helvetica,sans-serif,&quot;EmojiFont&quot;,&quot;Apple Color Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI Symbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols">
+<p>Dear Dr. Lammich,</p>
+<p><br>
+</p>
+<p>attached please find my homework submission for the first exercise sheet. <br>
+</p>
+<p>My administrative data is the following:</p>
+<p><br>
+</p>
+<p>Name: Katharina Schmitt</p>
+<p>Enrollment Number: 03630761</p>
+<p>TUM User ID: ga49ceq<br>
+</p>
+<p><br>
+</p>
+<p>Best regards,</p>
+<p>Katharina Schmitt<br>
+</p>
+</div>
+</body>
+</html>
+
+--_000_e99ef75ca2b04729a131c0996a060342tumde_--
+
+--_004_e99ef75ca2b04729a131c0996a060342tumde_
+Content-Type: application/octet-stream; name="ex01.thy"
+Content-Description: ex01.thy
+Content-Disposition: attachment; filename="ex01.thy"; size=1068; creation-date="Fri, 20 Apr 2018 15:06:46 GMT"; modification-date="Fri, 20 Apr 2018 15:06:46 GMT"
+Content-Transfer-Encoding: base64
+
+dGhlb3J5IGV4MDEKaW1wb3J0cyBNYWluCmJlZ2luCgpmdW4gbGlzdHN1bSA6OiAiaW50IGxpc3Qg
+XDxSaWdodGFycm93PiBpbnQiIHdoZXJlCiJsaXN0c3VtIFtdID0gMCIgfAoibGlzdHN1bSAoeCN4
+cykgPSAobGlzdHN1bSB4cykgKyB4IgoKdmFsdWUgImxpc3RzdW0gWzEsMiwzXSIKdmFsdWUgImxp
+c3RzdW0gW10iCnZhbHVlICJsaXN0c3VtIFsxLC0yLCAzXSIKCmxlbW1hIGxpc3RzdW1fZmlsdGVy
+X3ogOiAibGlzdHN1bSAoZmlsdGVyIChcPGxhbWJkYT54IC4geCBcPG5vdGVxPiAwICkgbCApID0g
+bGlzdHN1bSBsIgogIGFwcGx5KGluZHVjdGlvbiBsKQogIGFwcGx5KGF1dG8pCiAgZG9uZQoKbGVt
+bWEgbGlzdHN1bV9hcHAgOiAibGlzdHN1bSAoeHMgQCB5cykgPSAobGlzdHN1bSB4cykgKyAobGlz
+dHN1bSB5cykiCiAgYXBwbHkoaW5kdWN0aW9uIHhzKQogIGFwcGx5KGF1dG8pCiAgZG9uZQoKbGVt
+bWEgbGlzdHN1bV9yZXYgOiAibGlzdHN1bSAocmV2IHhzKSA9IGxpc3RzdW0geHMiCiAgYXBwbHko
+aW5kdWN0aW9uIHhzKQogIGFwcGx5KGF1dG8gc2ltcCBhZGQ6IGxpc3RzdW1fYXBwKQogIGRvbmUK
+CmxlbW1hIGxpc3RfZmlsdGVyIDogImxpc3RzdW0gKGZpbHRlciAoXDxsYW1iZGE+eCAuIHggXDxn
+ZT4gMCApIHhzICkgXDxnZT4gbGlzdHN1bSB4cyIKICBhcHBseShpbmR1Y3Rpb24geHMpCiAgYXBw
+bHkoYXV0bykKICBkb25lCgpmdW4gZmxhdHRlbiA6OiAiJ2EgbGlzdCBsaXN0IFw8UmlnaHRhcnJv
+dz4gJ2EgbGlzdCIgd2hlcmUKImZsYXR0ZW4gW10gPSBbXSIgfAoiZmxhdHRlbiAobCAjbHMpID0g
+bCBAIGZsYXR0ZW4gbHMiCgp2YWx1ZSAiZmxhdHRlbiBbWzEgLDIgLDMgXSxbMiBdXSA9IFsxICwy
+ICwzICwyIDo6aW50XSIKdmFsdWUgImZsYXR0ZW4gW1sxICwyICwzIF0sW10sWzIgXV0gPSBbMSAs
+MiAsMyAsMiA6OmludF0iCgpsZW1tYSBmbGF0dGVuX3N1bSA6ICJsaXN0c3VtIChmbGF0dGVuIHhz
+KSA9IGxpc3RzdW0gKG1hcCBsaXN0c3VtIHhzKSIKICBhcHBseShpbmR1Y3Rpb24geHMpCiAgYXBw
+bHkoYXV0byBzaW1wIGFkZDogbGlzdHN1bV9hcHApCiAgZG9uZQoKZW5k
+
+--_004_e99ef75ca2b04729a131c0996a060342tumde_--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/m.kirchmeier@tum.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,101 @@
+From m.kirchmeier@tum.de Thu Apr 19 22:44:33 2018
+Return-Path: <m.kirchmeier@tum.de>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ kx0qC3T/2Fo2QAAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Thu, 19 Apr 2018 22:44:33 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id 4ED821C202A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Thu, 19 Apr 2018
+ 22:44:33 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id 4D55B1E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Thu, 19 Apr 2018 22:44:33
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ 4A6C11C0378; Thu, 19 Apr 2018 22:44:33 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 426E71C0376; Thu, 19 Apr 2018 22:44:33 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id 07CE41C0378 for <lammich@in.tum.de>; Thu, 19 Apr 2018 22:44:28 +0200
+ (CEST)
+Received: from vmrbg98.informatik.tu-muenchen.de
+ (vmrbg98.informatik.tu-muenchen.de [131.159.0.123]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id F1B801C0376
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 22:44:27 +0200 (CEST)
+Received: from webmail.in.tum.de (localhost [IPv6:::1]) by
+ vmrbg98.informatik.tu-muenchen.de (Postfix) with ESMTP id EB36B404C6 for
+ <lammich@in.tum.de>; Thu, 19 Apr 2018 22:44:27 +0200 (CEST)
+MIME-Version: 1.0
+Content-Type: multipart/mixed; boundary="=_90323e05579a11977fede066d4576338"
+Date: Thu, 19 Apr 2018 22:44:27 +0200
+From: Maximilian Kirchmeier <m.kirchmeier@tum.de>
+To: Peter Lammich <lammich@in.tum.de>
+Subject: FDS Hausaufgabe
+Message-ID: <85e2ddb6d14da4c4f6612bfd78a289fe@tum.de>
+X-Sender: m.kirchmeier@tum.de
+User-Agent: Roundcube Webmail/1.3.3
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+--=_90323e05579a11977fede066d4576338
+Content-Type: text/plain; charset=UTF-8; format=flowed
+Content-Transfer-Encoding: 8bit
+
+Hallo Peter,
+
+ich höre dieses Semester FDS (will ja nicht dass meine Isabelle Skills 
+gleich wieder einschlafen ;D).
+
+Irgendwie ist aber die offizielle Hausaufgaben-Hochlademaske für FDS 
+anscheinend noch nicht aktiviert, dort gibt's nur Info 2 und Semantics 
+zur Auswahl.
+Deshalb schicke ich Dir die erste Hausaufgabe mal auf diesem Weg.
+
+Viele Grüße
+Max
+--=_90323e05579a11977fede066d4576338
+Content-Type: text/plain; name=hw01.thy
+Content-Disposition: attachment; filename=hw01.thy; size=763
+Content-Transfer-Encoding: 8bit
+
+theory hw01
+imports Main
+begin
+
+fun listsum :: "int list \<Rightarrow> int" where
+"listsum [] = 0" |
+"listsum (x # xs) = x + listsum xs"
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x. x \<noteq> 0) l) = listsum l"
+proof (induction l)
+qed (simp+)
+
+lemma listsum_add[simp]: "listsum (a @ b) = listsum a + listsum b"
+proof (induction a)
+qed (simp+)
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+proof (induction xs)
+qed (simp+)
+
+lemma listsum_filterneg: "listsum (filter (\<lambda>x. x > 0) l) \<ge> listsum l"
+proof (induction l)
+qed (auto+)
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+"flatten [] = []" |
+"flatten (l # ls) = l @ flatten ls"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+proof (induction xs)
+qed (simp+)
+
+end
+--=_90323e05579a11977fede066d4576338--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/markuswebel@gmail.com	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,134 @@
+From markuswebel@gmail.com Wed Apr 18 22:10:25 2018
+Return-Path: <markuswebel@gmail.com>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ MTlfMgel11qnAgAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Wed, 18 Apr 2018 22:10:25 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id DF1771C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Wed, 18 Apr 2018
+ 22:10:25 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id DDB5F1E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Wed, 18 Apr 2018 22:10:25
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ DACF21C0393; Wed, 18 Apr 2018 22:10:25 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id D6EDB1C038F; Wed, 18 Apr 2018 22:10:25 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id AC26C1C038A for <lammich@in.tum.de>; Wed, 18 Apr 2018 22:10:25 +0200
+ (CEST)
+Received: from vmmaildmz1.informatik.tu-muenchen.de
+ (vmmaildmz1.informatik.tu-muenchen.de [131.159.0.87]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id 97BDB1C0376
+ for <lammich@in.tum.de>; Wed, 18 Apr 2018 22:10:25 +0200 (CEST)
+Received: by vmmaildmz1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 93E711C2DAA; Wed, 18 Apr 2018 22:10:25 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz1.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-2.3 required=7.0 tests=AWL,BAYES_00,DKIM_SIGNED,
+ DKIM_VALID,DKIM_VALID_AU,FREEMAIL_FROM,HTML_MESSAGE,RCVD_IN_DNSWL_NONE,
+ RCVD_IN_MSPIKE_H2 autolearn=no autolearn_force=no version=3.4.0-tuminfo_1
+Received: from vmmaildmz1.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTP id E42C61C2DA9
+ for <lammich@in.tum.de>; Wed, 18 Apr 2018 22:10:23 +0200 (CEST)
+Received: from mail-io0-f181.google.com (mail-io0-f181.google.com
+ [209.85.223.181]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256
+ (128/128 bits)) (No client certificate requested) by
+ vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTPS id 957911C2DA5
+ for <lammich@in.tum.de>; Wed, 18 Apr 2018 22:10:23 +0200 (CEST)
+Received: by mail-io0-f181.google.com with SMTP id d6-v6so3959982iog.1 for
+ <lammich@in.tum.de>; Wed, 18 Apr 2018 13:10:23 -0700 (PDT)
+DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com;
+ s=20161025; h=mime-version:from:date:message-id:subject:to;
+ bh=uJbjzlK+e/v+4q8AyieWeCD3DqvNMeH/pcJr4Evobik=;
+ b=FGgwj1qb6/9tJIzGT18lt+M0BkyBK1XtH+/2JhJ9gG7+OBfStDBuw4aVodtWe86lfy
+ oHphrRXuweh33G61dIiF3ZxSv0o34OZgLLsRJzc83qY/wuSIqrXZs6q9htlTyoqRSwlf
+ dc5QAYHb/N3K+56qpgXij/x6M/nZQDNhtJlhEuKZMjE/3hIUiNFwDJkUF0d25Xk3XZ36
+ UUKDpRspxYNdPqsJ8U7I+rioNVSKE6mTVwxrkyJtaNmUL6Ec+f8eTA3/I1ZKoDIZDSSi
+ DhR9qQzJdXfpKnuwQF7S+SGBi2ulUfZXFLvrUea/ccrfkpnY/sn+edzV+EBRUBCK8mub Z4kw==
+X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net;
+ s=20161025;
+ h=x-gm-message-state:mime-version:from:date:message-id:subject:to;
+ bh=uJbjzlK+e/v+4q8AyieWeCD3DqvNMeH/pcJr4Evobik=;
+ b=na70PD3T5HQC2CTiyltVUShcCfCFSK2uwSj9EIJvklSc1tMFw2HZ8k4DQ5ojEB3qK7
+ /avwDV3i6zLl5ddJxXbvKgJsHFZqGUcuGJ8jUW7yPvN8bHfiooLKdTLHPg8R+x4ZukWr
+ /mqyt2m+Naxsd53NUk3oDJ7puTB1JVqOBdqsKIhTvTf0xK+O2XERnqTuWsQApyesnN9/
+ yiwLKMlZv+heKOFxhmThGAxAd9/2nbnrWZD9wNAc8Ec8lmDHyUHJUMKfyFkphS0lduN6
+ mzZzskKXBtgcZoqz2f70R9t/EAKGC/LbwUQBxEEmy/2Gh2DixkhauZc6ct9UA9G1EV+j Y51Q==
+X-Gm-Message-State:
+ ALQs6tCIVqYpRlUdQUL/8wNACyJcARYxzYl7qzeKlmEGbJ1tYjs3R0Mw
+ +fQBFRFxqI/0r6KXh7Z0TbdQ0Zx9yzNwMbOz50w=
+X-Google-Smtp-Source:
+ AB8JxZq2fpuNSxQQUpXwh3HUKSnfapc4m03HnAuPTOmYe5A+Lc6s3iDO0xa7fGbk2OvL8miMFNjdhfF1guhettewhFU=
+X-Received: by 2002:a6b:b889:: with SMTP id
+ i131-v6mr3517791iof.300.1524082221879; Wed, 18 Apr 2018 13:10:21 -0700 (PDT)
+MIME-Version: 1.0
+Received: by 10.107.50.203 with HTTP; Wed, 18 Apr 2018 13:10:21 -0700 (PDT)
+From: Markus Webel <markuswebel@gmail.com>
+Date: Wed, 18 Apr 2018 22:10:21 +0200
+Message-ID: <CAJC9A_Chi1OJ+L11JqxOFChzbNsa=32u8d+n3qk=-6p=TC8g2Q@mail.gmail.com>
+Subject: FDS Homework - Markus Webel - 03649123
+To: lammich@in.tum.de
+Content-Type: multipart/mixed; boundary="00000000000071d1b4056a250bf8"
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+--00000000000071d1b4056a250bf8
+Content-Type: multipart/alternative; boundary="00000000000071d1b0056a250bf6"
+
+
+--00000000000071d1b0056a250bf6
+Content-Type: text/plain; charset="UTF-8"
+Content-Transfer-Encoding: 8bit
+
+Hello Doctor Lammich,
+
+I forgot where to turn in my homework, so I just attached it to this email
+:)
+
+Greetings,
+
+Markus Webel
+
+--00000000000071d1b0056a250bf6
+Content-Type: text/html; charset="UTF-8"
+Content-Transfer-Encoding: 8bit
+
+<div dir="ltr">Hello Doctor Lammich,<div><br></div><div>I forgot where to turn in my homework, so I just attached it to this email :)</div><div><br></div><div>Greetings,</div><div><br></div><div>Markus Webel</div></div>
+
+--00000000000071d1b0056a250bf6--
+
+--00000000000071d1b4056a250bf8
+Content-Type: application/octet-stream; name="ex01.thy"
+Content-Disposition: attachment; filename="ex01.thy"
+Content-Transfer-Encoding: base64
+X-Attachment-Id: f_jg5j62jb0
+
+dGhlb3J5IGV4MDEKaW1wb3J0cyBNYWluCmJlZ2luCgpmdW4gbGlzdHN1bSA6OiAiaW50IGxpc3Qg
+XDxSaWdodGFycm93PiBpbnQiIHdoZXJlCiAgImxpc3RzdW0gW10gPSAwIiB8CiAgImxpc3RzdW0g
+KHgjeHMpID0geCArIGxpc3RzdW0geHMiCgp2YWx1ZSAibGlzdHN1bSBbMSwyLDNdID0gNiIKdmFs
+dWUgImxpc3RzdW0gW10gPSAwIgp2YWx1ZSAibGlzdHN1bSBbMSwtMiwzXSA9IDIiCgpsZW1tYSBs
+aXN0c3VtX2ZpbHRlcl96IDogImxpc3RzdW0gKGZpbHRlciAoXDxsYW1iZGE+eC4geCBcPG5vdGVx
+PiAwKSBsKSA9IGxpc3RzdW0gbCIKICBhcHBseSAoaW5kdWN0aW9uIGwpIGJ5IGF1dG8KCmxlbW1h
+IGxpc3RzdW1fYXBwIFtzaW1wXSA6ICJsaXN0c3VtICh4c0B5cykgPSBsaXN0c3VtIHhzICsgbGlz
+dHN1bSB5cyIKICBhcHBseSAoaW5kdWN0aW9uIHhzKSBieSBhdXRvCgpsZW1tYSBsaXN0c3VtX3Jl
+diA6ICJsaXN0c3VtIChyZXYgeHMpID0gbGlzdHN1bSB4cyIKICBhcHBseSAoaW5kdWN0aW9uIHhz
+KQogIGFwcGx5IGF1dG8KICBkb25lCgpsZW1tYSBsaXN0c3VtX2ZpbHRlcl9uZWcgOiAibGlzdHN1
+bSAoZmlsdGVyIChcPGxhbWJkYT54LiB4IFw8Z2U+IDApIGwpIFw8Z2U+IGxpc3RzdW0gbCIKICBh
+cHBseSAoaW5kdWN0aW9uIGwpIGJ5IGF1dG8KCmZ1biBmbGF0dGVuIDo6ICInYSBsaXN0IGxpc3Qg
+XDxSaWdodGFycm93PiAnYSBsaXN0IiB3aGVyZQogICJmbGF0dGVuIFtdID0gW10iIHwKICAiZmxh
+dHRlbiAobCNscykgPSBsIEAgZmxhdHRlbiBscyIKCnZhbHVlICJmbGF0dGVuIFtbMSwyLDNdLFsy
+XV0gPSBbMSwyLDMsMjo6aW50XSIKdmFsdWUgImZsYXR0ZW4gW1sxLDIsM10sW10sWzJdXSA9IFsx
+LDIsMywyOjppbnRdIgoKbGVtbWEgImxpc3RzdW0gKGZsYXR0ZW4geHMpID0gbGlzdHN1bSAobWFw
+IGxpc3RzdW0geHMpIgogIGFwcGx5IChpbmR1Y3Rpb24geHMpIGJ5IGF1dG8KCigqIEZvciBzb21l
+IHJlYXNvbiBJIGFscmVhZHkgcHJvdmVkIHRoaXMuIFRha2UgdGhhdCEgKikKCmVuZAo=
+--00000000000071d1b4056a250bf8--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/martin.rau@tum.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,148 @@
+From martin.rau@tum.de Fri Apr 20 12:16:42 2018
+Return-Path: <martin.rau@tum.de>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ uNcsJAq+2VrrRQAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Fri, 20 Apr 2018 12:16:42 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id 92F0B1C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Fri, 20 Apr 2018
+ 12:16:42 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id 919731E0126
+ for <lammich@mail.informatik.tu-muenchen.de>; Fri, 20 Apr 2018 12:16:42
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ 8ECD91C038B; Fri, 20 Apr 2018 12:16:42 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 8C3591C038A; Fri, 20 Apr 2018 12:16:42 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id 687E21C0378 for <lammich@in.tum.de>; Fri, 20 Apr 2018 12:16:42 +0200
+ (CEST)
+Received: from vmmaildmz2.informatik.tu-muenchen.de
+ (vmmaildmz2.informatik.tu-muenchen.de [131.159.0.88]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id 550EB1C0376
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 12:16:42 +0200 (CEST)
+Received: by vmmaildmz2.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 536F51C24B8; Fri, 20 Apr 2018 12:16:42 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz2.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-4.3 required=7.0 tests=AWL,BAYES_00,DKIM_SIGNED,
+ DKIM_VALID,DKIM_VALID_AU,RCVD_IN_DNSWL_MED autolearn=no autolearn_force=no
+ version=3.4.0-tuminfo_1
+Received: from vmmaildmz2.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz2.informatik.tu-muenchen.de (Postfix) with ESMTP id A95FD1C24B4
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 12:16:40 +0200 (CEST)
+Received: from postout1.mail.lrz.de (postout1.mail.lrz.de
+ [129.187.255.137]) (using TLSv1.2 with cipher AECDH-AES256-SHA (256/256
+ bits)) (No client certificate requested) by
+ vmmaildmz2.informatik.tu-muenchen.de (Postfix) with ESMTPS id 9F4731C24AD
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 12:16:40 +0200 (CEST)
+Received: from lxmhs51.srv.lrz.de (localhost [127.0.0.1]) by
+ postout1.mail.lrz.de (Postfix) with ESMTP id 40SBbX4FVmz100N for
+ <lammich@in.tum.de>; Fri, 20 Apr 2018 12:16:40 +0200 (CEST)
+Authentication-Results: postout.lrz.de (amavisd-new); dkim=pass (2048-bit
+ key) reason="pass (just generated, assumed good)" header.d=tum.de
+DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/simple; d=tum.de; h=
+ content-language:content-type:content-type:mime-version
+ :user-agent:date:date:message-id:subject:subject:from:from
+ :received:received; s=postout; t=1524219400; bh=z3oZ/uUgFq8l31wP
+ Rz/1ZqyZkZVpe+WiJFVvRBNTmdA=; b=ykrNntTooA3xYuyap5neT1iyHr0c0kYA
+ WL8pCxbxg7A8glFBHTyO1KlSVzwTNSMEDQ8tsS8AVayka1OU2dg7phbnmEfsTQT1
+ 9imHDVCwAgYUfMctTEoE3BG5MaCnrTO+oEfDJthVxJAql0z1gC46JBRSCAEP/YsL
+ Or16dbPr/IRjnJPn98lHGw1sk61AkOKYFR4/s3TAe39Cv2JPbHdxoGtZC0KY89HU
+ cJs2IRKfwGWaPcDW0lY90KgU03i1TMpc5HX7VGyaA5qIDnCKbjObwIChn/d+ijmt
+ 5oOWEYGASylz7FIZep2jLvHcH3odJ4vwIs/YhmturTp821cCixQTAw==
+X-Virus-Scanned: by amavisd-new at lrz.de in lxmhs51.srv.lrz.de
+Received: from postout1.mail.lrz.de ([127.0.0.1]) by lxmhs51.srv.lrz.de
+ (lxmhs51.srv.lrz.de [127.0.0.1]) (amavisd-new, port 20024) with LMTP id
+ YaJL5brzaIOL for <lammich@in.tum.de>; Fri, 20 Apr 2018 12:16:40 +0200 (CEST)
+Received: from [IPv6:2a02:810d:4240:1778:d5a1:cb55:53de:306f] (unknown
+ [IPv6:2a02:810d:4240:1778:d5a1:cb55:53de:306f]) (using TLSv1.2 with cipher
+ ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (No client certificate
+ requested) by postout1.mail.lrz.de (Postfix) with ESMTPSA id
+ 40SBbX0WRdz100L for <lammich@in.tum.de>; Fri, 20 Apr 2018 12:16:40 +0200
+ (CEST)
+To: lammich@in.tum.de
+From: Martin Rau <martin.rau@tum.de>
+Subject: [FDS-Homework] Martin Rau
+Message-ID: <4394f576-e47e-5e49-ddbf-d4eb819b38fa@tum.de>
+Date: Fri, 20 Apr 2018 12:16:38 +0200
+User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101
+ Thunderbird/52.7.0
+MIME-Version: 1.0
+Content-Type: multipart/mixed; boundary="------------E616297312A9093A0C12E8BD"
+Content-Language: en-US
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+This is a multi-part message in MIME format.
+--------------E616297312A9093A0C12E8BD
+Content-Type: text/plain; charset=utf-8; format=flowed
+Content-Transfer-Encoding: 8bit
+
+Submission for Homework 1.
+
+Kind regards,
+
+Martin Rau
+
+--------------E616297312A9093A0C12E8BD
+Content-Type: text/plain; charset=UTF-8; name="Home01.thy"
+Content-Disposition: attachment; filename="Home01.thy"
+Content-Transfer-Encoding: 8bit
+
+theory Home01
+imports Main
+begin 
+
+text {* Homework 1 *}
+
+fun listsum :: "int list \<Rightarrow> int" where
+  "listsum [] = 0"
+| "listsum (h#t) = h + listsum t"
+
+value "listsum [1,2,3] = 6"
+value "listsum [] = 0"
+value "listsum [1,-2,3] = 2"
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x. x\<noteq>0) l) = listsum l"
+apply (induction l)
+apply (auto)
+done
+
+lemma listsum_append[simp]: "listsum (xs @ ys) = listsum xs + listsum ys"
+apply (induction xs)
+apply (auto)
+done
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+apply (induction xs)
+apply (auto)
+done
+
+lemma listsum_filter_negative: "listsum (filter (\<lambda>x. x\<ge>0) l) \<ge> listsum l"
+apply (induction l)
+apply (auto)
+done
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+  "flatten [] = []"
+| "flatten (l#ls) = l @ flatten ls"
+
+value "flatten [[1,2,3],[2]] = [1,2,3,2::int]"
+value "flatten [[1,2,3],[],[2]]= [1,2,3,2::int]"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+apply (induction xs)
+apply (auto)
+done
+
+end
+--------------E616297312A9093A0C12E8BD--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/mitja.krebs@tum.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,90 @@
+From mitja.krebs@tum.de Thu Apr 19 21:33:46 2018
+Return-Path: <mitja.krebs@tum.de>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ roB7F/Xu2FrYbQAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Thu, 19 Apr 2018 21:33:46 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id 79FCB1C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Thu, 19 Apr 2018
+ 21:33:46 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id 783B21E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Thu, 19 Apr 2018 21:33:46
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ 7599D1C0378; Thu, 19 Apr 2018 21:33:46 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 72D8F1C038B; Thu, 19 Apr 2018 21:33:46 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id 4F1791C0378 for <lammich@in.tum.de>; Thu, 19 Apr 2018 21:33:46 +0200
+ (CEST)
+Received: from vmmaildmz2.informatik.tu-muenchen.de
+ (vmmaildmz2.informatik.tu-muenchen.de [131.159.0.88]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id 449241C0376
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 21:33:46 +0200 (CEST)
+Received: by vmmaildmz2.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 432261C24B8; Thu, 19 Apr 2018 21:33:46 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz2.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-4.2 required=7.0 tests=BAYES_00,RCVD_IN_DNSWL_MED
+ autolearn=no autolearn_force=no version=3.4.0-tuminfo_1
+Received: from vmmaildmz2.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz2.informatik.tu-muenchen.de (Postfix) with ESMTP id 6016F1C24B7
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 21:33:44 +0200 (CEST)
+Received: from rmail.zv.tum.de (mail.zv.tum.de [129.187.125.248]) by
+ vmmaildmz2.informatik.tu-muenchen.de (Postfix) with ESMTP id 556391C03AC
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 21:33:44 +0200 (CEST)
+Message-ID: <-1687527553.1524166399008.JavaMail.javamailuser@localhost>
+Date: Thu, 19 Apr 2018 21:33:19 +0200 (CEST)
+From: Mitja Daniel Krebs <mitja.krebs@tum.de>
+To: lammich@in.tum.de
+Subject: Functional data structures, homework 1
+Mime-Version: 1.0
+Content-Type: multipart/mixed;  boundary="----=_Part_0_409274085.1524166399002"
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+------=_Part_0_409274085.1524166399002
+Content-Type: text/plain; charset="utf-8"
+Content-Transfer-Encoding: 8bit
+
+Hallo Herr Dr. Lammich,
+
+da es im Abgabesystem auf https://vmnipkow3.in.tum.de/ noch keinen Eintrag für die Vorlesung Functional data structures gibt, lasse ich Ihnen meinen Lösungsvorschlag für die erste Hausaufgabe (siehe Anhang) per E-Mail zukommen. Ich hoffe, das passt so.
+
+Viele Grüße
+Mitja Krebs
+------=_Part_0_409274085.1524166399002
+Content-Type: application/octet-stream; name=hw01.thy
+Content-Transfer-Encoding: base64
+Content-Disposition: attachment; filename=hw01.thy
+
+dGhlb3J5IGh3MDEKaW1wb3J0cyBNYWluCmJlZ2luCgpmdW4gbGlzdHN1bSA6OiAiaW50IGxpc3Qg
+XDxSaWdodGFycm93PiBpbnQiIHdoZXJlCiAgImxpc3RzdW0gW10gPSAwIgp8ICJsaXN0c3VtICh4
+ICMgeHMpID0geCArIGxpc3RzdW0geHMiCgp2YWx1ZSAibGlzdHN1bSBbMSwgMiwgM10gPSA2Igp2
+YWx1ZSAibGlzdHN1bSBbXSA9IDAiCnZhbHVlICJsaXN0c3VtIFsxLCAtMiwgM10gPSAyIgoKbGVt
+bWEgbGlzdHN1bV9maWx0ZXJfejogImxpc3RzdW0gKGZpbHRlciAoXDxsYW1iZGE+eC4geCBcPG5v
+dGVxPiAwKSBsKSA9IGxpc3RzdW0gbCIKICBhcHBseSAoaW5kdWN0aW9uIGwpCiAgYXBwbHkgYXV0
+bwogIGRvbmUKCmxlbW1hIGxpc3RzdW1fcmV2X2F1eFtzaW1wXTogImxpc3RzdW0gKHhzIEAgeXMp
+ID0gbGlzdHN1bSB4cyArIGxpc3RzdW0geXMiCiAgYXBwbHkgKGluZHVjdGlvbiB4cykKICBhcHBs
+eSAoaW5kdWN0aW9uIHlzKQogIGFwcGx5IGF1dG8KICBkb25lCgpsZW1tYSBsaXN0c3VtX3Jldjog
+Imxpc3RzdW0gKHJldiB4cykgPSBsaXN0c3VtIHhzIgogIGFwcGx5IChpbmR1Y3Rpb24geHMpCiAg
+YXBwbHkgYXV0bwogIGRvbmUKCmxlbW1hICJsaXN0c3VtIChmaWx0ZXIgKFw8bGFtYmRhPnguIHgg
+XDxnZT4gMCkgbCkgXDxnZT4gbGlzdHN1bSBsIgogIGFwcGx5IChpbmR1Y3Rpb24gbCkKICBhcHBs
+eSBhdXRvCiAgZG9uZQoKZnVuIGZsYXR0ZW4gOjogIidhIGxpc3QgbGlzdCBcPFJpZ2h0YXJyb3c+
+ICdhIGxpc3QiIHdoZXJlCiAgImZsYXR0ZW4gW10gPSBbXSIKfCAiZmxhdHRlbiAobCAjIGxzKSA9
+IGwgQCBmbGF0dGVuIGxzIgoKdmFsdWUgImZsYXR0ZW4gW1sxLCAyLCAzXSwgWzJdXSA9IFsxLCAy
+LCAzLCAyOjppbnRdIgp2YWx1ZSAiZmxhdHRlbiBbWzEsIDIsIDNdLCBbXSwgWzJdXSA9IFsxLCAy
+LCAzLCAyOjppbnRdIgoKbGVtbWEgImxpc3RzdW0gKGZsYXR0ZW4geHMpID0gbGlzdHN1bSAobWFw
+IGxpc3RzdW0geHMpIgogIGFwcGx5IChpbmR1Y3Rpb24geHMpCiAgYXBwbHkgYXV0bwogIGRvbmUK
+CmVuZA==
+------=_Part_0_409274085.1524166399002--
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/odnoshivkin@me.com	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,142 @@
+From odnoshivkin@me.com Fri Apr 20 10:22:18 2018
+Return-Path: <odnoshivkin@me.com>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ min3Njej2Vp0KgAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Fri, 20 Apr 2018 10:22:18 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id 8868C1C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Fri, 20 Apr 2018
+ 10:22:18 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id 7901A1E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Fri, 20 Apr 2018 10:22:18
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ 76A891C0393; Fri, 20 Apr 2018 10:22:18 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 73F0F1C0394; Fri, 20 Apr 2018 10:22:18 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id 4F1C61C0376 for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:22:18 +0200
+ (CEST)
+Received: from vmmaildmz1.informatik.tu-muenchen.de
+ (vmmaildmz1.informatik.tu-muenchen.de [131.159.0.87]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id 452131C0393
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:22:18 +0200 (CEST)
+Received: by vmmaildmz1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 43CA51C2DAB; Fri, 20 Apr 2018 10:22:18 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz1.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-3.1 required=7.0 tests=AWL,BAYES_00,DKIM_SIGNED,
+ DKIM_VALID,DKIM_VALID_AU,RCVD_IN_DNSWL_LOW,T_DKIMWL_WL_MED autolearn=no
+ autolearn_force=no version=3.4.0-tuminfo_1
+Received: from vmmaildmz1.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTP id BF1201C2DA9
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:22:15 +0200 (CEST)
+Received: from mr26p50im-ztdg04121101.me.com (mr26p50im-ztdg04121101.me.com
+ [17.120.69.158]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256
+ (128/128 bits)) (No client certificate requested) by
+ vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTPS id 912C21C2D9F
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:22:15 +0200 (CEST)
+Received: from process-dkim-sign-daemon.mr26p50im-ztdg04121101.me.com by
+ mr26p50im-ztdg04121101.me.com (Oracle Communications Messaging Server
+ 8.0.1.2.20170607 64bit (built Jun  7 2017)) id
+ <0P7H007005TSZO00@mr26p50im-ztdg04121101.me.com> for lammich@in.tum.de;
+ Fri, 20 Apr 2018 08:21:35 +0000 (GMT)
+DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=me.com; s=04042017;
+ t=1524212495; bh=wg9UDOsO0kj67jkmQkBA75mEBLbKUNkmqQMdRF4urXw=;
+ h=From:Content-type:MIME-version:Subject:Message-id:Date:To;
+ b=Qu5UQBK+x4JOEqsRAX9pWu7C2x67wXqMIQbOXwgFPVbEW/n9Gfr4YYwcPV5AXwaEj
+ xKQqvIneYmGGXKmohcyJqGSyyEzeUw3BAWll4AydIHJR/Tz0lsfg3EVtLhnmzC+WCb
+ DWCpsYb/qsKkGmcL0rmAsydmrh0nSDrxRJUUpC8gnOaIPYCa8oMXD2ei/pSVtMDVhF
+ LJCDXR3LasJh/gS4pOWr9OXMXt7P0zvxn0Lm+c86S8ogRCrLwbuWnHo4GNcZUGwwlf
+ bw4ZuCce+hLzYu5G3h67wrbU8QslbQU6u9dGt2vg3AgXkwd9+8xFQyZjAjmGVedjl3
+ mqugV8wVYQOgQ==
+Received: from icloud.com ([127.0.0.1]) by mr26p50im-ztdg04121101.me.com
+ (Oracle Communications Messaging Server 8.0.1.2.20170607 64bit (built Jun 
+ 7 2017)) with ESMTPSA id <0P7H00B545VWPT40@mr26p50im-ztdg04121101.me.com>
+ for lammich@in.tum.de; Fri, 20 Apr 2018 08:21:35 +0000 (GMT)
+X-Proofpoint-Virus-Version: vendor=fsecure engine=2.50.10432:,,
+ definitions=2018-04-20_02:,, signatures=0
+X-Proofpoint-Spam-Details: rule=notspam policy=default score=0 spamscore=0
+ clxscore=1011 suspectscore=1 malwarescore=0 phishscore=0 adultscore=0
+ bulkscore=0 classifier=spam adjust=0 reason=mlx scancount=1
+ engine=8.0.1-1707230000 definitions=main-1804200085
+From: Mykola Odnoshyvkin <odnoshivkin@me.com>
+Content-type: multipart/mixed; boundary="Apple-Mail=_700B3C9B-E730-46AD-B3A8-FBA5C506C25A"
+MIME-version: 1.0 (Mac OS X Mail 10.3 \(3273\))
+Subject: [FDS-Homework] Mykola Odnoshyvkin (03662600)
+Message-id: <798DBA6B-8A98-4384-9B3B-0DEC2CE7151D@me.com>
+Date: Fri, 20 Apr 2018 10:21:31 +0200
+To: lammich@in.tum.de
+X-Mailer: Apple Mail (2.3273)
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+--Apple-Mail=_700B3C9B-E730-46AD-B3A8-FBA5C506C25A
+Content-Type: text/plain; charset=us-ascii
+Content-Transfer-Encoding: 8bit
+
+Hi,
+Here is my homework 1.
+
+Best Regards,
+Mykola
+--Apple-Mail=_700B3C9B-E730-46AD-B3A8-FBA5C506C25A
+Content-Disposition: attachment; filename=hw1.thy
+Content-Type: application/octet-stream; x-unix-mode=0644; name="hw1.thy"
+Content-Transfer-Encoding: 7bit
+
+theory hw1
+  imports Main
+
+begin
+fun listsum :: "int list \<Rightarrow> int" where
+"listsum [] = 0"|
+"listsum (x#xs) = x + listsum xs"
+
+value "listsum [1,2,3] = 6"
+value "listsum [] = 0"
+value "listsum [1,-2,3] = 2"
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x. x \<noteq> 0) l) = listsum l"
+apply(induction l)
+apply(auto)
+  done
+
+lemma listsum_app[simp]: "listsum (xs@ys) = listsum(xs) + listsum(ys)"
+  apply(induction xs)
+   apply(auto)
+  done 
+  
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+apply(induction xs)
+apply(auto)
+done
+
+lemma listsum_filter_neg: "listsum (filter (\<lambda>x. x>0) l) \<ge> listsum l"
+  apply(induction l)
+   apply(auto)
+  done
+
+fun flatten :: " 'a list list \<Rightarrow> 'a list" where
+"flatten [] = []"
+| "flatten (l#ls) = l @ flatten ls"
+
+value "flatten [[1,2,3],[2]] = [1,2,3,2::int]"
+value "flatten [[1,2,3],[],[2]] = [1,2,3,2::int]"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply(induction xs)
+  apply (auto)
+  done
+
+end
+--Apple-Mail=_700B3C9B-E730-46AD-B3A8-FBA5C506C25A--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/omar.badramany@tum.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,166 @@
+From omar.badramany@tum.de Thu Apr 19 22:16:36 2018
+Return-Path: <omar.badramany@tum.de>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ iUB0OQL52FpcawAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Thu, 19 Apr 2018 22:16:36 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id D85961C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Thu, 19 Apr 2018
+ 22:16:36 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id D6FB71E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Thu, 19 Apr 2018 22:16:36
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ D40B61C0376; Thu, 19 Apr 2018 22:16:36 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id D157D1C038A; Thu, 19 Apr 2018 22:16:36 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id ACDB91C0378 for <lammich@in.tum.de>; Thu, 19 Apr 2018 22:16:36 +0200
+ (CEST)
+Received: from vmmaildmz1.informatik.tu-muenchen.de
+ (vmmaildmz1.informatik.tu-muenchen.de [131.159.0.87]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id A24A91C0376
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 22:16:36 +0200 (CEST)
+Received: by vmmaildmz1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id A04B31C2DAD; Thu, 19 Apr 2018 22:16:36 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz1.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-4.3 required=7.0 tests=AWL,BAYES_00,DKIM_SIGNED,
+ DKIM_VALID,DKIM_VALID_AU,HTML_MESSAGE,RCVD_IN_DNSWL_MED autolearn=no
+ autolearn_force=no version=3.4.0-tuminfo_1
+Received: from vmmaildmz1.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTP id 6F0571C2DA9
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 22:16:31 +0200 (CEST)
+Received: from postout2.mail.lrz.de (postout2.mail.lrz.de
+ [129.187.255.138]) (using TLSv1.2 with cipher AECDH-AES256-SHA (256/256
+ bits)) (No client certificate requested) by
+ vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTPS id 63F3B1C2D8A
+ for <lammich@in.tum.de>; Thu, 19 Apr 2018 22:16:31 +0200 (CEST)
+Received: from lxmhs52.srv.lrz.de (localhost [127.0.0.1]) by
+ postout2.mail.lrz.de (Postfix) with ESMTP id 40Rqy72S28z11VS for
+ <lammich@in.tum.de>; Thu, 19 Apr 2018 22:16:31 +0200 (CEST)
+Authentication-Results: postout.lrz.de (amavisd-new); dkim=pass (2048-bit
+ key) reason="pass (just generated, assumed good)" header.d=tum.de
+DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/simple; d=tum.de; h=
+ mime-version:content-type:content-type:content-language
+ :accept-language:message-id:date:date:subject:subject:from:from
+ :received:received:received:received; s=postout; t=1524168991;
+ bh=zcM90mISy8XsE+i9pj/WBzd2yBJGMqR97i+bVB8HB/o=; b=h4GGgxVW2LZl
+ eoVSZn0uKami9T9jBVzH1DoMbxo1WMV4KEXy1qh8AacEdiIqazNJFo+Ajn7kJ3+t
+ O9NouYzwgx5yWWHkzRpZokeN+WNJC3g2Lm02/ddGf1njpc5bANYcB1x6UmVVqjRV
+ k1QCwWww050bB+R72Ygt8XWCov6FESi22u73aMTF4SVdgWUJ8PQPWsrkQ0bc0e+W
+ F3qlNQJ9Eput0aF3Dy+2/5XsD2qgvFNVWQgx+x0G38J8mGg7BhxudbQq7eZHSgEE
+ 6HYUGBsQ3boy/wbWH9QP6+KOvzqoSVUStY1v+bEgckaCtrgKPFP9/WCtbSSrPW61
+ coQP/qLLQA==
+X-Virus-Scanned: by amavisd-new at lrz.de in lxmhs52.srv.lrz.de
+Received: from postout2.mail.lrz.de ([127.0.0.1]) by lxmhs52.srv.lrz.de
+ (lxmhs52.srv.lrz.de [127.0.0.1]) (amavisd-new, port 20024) with LMTP id
+ GRQCsaeWMLzT for <lammich@in.tum.de>; Thu, 19 Apr 2018 22:16:31 +0200 (CEST)
+Received: from BADWLRZ-SWMBX08.ads.mwn.de (BADWLRZ-SWMBX08.ads.mwn.de
+ [IPv6:2001:4ca0:0:108::164]) (using TLSv1.2 with cipher
+ ECDHE-RSA-AES256-SHA384 (256/256 bits)) (Client CN "BADWLRZ-SWMBX08",
+ Issuer "BADWLRZ-SWMBX08" (not verified)) by postout2.mail.lrz.de (Postfix)
+ with ESMTPS id 40Rqy70M1gz11VN for <lammich@in.tum.de>; Thu, 19 Apr 2018
+ 22:16:31 +0200 (CEST)
+Received: from BADWLRZ-SWMBX09.ads.mwn.de (2001:4ca0:0:108::165) by
+ BADWLRZ-SWMBX08.ads.mwn.de (2001:4ca0:0:108::164) with Microsoft SMTP
+ Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256)
+ id 15.1.1466.3; Thu, 19 Apr 2018 22:16:29 +0200
+Received: from BADWLRZ-SWMBX09.ads.mwn.de ([fe80::28c9:20b8:a4d6:473c]) by
+ BADWLRZ-SWMBX09.ads.mwn.de ([fe80::28c9:20b8:a4d6:473c%12]) with mapi id
+ 15.01.1466.003; Thu, 19 Apr 2018 22:16:29 +0200
+From: "Elbadramany, Omar Adel Farouk Moussa" <omar.badramany@tum.de>
+To: "lammich@in.tum.de" <lammich@in.tum.de>
+Subject: FDS: Hausaufgabe 1
+Thread-Topic: Hausaufgabe 1
+Thread-Index: AQHT2Bs747UG6cCQBkKcPjlEMkVZag==
+Date: Thu, 19 Apr 2018 20:16:29 +0000
+Message-ID: <b638bbae24e14aaca254f80f47988929@tum.de>
+Accept-Language: en-US
+Content-Language: en-US
+X-MS-Exchange-Organization-AuthAs: Internal
+X-MS-Exchange-Organization-AuthMechanism: 04
+X-MS-Exchange-Organization-AuthSource: BADWLRZ-SWMBX09.ads.mwn.de
+X-MS-Has-Attach: yes
+X-MS-TNEF-Correlator: 
+x-originating-ip: [77.47.96.248]
+Content-Type: multipart/mixed; boundary="_004_b638bbae24e14aaca254f80f47988929tumde_"
+MIME-Version: 1.0
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+--_004_b638bbae24e14aaca254f80f47988929tumde_
+Content-Type: multipart/alternative; boundary="_000_b638bbae24e14aaca254f80f47988929tumde_"
+
+
+--_000_b638bbae24e14aaca254f80f47988929tumde_
+Content-Type: text/plain; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+Sehr geehrter Herr Lammich,
+
+ich habe versucht die Hausaufgabe auf der gegebenen Webseite hochzuladen aber es gibt leider kein Link fr die Vorlesung Funktionale Datenstrukturen.
+Anbei finden Sie meine Lsung.
+
+Viele Gre,
+Omar
+
+--_000_b638bbae24e14aaca254f80f47988929tumde_
+Content-Type: text/html; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" style="font-size:12pt;color:#000000;font-family:Calibri,Helvetica,sans-serif;" dir="ltr">
+Sehr geehrter Herr Lammich,
+<div><br>
+</div>
+<div>ich habe versucht die Hausaufgabe auf der gegebenen Webseite hochzuladen aber es gibt leider kein Link fr die Vorlesung Funktionale Datenstrukturen.</div>
+<div>Anbei finden Sie meine Lsung.</div>
+<div><br>
+</div>
+<div>Viele Gre,</div>
+<div>Omar</div>
+</div>
+</body>
+</html>
+
+--_000_b638bbae24e14aaca254f80f47988929tumde_--
+
+--_004_b638bbae24e14aaca254f80f47988929tumde_
+Content-Type: application/octet-stream; name="hw01.thy"
+Content-Description: hw01.thy
+Content-Disposition: attachment; filename="hw01.thy"; size=901; creation-date="Thu, 19 Apr 2018 20:15:55 GMT"; modification-date="Thu, 19 Apr 2018 20:15:55 GMT"
+Content-Transfer-Encoding: base64
+
+dGhlb3J5IGh3MDEKaW1wb3J0cyBNYWluCmJlZ2luCgpmdW4gbGlzdHN1bSA6OiAiaW50IGxpc3Qg
+XDxSaWdodGFycm93PiBpbnQiIHdoZXJlCiAgImxpc3RzdW0gW10gPSAoMDo6aW50KSIKfCAibGlz
+dHN1bSAoeCN4cykgPSB4ICsgKGxpc3RzdW0geHMpIgoKdmFsdWUgImxpc3RzdW0gWzEsMiwzXSIK
+dmFsdWUgImxpc3RzdW0gW10iCnZhbHVlICJsaXN0c3VtIFsxLC0yLDNdIgoKbGVtbWEgbGlzdHN1
+bV9maWx0ZXJfeiA6ICJsaXN0c3VtIChmaWx0ZXIgKFw8bGFtYmRhPnguIHggXDxub3RlcT4gMCkg
+bCkgPSBsaXN0c3VtIGwiCiAgYXBwbHkgKGluZHVjdGlvbiBsKQogIGFwcGx5IGF1dG8KICBkb25l
+CgpsZW1tYSBhdXggOiAibGlzdHN1bSAoeHNAeXMpID0gbGlzdHN1bSB4cyArIGxpc3RzdW0geXMi
+CiAgYXBwbHkgKGluZHVjdGlvbiB4cykKICBhcHBseSBhdXRvCiAgZG9uZQogIApsZW1tYSBsaXN0
+c3VtX3JldiA6ICJsaXN0c3VtIChyZXYgeHMpID0gbGlzdHN1bSB4cyIKICBhcHBseSAoaW5kdWN0
+aW9uIHhzKQogIGFwcGx5IChhdXRvIHNpbXA6IGF1eCkKICBkb25lCgpsZW1tYSB0IDogImxpc3Rz
+dW0gKGZpbHRlciAoXDxsYW1iZGE+eC4geCA+IDApIHhzKSBcPGdlPiBsaXN0c3VtIHhzICIKICBh
+cHBseSAoaW5kdWN0aW9uIHhzKQogIGFwcGx5IGF1dG8KICBkb25lCgpmdW4gZmxhdHRlbiA6OiAi
+J2EgbGlzdCBsaXN0IFw8UmlnaHRhcnJvdz4gJ2EgbGlzdCAiIHdoZXJlIAogICJmbGF0dGVuIFtd
+ID0gW10iCnwgImZsYXR0ZW4gKHgjeHMpID0geEAoZmxhdHRlbiB4cykiCgpsZW1tYSAibGlzdHN1
+bSAoZmxhdHRlbiB4cykgPSBsaXN0c3VtIChtYXAgbGlzdHN1bSB4cykiCiAgYXBwbHkgKGluZHVj
+dGlvbiB4cykKICBhcHBseSAoYXV0byBzaW1wIDogYXV4KQogIGRvbmUKCmVuZA==
+
+--_004_b638bbae24e14aaca254f80f47988929tumde_--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/s.griebel@tum.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,153 @@
+From s.griebel@tum.de Fri Apr 20 10:03:28 2018
+Return-Path: <s.griebel@tum.de>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ TKAGMoye2VozXwAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Fri, 20 Apr 2018 10:03:28 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id D16831C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Fri, 20 Apr 2018
+ 10:03:28 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id CFD601E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Fri, 20 Apr 2018 10:03:28
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ CD43C1C038B; Fri, 20 Apr 2018 10:03:28 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id CADC71C038A; Fri, 20 Apr 2018 10:03:28 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id A70021C0378 for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:03:28 +0200
+ (CEST)
+Received: from vmmaildmz1.informatik.tu-muenchen.de
+ (vmmaildmz1.informatik.tu-muenchen.de [131.159.0.87]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id 9BF991C0376
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:03:28 +0200 (CEST)
+Received: by vmmaildmz1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 9AAEC1C2DAB; Fri, 20 Apr 2018 10:03:28 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz1.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-4.2 required=7.0 tests=AWL,BAYES_00,HTML_MESSAGE,
+ RCVD_IN_DNSWL_MED autolearn=no autolearn_force=no version=3.4.0-tuminfo_1
+Received: from vmmaildmz1.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTP id EFEA71C2DA9
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:03:25 +0200 (CEST)
+Received: from forwout2.mail.lrz.de (forwout2.mail.lrz.de
+ [129.187.255.131]) (using TLSv1.2 with cipher AECDH-AES256-SHA (256/256
+ bits)) (No client certificate requested) by
+ vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTPS id E502D1C2D9F
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:03:25 +0200 (CEST)
+Received: from postforw1.mail.lrz.de (lxmhs61.srv.lrz.de
+ [IPv6:2001:4ca0:0:116::a9c:63d]) by forwout2.mail.lrz.de (Postfix) with
+ ESMTP id 40S7dn622lzTb for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:03:25
+ +0200 (CEST)
+Received: from BADWLRZ-SWMBB05.ads.mwn.de (BADWLRZ-SWMBB05.ads.mwn.de
+ [10.156.54.156]) by postforw1.mail.lrz.de (Postfix) with ESMTP id
+ 40S7dn5tdFzydV for <ga57nid@exchwl.mytum.de>; Fri, 20 Apr 2018 10:03:25
+ +0200 (CEST)
+Received: from BADWLRZ-SWMBX01.ads.mwn.de (2001:4ca0:0:108::157) by
+ BADWLRZ-SWMBB05.ads.mwn.de (2001:4ca0:0:108::156) with Microsoft SMTP
+ Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256)
+ id 15.1.1466.3; Fri, 20 Apr 2018 10:03:24 +0200
+Received: from BADWLRZ-SWMBX01.ads.mwn.de ([fe80::7d02:f283:edbd:b19c]) by
+ BADWLRZ-SWMBX01.ads.mwn.de ([fe80::7d02:f283:edbd:b19c%12]) with mapi id
+ 15.01.1466.003; Fri, 20 Apr 2018 10:03:24 +0200
+From: "Griebel, Simon" <s.griebel@tum.de>
+To: "Lammich, Peter" <peter.lammich@tum.de>
+Subject: [FDS-Homework] Solution Ex. 1 Simon Griebel
+Thread-Topic: [FDS-Homework] Solution Ex. 1 Simon Griebel
+Thread-Index: AQHT2H4O0nMyF0BsFk2xEnrWTm0pNQ==
+Date: Fri, 20 Apr 2018 08:03:24 +0000
+Message-ID: <3ccc8a6942bf4f12ac9b8e400a6b66da@tum.de>
+Accept-Language: de-DE, en-US
+Content-Language: de-DE
+X-MS-Exchange-Organization-AuthAs: Internal
+X-MS-Has-Attach: yes
+X-MS-TNEF-Correlator: 
+x-originating-ip: [2001:4ca0:2fff:1::5f]
+Content-Type: multipart/mixed; boundary="_004_3ccc8a6942bf4f12ac9b8e400a6b66datumde_"
+MIME-Version: 1.0
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+--_004_3ccc8a6942bf4f12ac9b8e400a6b66datumde_
+Content-Type: multipart/alternative; boundary="_000_3ccc8a6942bf4f12ac9b8e400a6b66datumde_"
+
+
+--_000_3ccc8a6942bf4f12ac9b8e400a6b66datumde_
+Content-Type: text/plain; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+Hallo Peter,
+
+anbei befindet sich meine Lsung zur ersten Hausaufgabe.
+
+
+Gre,
+
+Simon Griebel
+
+
+
+--_000_3ccc8a6942bf4f12ac9b8e400a6b66datumde_
+Content-Type: text/html; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" style="font-size:12pt;color:#000000;font-family:Calibri,Helvetica,sans-serif;" dir="ltr">
+<p>Hallo Peter,</p>
+<p>anbei befindet sich meine Lsung zur ersten Hausaufgabe.</p>
+<p><br>
+</p>
+<p>Gre,</p>
+<p>Simon Griebel<br>
+</p>
+<p><br>
+</p>
+<p><br>
+</p>
+</div>
+</body>
+</html>
+
+--_000_3ccc8a6942bf4f12ac9b8e400a6b66datumde_--
+
+--_004_3ccc8a6942bf4f12ac9b8e400a6b66datumde_
+Content-Type: application/octet-stream; name="homework_1.thy"
+Content-Description: homework_1.thy
+Content-Disposition: attachment; filename="homework_1.thy"; size=1079; creation-date="Fri, 20 Apr 2018 07:57:14 GMT"; modification-date="Fri, 20 Apr 2018 07:57:14 GMT"
+Content-Transfer-Encoding: base64
+
+dGhlb3J5IGhvbWV3b3JrXzEKICBpbXBvcnRzIE1haW4KYmVnaW4KCmZ1biBsaXN0c3VtIDo6ICJp
+bnQgbGlzdCBcPFJpZ2h0YXJyb3c+IGludCIgd2hlcmUKICAibGlzdHN1bSBbXSA9IDAiCnwgImxp
+c3RzdW0gKHgjeHMpID0geCArIChsaXN0c3VtIHhzKSIKCgp2YWx1ZSAibGlzdHN1bSBbMSwgMiwg
+M10gPSA2Igp2YWx1ZSAibGlzdHN1bSBbXSA9IDAiCnZhbHVlICJsaXN0c3VtIFsxLCAtMiwgM10g
+PSAyIgoKCmxlbW1hIGxpc3RzdW1fZmlsdGVyX3o6ICJsaXN0c3VtIChmaWx0ZXIgKFw8bGFtYmRh
+PnguIHggXDxub3RlcT4gMCkgbCkgPSBsaXN0c3VtIGwiCiAgYXBwbHkoaW5kdWN0aW9uIGwpCiAg
+IGFwcGx5KGF1dG8pCiAgZG9uZQoKbGVtbWEgbGlzdHN1bV9hcHBlbmQgOiAibGlzdHN1bSAoeHNA
+eXMpID0gbGlzdHN1bSB4cyArIGxpc3RzdW0geXMiCiAgYXBwbHkoaW5kdWN0aW9uIHhzKQogICBh
+cHBseShhdXRvKQogIGRvbmUKCmxlbW1hIGxpc3RzdW1fcmV2OiAibGlzdHN1bSAocmV2IHhzKSA9
+IGxpc3RzdW0geHMiCiAgYXBwbHkoaW5kdWN0aW9uIHhzKQogICBhcHBseShhdXRvIHNpbXA6IGxp
+c3RzdW1fYXBwZW5kKQogIGRvbmUKICAKbGVtbWEgbGlzdHN1bV9maWx0ZXJfbmVnOiAibGlzdHN1
+bSAoZmlsdGVyIChcPGxhbWJkYT4geC4geCBcPGdlPiAwKSBsKSBcPGdlPiBsaXN0c3VtIGwiCiAg
+YXBwbHkoaW5kdWN0aW9uIGwpCiAgIGFwcGx5KGF1dG8pCiAgZG9uZQoKZnVuIGZsYXR0ZW46OiAi
+J2EgbGlzdCBsaXN0IFw8UmlnaHRhcnJvdz4gJ2EgbGlzdCIgd2hlcmUKICAiZmxhdHRlbiBbXSA9
+IFtdIgp8ICJmbGF0dGVuIChsI2xzKSA9IGwgQCBmbGF0dGVuIGxzIgoKdmFsdWUgImZsYXR0ZW4g
+W1sxICwyICwzIF0sWzIgXV0gPSBbMSAsMiAsMyAsMiA6OmludF0iCnZhbHVlICJmbGF0dGVuIFtb
+MSAsMiAsMyBdLFtdLFsyIF1dID0gWzEgLDIgLDMgLDIgOjppbnRdIgoKbGVtbWEgImxpc3RzdW0g
+KGZsYXR0ZW4geHMpID0gbGlzdHN1bSAobWFwIGxpc3RzdW0geHMpIgogIGFwcGx5KGluZHVjdGlv
+biB4cykKICAgYXBwbHkoYXV0byBzaW1wOiBsaXN0c3VtX2FwcGVuZCkKICBkb25lCgplbmQ=
+
+--_004_3ccc8a6942bf4f12ac9b8e400a6b66datumde_--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/sabine.rieder@tum.de	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,174 @@
+From sabine.rieder@tum.de Fri Apr 20 10:38:22 2018
+Return-Path: <sabine.rieder@tum.de>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ 21ttCfal2VrGUwAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Fri, 20 Apr 2018 10:38:22 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id 3F0881C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Fri, 20 Apr 2018
+ 10:38:22 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id 3D8F01E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Fri, 20 Apr 2018 10:38:22
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ 3AD621C038B; Fri, 20 Apr 2018 10:38:22 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 37B8F1C038A; Fri, 20 Apr 2018 10:38:22 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id 1387C1C0378 for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:38:22 +0200
+ (CEST)
+Received: from vmmaildmz2.informatik.tu-muenchen.de
+ (vmmaildmz2.informatik.tu-muenchen.de [131.159.0.88]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id 088AD1C0376
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:38:22 +0200 (CEST)
+Received: by vmmaildmz2.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 06C4C1C24B7; Fri, 20 Apr 2018 10:38:21 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz2.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-4.3 required=7.0 tests=BAYES_00,DKIM_SIGNED,
+ DKIM_VALID,DKIM_VALID_AU,HTML_MESSAGE,RCVD_IN_DNSWL_MED autolearn=no
+ autolearn_force=no version=3.4.0-tuminfo_1
+Received: from vmmaildmz2.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz2.informatik.tu-muenchen.de (Postfix) with ESMTP id 48ABF1C24B4
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:38:20 +0200 (CEST)
+Received: from postout2.mail.lrz.de (postout2.mail.lrz.de
+ [129.187.255.138]) (using TLSv1.2 with cipher AECDH-AES256-SHA (256/256
+ bits)) (No client certificate requested) by
+ vmmaildmz2.informatik.tu-muenchen.de (Postfix) with ESMTPS id 3DA461C24AD
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:38:20 +0200 (CEST)
+Received: from lxmhs52.srv.lrz.de (localhost [127.0.0.1]) by
+ postout2.mail.lrz.de (Postfix) with ESMTP id 40S8Q41Q7HzygM for
+ <lammich@in.tum.de>; Fri, 20 Apr 2018 10:38:20 +0200 (CEST)
+Authentication-Results: postout.lrz.de (amavisd-new); dkim=pass (2048-bit
+ key) reason="pass (just generated, assumed good)" header.d=tum.de
+DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/simple; d=tum.de; h=
+ mime-version:content-type:content-type:content-language
+ :accept-language:message-id:date:date:subject:subject:from:from
+ :received:received:received:received; s=postout; t=1524213499;
+ bh=8m/2ysAriPk6B7XKF9NSB8tOT7cK5Bdgjb3ZK8QU/CA=; b=IekhLxpDgkK+
+ uvV/Yf5VOQJDQErR2WV+JWxvSr9OiQ6OQhq8uU04ZpUckWQxMOsqc3zf/yVGjahA
+ wnnZpTFaru9fIzYA4HwzEF1p3HwzyGzpgPH8VMmsTXikpymXqNIskIBBi4qVv8FN
+ gwa+lsI43m+7tKmcGXlh6+aUc51ZbVJqDgKi8qO1qQC49V+eSZYA0d0eSi/1xrse
+ wIKbWqTCPUt7chZepxsmvsgqhXTfNE7DpQ7ldQweF2VsjpZ6bpRjvnAwjS9J3U82
+ MAZLEkKBqI4tgKEW/NV52j1MSqyZtCPPgRc5+RpHc6zePKayiZZE5Afxw1w/0oAq
+ icPmN2uL2g==
+X-Virus-Scanned: by amavisd-new at lrz.de in lxmhs52.srv.lrz.de
+Received: from postout2.mail.lrz.de ([127.0.0.1]) by lxmhs52.srv.lrz.de
+ (lxmhs52.srv.lrz.de [127.0.0.1]) (amavisd-new, port 20024) with LMTP id
+ LR70hxbOGEDr for <lammich@in.tum.de>; Fri, 20 Apr 2018 10:38:19 +0200 (CEST)
+Received: from BADWLRZ-SWMBX07.ads.mwn.de (BADWLRZ-SWMBX07.ads.mwn.de
+ [IPv6:2001:4ca0:0:108::163]) (using TLSv1.2 with cipher
+ ECDHE-RSA-AES256-SHA384 (256/256 bits)) (Client CN "BADWLRZ-SWMBX07",
+ Issuer "BADWLRZ-SWMBX07" (not verified)) by postout2.mail.lrz.de (Postfix)
+ with ESMTPS id 40S8Q36v3Sz11Sr for <lammich@in.tum.de>; Fri, 20 Apr 2018
+ 10:38:19 +0200 (CEST)
+Received: from BADWLRZ-SWMBX09.ads.mwn.de (2001:4ca0:0:108::165) by
+ BADWLRZ-SWMBX07.ads.mwn.de (2001:4ca0:0:108::163) with Microsoft SMTP
+ Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256)
+ id 15.1.1466.3; Fri, 20 Apr 2018 10:38:18 +0200
+Received: from BADWLRZ-SWMBX09.ads.mwn.de ([fe80::28c9:20b8:a4d6:473c]) by
+ BADWLRZ-SWMBX09.ads.mwn.de ([fe80::28c9:20b8:a4d6:473c%12]) with mapi id
+ 15.01.1466.003; Fri, 20 Apr 2018 10:38:18 +0200
+From: "Rieder, Sabine" <sabine.rieder@tum.de>
+To: "lammich@in.tum.de" <lammich@in.tum.de>
+Subject: [FDS-Homework]
+Thread-Topic: [FDS-Homework]
+Thread-Index: AQHT2IIkqYhIPY2qi0GINJCTB/9WOg==
+Date: Fri, 20 Apr 2018 08:38:18 +0000
+Message-ID: <baa471b5f7384579a95a81f65e405cd8@tum.de>
+Accept-Language: de-DE, en-US
+Content-Language: de-DE
+X-MS-Exchange-Organization-AuthAs: Internal
+X-MS-Exchange-Organization-AuthMechanism: 04
+X-MS-Exchange-Organization-AuthSource: BADWLRZ-SWMBX09.ads.mwn.de
+X-MS-Has-Attach: yes
+X-MS-TNEF-Correlator: 
+x-originating-ip: [131.159.201.175]
+Content-Type: multipart/mixed; boundary="_004_baa471b5f7384579a95a81f65e405cd8tumde_"
+MIME-Version: 1.0
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+--_004_baa471b5f7384579a95a81f65e405cd8tumde_
+Content-Type: multipart/alternative; boundary="_000_baa471b5f7384579a95a81f65e405cd8tumde_"
+
+
+--_000_baa471b5f7384579a95a81f65e405cd8tumde_
+Content-Type: text/plain; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+Dear Dr. Lammich,
+Attached you can find my homework for week 1.
+
+Best regards,
+Sabine Rieder
+
+
+--_000_baa471b5f7384579a95a81f65e405cd8tumde_
+Content-Type: text/html; charset="iso-8859-1"
+Content-Transfer-Encoding: 8bit
+
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" dir="ltr" style="font-size: 12pt; color: rgb(0, 0, 0); font-family: Calibri, Helvetica, sans-serif, &quot;EmojiFont&quot;, &quot;Apple Color Emoji&quot;, &quot;Segoe UI Emoji&quot;, NotoColorEmoji, &quot;Segoe UI Symbol&quot;, &quot;Android Emoji&quot;, EmojiSymbols;">
+<p></p>
+<div>
+<p class="MsoNormal"><span style="mso-ansi-language:EN-GB" lang="EN-GB">Dear Dr. Lammich,</span></p>
+<p class="MsoNormal"><span style="mso-ansi-language:EN-GB" lang="EN-GB">Attached you can find my homework for week 1.</span></p>
+<p class="MsoNormal"><span style="mso-ansi-language:EN-GB" lang="EN-GB"><br>
+</span></p>
+<p class="MsoNormal"><span style="mso-ansi-language:EN-GB" lang="EN-GB">Best regards,</span></p>
+<p class="MsoNormal"><span style="mso-ansi-language:EN-GB" lang="EN-GB">Sabine Rieder</span></p>
+</div>
+<p><br>
+</p>
+</div>
+</body>
+</html>
+
+--_000_baa471b5f7384579a95a81f65e405cd8tumde_--
+
+--_004_baa471b5f7384579a95a81f65e405cd8tumde_
+Content-Type: application/octet-stream; name="hw01.thy"
+Content-Description: hw01.thy
+Content-Disposition: attachment; filename="hw01.thy"; size=1297; creation-date="Fri, 20 Apr 2018 08:36:24 GMT"; modification-date="Fri, 20 Apr 2018 08:36:24 GMT"
+Content-Transfer-Encoding: base64
+
+dGhlb3J5IGh3MDEKICBpbXBvcnRzIE1haW4KCmJlZ2luCmZ1biBsaXN0c3VtIDo6ICJpbnQgbGlz
+dCA9PiBpbnQiIHdoZXJlCiAgImxpc3RzdW0gKE5pbCkgPSAwIiB8CiAgImxpc3RzdW0gKHggIyB4
+cykgPSB4ICsgKGxpc3RzdW0geHMpIgoKdmFsdWUgImxpc3RzdW0gWzEgLDIgLDMgXSA9IDYiCmxl
+bW1hICJsaXN0c3VtIFsxICwyICwzIF0gPSA2IiBieSBzaW1wCgp2YWx1ZSAibGlzdHN1bSBbXSA9
+IDAiCmxlbW1hICJsaXN0c3VtIFtdID0gMCIgYnkgc2ltcAoKdmFsdWUgImxpc3RzdW0gWzEgLC0y
+ICwzIF0gPSAyIgpsZW1tYSAibGlzdHN1bSBbMSwgLTIsIDNdID0gMiIgYnkgc2ltcAoKbGVtbWEg
+bGlzdHN1bV9maWx0ZXJfejogImxpc3RzdW0gKGZpbHRlciAoXDxsYW1iZGE+eC4geCBcPG5vdGVx
+PjAgKSBsICkgPSBsaXN0c3VtIGwiCiAgYXBwbHkoaW5kdWN0aW9uIGwpCiAgYXBwbHkgYXV0bwog
+IGRvbmUKCmxlbW1hIGxpc3RzdW1fYXBwW3NpbXBdOiAibGlzdHN1bSAoeHMgQCB5cykgPSBsaXN0
+c3VtIHlzICArIGxpc3RzdW0geHMiCiAgYXBwbHkoaW5kdWN0aW9uIHhzIGFyYml0cmFyeTogeXMp
+CiAgYXBwbHkoYXV0bykKICBkb25lCgpsZW1tYSBsaXN0c3VtX3JldltzaW1wXTogImxpc3RzdW0g
+KHJldiB4cykgPSBsaXN0c3VtIHhzIgogIGFwcGx5KGluZHVjdGlvbiB4cykKICBhcHBseShhdXRv
+KQogIGRvbmUKCmxlbW1hIGxpc3RzdW1fZmlsdGVyX25lZyA6ICJsaXN0c3VtIChmaWx0ZXIgKFw8
+bGFtYmRhPnguIHggXDxnZT4gMCApIGwgKSBcPGdlPiBsaXN0c3VtIGwiCiAgYXBwbHkoaW5kdWN0
+aW9uIGwpCiAgYXBwbHkoYXV0bykKICBkb25lCgpmdW4gZmxhdHRlbiA6OiAiJ2EgbGlzdCBsaXN0
+IFw8UmlnaHRhcnJvdz4gICdhIGxpc3QiIHdoZXJlCiAgImZsYXR0ZW4gW10gPSBbXSIgfAogICJm
+bGF0dGVuIChsI2xzKSA9IGwgQCAoZmxhdHRlbiBscykiCgp2YWx1ZSAiZmxhdHRlbiBbWzEgLDIg
+LDMgXSxbMiBdXSA9IFsxICwyICwzICwyIDo6aW50XSIKbGVtbWEgImZsYXR0ZW4gW1sxICwyICwz
+IF0sWzIgXV0gPSBbMSAsMiAsMyAsMiA6OmludF0iIGJ5IHNpbXAKCnZhbHVlICJmbGF0dGVuIFtb
+MSAsMiAsMyBdLFtdLFsyIF1dID0gWzEgLDIgLDMgLDIgOjppbnRdIgpsZW1tYSAiZmxhdHRlbiBb
+WzEgLDIgLDMgXSxbXSxbMiBdXSA9IFsxICwyICwzICwyIDo6aW50XSIgYnkgc2ltcAoKCmxlbW1h
+ICJsaXN0c3VtIChmbGF0dGVuIHhzKSA9IGxpc3RzdW0gKG1hcCBsaXN0c3VtIHhzKSIKICBhcHBs
+eShpbmR1Y3Rpb24geHMpCiAgYXBwbHkoYXV0bykKICBkb25lCgoKZW5kCg==
+
+--_004_baa471b5f7384579a95a81f65e405cd8tumde_--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/extracted/smith.nickh@gmail.com	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,137 @@
+From smith.nickh@gmail.com Fri Apr 20 09:52:31 2018
+Return-Path: <smith.nickh@gmail.com>
+Delivered-To: <lammich@mailstore.informatik.tu-muenchen.de>
+Received: from vmmailstore1.informatik.tu-muenchen.de by
+ vmmailstore1.informatik.tu-muenchen.de (Dovecot) with LMTP id
+ e5TbODWc2VqXOwAArPjJig for <lammich@mailstore.informatik.tu-muenchen.de>;
+ Fri, 20 Apr 2018 09:52:31 +0200
+Received: from vmmailproxy1.informatik.tu-muenchen.de
+ (vmmailproxy1.informatik.tu-muenchen.de [131.159.0.83]) by
+ vmmailstore1.informatik.tu-muenchen.de (Postfix) with ESMTP id 734D31C108A
+ for <lammich@mailstore.informatik.tu-muenchen.de>; Fri, 20 Apr 2018
+ 09:52:31 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de
+ (mailrelay1.informatik.tu-muenchen.de [131.159.254.14]) by
+ vmmailproxy1.informatik.tu-muenchen.de (Postfix) with ESMTP id 7204D1E0125
+ for <lammich@mail.informatik.tu-muenchen.de>; Fri, 20 Apr 2018 09:52:31
+ +0200 (CEST)
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix) id
+ 6E3081C0376; Fri, 20 Apr 2018 09:52:31 +0200 (CEST)
+Delivered-To: peter.lammich@informatik.tu-muenchen.de
+Received: by vmmailrelay1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 692E21C038A; Fri, 20 Apr 2018 09:52:31 +0200 (CEST)
+Received: from vmmailrelay1.informatik.tu-muenchen.de (localhost
+ [127.0.0.1]) by vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP
+ id 3E7A01C0378 for <lammich@in.tum.de>; Fri, 20 Apr 2018 09:52:31 +0200
+ (CEST)
+Received: from vmmaildmz1.informatik.tu-muenchen.de
+ (vmmaildmz1.informatik.tu-muenchen.de [131.159.0.87]) by
+ vmmailrelay1.informatik.tu-muenchen.de (Postfix) with ESMTP id 33E841C0376
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 09:52:31 +0200 (CEST)
+Received: by vmmaildmz1.informatik.tu-muenchen.de (Postfix, from userid
+ 109) id 324F51C2DAA; Fri, 20 Apr 2018 09:52:31 +0200 (CEST)
+X-Spam-Checker-Version: SpamAssassin 3.4.0-tuminfo_1 (2014-02-07) on
+ vmmaildmz1.informatik.tu-muenchen.de
+X-Spam-Level: 
+X-Spam-Status: No, score=-2.0 required=7.0 tests=AWL,BAYES_00,DKIM_SIGNED,
+ DKIM_VALID,DKIM_VALID_AU,FREEMAIL_FROM,HTML_MESSAGE,RCVD_IN_DNSWL_NONE,
+ RCVD_IN_MSPIKE_H2 autolearn=no autolearn_force=no version=3.4.0-tuminfo_1
+Received: from vmmaildmz1.informatik.tu-muenchen.de (localhost [127.0.0.1])
+ by vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTP id 8C5551C2DA9
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 09:52:28 +0200 (CEST)
+Received: from mail-wr0-f181.google.com (mail-wr0-f181.google.com
+ [209.85.128.181]) (using TLSv1.2 with cipher ECDHE-RSA-AES128-GCM-SHA256
+ (128/128 bits)) (No client certificate requested) by
+ vmmaildmz1.informatik.tu-muenchen.de (Postfix) with ESMTPS id 715121C2D9F
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 09:52:28 +0200 (CEST)
+Received: by mail-wr0-f181.google.com with SMTP id u11-v6so20368573wri.12
+ for <lammich@in.tum.de>; Fri, 20 Apr 2018 00:52:28 -0700 (PDT)
+DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com;
+ s=20161025; h=mime-version:from:date:message-id:subject:to;
+ bh=Hd8Q1SxbWxtkW6AKW6jOcmtASJFKs1b325FkiEPYo3E=;
+ b=qZ/MUESEiH9Ja/NMH//3TiOi23FluWY7yt4HOPG8EfWwoUsVTMW6xhcrh5VVFlKqkm
+ X+KbA3Ay6O5SnpfMtVOuSitOItbfE4TtBnzI40MtalhWZ5o0r0vI4vF/Dy84q/HRf3bN
+ +rEq4h62SjnnBUJAQM2Fc4Ot50Z/U5v4hnVjNi09TnCmYdj3FN/1Y7fSgLelknAwa6/+
+ 9F0QMt6ojiU/wro9HAg4K1lgv6qXWYn76UeaRdqJ4KaKTONnakcx34DaBt0ahc1wkvrQ
+ 0ksH3zkIAnkIiM1cW8RqbhOzmebhELRbUv6/aMFM50fvUBOKw7Uc2/p9RtuQ/bIKsqfW tIYA==
+X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net;
+ s=20161025;
+ h=x-gm-message-state:mime-version:from:date:message-id:subject:to;
+ bh=Hd8Q1SxbWxtkW6AKW6jOcmtASJFKs1b325FkiEPYo3E=;
+ b=MhT/rR2MtWuXhayv5YzwS9dOYdwG0r9XgnXih3U8yu0Q4bu4imYYaz6BMf0Btjt1Bx
+ xzgP9e5by956IPj0nRokkdU/Ep7m096uUCwjdSxGeQkpwye0WXFcNu9H0NKWYU518LdB
+ RdwcjUdt+z2Q37fbSvTBfywmPjaO1R3tm5NOC2Xtu2cwuiwzasoy5VLK53OuKdzD0lZ1
+ 0RxlPpo50ql9Oo+QrH0vAQGhlnbpwv0pR/nD5qo4wL8xUHfY/UH+aFh+FFIUa+DpSptJ
+ DqSkmEUJAjwnj0veZSMh4nlG7xARMyUT5LvgYb/LnGiqekATJdU+WfIbBFvGRFoWLtwi Xwog==
+X-Gm-Message-State:
+ ALQs6tB0oX+vqvBJ9ErIbz2gqGPpdPUtFnVbXSlrbhEvUjf1UuFA4ETc
+ XuRa5aaOlRqVICTUl7di/kgRtsjWuqNcey3kWhw=
+X-Google-Smtp-Source:
+ AIpwx49KCPfQbSdxt4LAcK89PcqK6ek48aJcpurMRQZuhmeKb13SDsxZ6YMcGUkHkAep+PLx0IqLQDQJEjlhXutfIfk=
+X-Received: by 10.28.58.81 with SMTP id h78mr1082143wma.110.1524210747485;
+ Fri, 20 Apr 2018 00:52:27 -0700 (PDT)
+MIME-Version: 1.0
+Received: by 10.223.128.9 with HTTP; Fri, 20 Apr 2018 00:52:06 -0700 (PDT)
+From: Nicholas Smith <smith.nickh@gmail.com>
+Date: Fri, 20 Apr 2018 09:52:06 +0200
+Message-ID: <CALgGdVFb-o9XByc7aQDbWr08YnpYnmoRRXb41fTyLcMtLJyjSg@mail.gmail.com>
+Subject: [FDS-Homework]
+To: Peter Lammich <lammich@in.tum.de>
+Content-Type: multipart/mixed; boundary="001a1148d7082aee9e056a42f823"
+X-Evolution-Source: 1479990504.8344.16@lapnipkow10
+
+
+--001a1148d7082aee9e056a42f823
+Content-Type: multipart/alternative; boundary="001a1148d7082aee9c056a42f821"
+
+
+--001a1148d7082aee9c056a42f821
+Content-Type: text/plain; charset="UTF-8"
+Content-Transfer-Encoding: 8bit
+
+Attached is my homework for HW1.
+Thanks
+
+-- 
+Nicholas Smith
+(310) 291-0777
+
+--001a1148d7082aee9c056a42f821
+Content-Type: text/html; charset="UTF-8"
+Content-Transfer-Encoding: 8bit
+
+<div dir="ltr">Attached is my homework for HW1.<div>Thanks<br clear="all"><div><br></div>-- <br><div class="gmail_signature" data-smartmail="gmail_signature">Nicholas Smith<br>(310) 291-0777</div>
+</div></div>
+
+--001a1148d7082aee9c056a42f821--
+
+--001a1148d7082aee9e056a42f823
+Content-Type: application/octet-stream; name="HW1.thy"
+Content-Disposition: attachment; filename="HW1.thy"
+Content-Transfer-Encoding: base64
+X-Attachment-Id: f_jg7npmt00
+
+dGhlb3J5IEhXMQppbXBvcnRzIE1haW4KYmVnaW4KCmZ1biBsaXN0c3VtIDo6ICJpbnQgbGlzdCBc
+PFJpZ2h0YXJyb3c+IGludCIgd2hlcmUKICAiIGxpc3RzdW0gW10gPSAoMCA6OiBpbnQpICIgfAog
+ICIgbGlzdHN1bSAoeCN4cykgPSAgKHg6OiBpbnQpICsgKGxpc3RzdW0geHMpICIKCgoKdmFsdWUg
+Imxpc3RzdW0gWzEsMiwzXSIKdmFsdWUgImxpc3RzdW0gW10iCnZhbHVlICJsaXN0c3VtIFsxLC0y
+LDNdIgp2YWx1ZSAiWzM6Om5hdF0gQCBbMSwyXSIKCmxlbW1hIGxpc3RzdW1fZmlsdGVyX3ogOiJs
+aXN0c3VtIChmaWx0ZXIoIFw8bGFtYmRhPnguIHggXDxub3RlcT4gMCkgbCkgPSBsaXN0c3VtIGwi
+CiAgYXBwbHkgKGluZHVjdGlvbiBsKSAgICAKICBhcHBseSAoYXV0bykKICBkb25lCgpsZW1tYSBs
+aXN0c3VtX3Jldl9BVVg6ICJsaXN0c3VtKHhzIEAgW3hdKSA9IGxpc3RzdW0oeHMpICsgeCIKICBh
+cHBseSAoaW5kdWN0aW9uIHhzKSAgIAogIGFwcGx5IChhdXRvKQogIGRvbmUKCmxlbW1hIGxpc3Rz
+dW1fcmV2OiAibGlzdHN1bSAocmV2IGxzKSA9IGxpc3RzdW0gbHMiCiAgYXBwbHkgKGluZHVjdGlv
+biBscykKICBhcHBseSAoYXV0byBzaW1wOiBsaXN0c3VtX3Jldl9BVVgpCiAgZG9uZQoKbGVtbWEg
+bmVnbnVtX2ZpbHRlcjogImxpc3RzdW0oZmlsdGVyKCBcPGxhbWJkYT54LiB4IDwgMCkgbCApIFw8
+bGU+IGxpc3RzdW0obCkiCiAgYXBwbHkgKGluZHVjdGlvbiBsKQogIGFwcGx5IChhdXRvKQogIGRv
+bmUKCmZ1biBmbGF0dGVuIDo6ICInYSBsaXN0IGxpc3QgXDxSaWdodGFycm93PiAnYSBsaXN0IiB3
+aGVyZQogICJmbGF0dGVuIFtdID0gW10iIHwKICAiZmxhdHRlbiAobCNscykgPSBsIEAgKGZsYXR0
+ZW4gbHMpICIKCnZhbHVlICIgZmxhdHRlbiAoW1sxLDIsM10sWzQsNV1dIDo6IG5hdCBsaXN0IGxp
+c3QpIgp2YWx1ZSAiZmxhdHRlbiBbWzEsMiwzXSxbMiBdXSA9IFsxICwyLDMsMiA6OmludF0iCnZh
+bHVlICJtYXAgbGlzdHN1bSBbWzEsMiwzXSxbNV0sWzYsNyw4XV0iCgpsZW1tYSBsaXN0c3VtX0FV
+WFtzaW1wXTogImxpc3RzdW0gKHhzQHlzKSA9IGxpc3RzdW0oeHMpICsgbGlzdHN1bSh5cykiCiAg
+YXBwbHkgKGluZHVjdGlvbiB4cykKICBhcHBseSAoYXV0bykKICBkb25lCgpsZW1tYSBsaXN0c3Vt
+X3N1bTogIiBsaXN0c3VtKCBmbGF0dGVuIChscykgKSAgPSBsaXN0c3VtIChtYXAgbGlzdHN1bShs
+cykgKSIKICBhcHBseSAoaW5kdWN0aW9uIGxzKQogIGFwcGx5IChhdXRvKQogIGRvbmUKCmVuZA==
+--001a1148d7082aee9e056a42f823--
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/felix.wielander@tum.de/hw01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,53 @@
+(** Score: 10/10
+*)
+theory hw01
+imports Main
+begin
+
+(* 1 *)
+fun listsum :: "int list \<Rightarrow> int" where
+  "listsum []    = 0" |
+  "listsum (x#xs)  = x + listsum xs"
+
+value "listsum [1,2,3] = 6"
+value "listsum [] = 0"
+value "listsum [1,-2,3] = 2"
+
+(* 2 *)
+lemma listsum_filter_z : "listsum (filter (\<lambda>x . x \<noteq> 0) l) = listsum l"
+  apply(induction l)
+  apply(auto)
+  done
+
+(* 3 *)
+lemma listsum_rev_aux[simp]: "listsum (xs @ ys) = listsum xs + listsum ys"
+  apply(induction xs)
+  apply(auto)
+  done
+
+lemma listsum_rev : "listsum (rev xs) = listsum xs"
+  apply(induction xs)
+  apply(auto)
+  done
+
+(* 4 *)
+lemma listsum_filter_neg : "listsum (filter (\<lambda>x . x \<ge> 0) xs) \<ge> listsum xs"
+  apply(induction xs)
+  apply(auto)
+  done
+
+(* 5 *)
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+  "flatten [] = []" |
+  "flatten (l #ls) = l @ flatten ls"
+
+value "flatten [[1 ,2 ,3 ],[2]] = [1 ,2 ,3 ,2 ::int]"
+value "flatten [[1 ,2 ,3 ],[],[2]] = [1 ,2 ,3 ,2 ::int]"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply(induction xs)
+  apply(auto)
+  done
+
+
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/felix.wielander@tum.de/msg-30498-8.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,7 @@
+Hallo Herr Lammich,
+
+im Anhang finden Sie meine Homework1.
+
+Viele Grüße,
+Felix Wielander
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/florian.stamer@tum.de/ex01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,39 @@
+(** Score: 10/10
+*)
+theory ex01
+imports Main
+begin
+  (*h1 *)
+  fun listsum :: "int list \<Rightarrow> int" where
+    "listsum [] = 0"
+  | "listsum (x#xs) = x + listsum xs"
+
+  lemma listsum_filter_z: "listsum (filter (\<lambda>x. x\<noteq>0) l) = listsum l"
+  apply (induction l)
+  apply (auto)
+  done
+
+  lemma listsum_app: "listsum (xs @ ys) = listsum xs + listsum ys"
+  apply (induction xs)
+  apply (auto)
+  done
+
+  lemma listsum_rev: "listsum (rev xs) = listsum xs"
+  apply (induction xs)
+  apply (auto simp add: listsum_app)
+  done
+
+  lemma listsum_filter_pos: "listsum (filter (\<lambda>x. x\<ge>0) l) \<ge> listsum l"
+  apply (induction l)
+  apply (auto)
+  done
+
+  fun flatten :: "'a list list \<Rightarrow> 'a list" where
+    "flatten [] = []"
+  | "flatten (l#ls) = l @ flatten ls"
+
+  lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply (induction xs)
+  apply (auto simp add: listsum_app)
+  done
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/florian.stamer@tum.de/msg-30498-10.html	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,18 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" style="font-size:12pt;color:#000000;font-family:Calibri,Helvetica,sans-serif;" dir="ltr">
+<p>Dear Mr. Lammich,</p>
+<p><br>
+</p>
+<p>the file is in the attachment.</p>
+<p><br>
+</p>
+<p>Best regards</p>
+<p>Florian Stamer [03664701]</p>
+</div>
+</body>
+</html>
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/florian.stamer@tum.de/msg-30498-9.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,9 @@
+Dear Mr. Lammich,
+
+
+the file is in the attachment.
+
+
+Best regards
+
+Florian Stamer [03664701]
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/g.bidlingmaier@tum.de/ex01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,49 @@
+(** Score: 10/10
+*)
+theory ex01
+imports Main
+begin
+
+fun listsum :: "int list \<Rightarrow> int" where
+    "listsum [] = 0"
+  | "listsum (x#xs) = x + listsum xs"
+
+value "listsum [1 ,2 ,3 ] = 6"
+value "listsum [] = 0"
+value "listsum [1 ,-2 ,3 ] = 2"
+
+lemma listsum_filter_z:
+"listsum (filter (\<lambda>x. x \<noteq> 0 ) l ) = listsum l"
+  apply (induction l)
+  apply auto
+  done
+
+lemma listsum_app: "listsum (xs @ ys) = listsum xs + listsum ys"
+  apply (induction xs)
+   apply auto
+  done
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+  apply (induction xs)
+  apply (auto simp: listsum_app)
+  done
+
+lemma "listsum (filter (\<lambda>x. x \<ge> 0) l) \<ge> listsum l"
+  apply (induction l)
+  apply auto
+  done
+
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+    "flatten [] = []"
+  | "flatten (l#ls) = l @ flatten ls"
+
+value "flatten [[1 ,2 ,3 ],[2 ]] = [1 ,2 ,3 ,2 ::int]"
+value "flatten [[1 ,2 ,3 ],[],[2 ]] = [1 ,2 ,3 ,2 ::int]"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply (induction xs)
+  apply (auto simp: listsum_app)
+  done
+
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/g.bidlingmaier@tum.de/msg-30498-13.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,4 @@
+Gunther Bidlingmaier
+
+03663324
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/ga53qud@mytum.de/hw01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,47 @@
+(** Score: 10/10
+*)
+theory hw01
+  imports Main
+begin
+
+fun listsum:: "int list \<Rightarrow> int" where
+  "listsum [] = 0"
+| "listsum (x # xs) =  listsum xs + x"
+
+value "listsum [1,2,3] = 6"
+value "listsum [] = 0"
+value "listsum [1,-2,3] = 2"
+
+lemma listsum_filter_x: "listsum (filter (\<lambda>x. x\<noteq>0) l) = listsum l"
+  apply(induction l)
+  apply(auto)
+  done
+
+lemma listsum_append: "listsum (xs @ ys) = listsum xs + listsum ys"
+  apply(induction xs)
+   apply(auto)
+  done
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+  apply(induction xs)
+   apply(auto simp:listsum_append)
+  done
+
+lemma listsum_noneg: "listsum (filter (\<lambda>x. x>0) l) \<ge> listsum l"
+  apply(induction l)
+   apply(auto)
+  done
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+  "flatten [] = []"
+| "flatten (l#ls) = l @ flatten ls"
+
+value "flatten [[1,2,3],[2]] = [1,2,3,2::int]"
+value "flatten [[1,2,3],[],[2]] = [1,2,3,2::int]"
+
+lemma "listsum (flatten xs) = listsum(map listsum xs)"
+  apply(induction xs)
+  apply(auto simp:listsum_append)
+  done
+
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/ga53qud@mytum.de/msg-30498-11.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,11 @@
+Dear Sir,
+
+
+Please find attached my homework for week 1 of Functional Data Structures.
+
+
+Thanking you,
+
+Amartya Das Sharma
+
+Enrollment 03694265
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/ga53qud@mytum.de/msg-30498-12.html	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,21 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" style="font-size:12pt;color:#000000;font-family:Calibri,Helvetica,sans-serif;" dir="ltr">
+<p>Dear Sir,</p>
+<p><br>
+</p>
+<p>Please find attached my homework for week 1 of Functional Data Structures.</p>
+<p><br>
+</p>
+<p>Thanking you, <br>
+</p>
+<p>Amartya Das Sharma</p>
+<p>Enrollment 03694265<br>
+</p>
+</div>
+</body>
+</html>
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/ge69kel@mytum.de/Homework01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,50 @@
+(** Score: 10/10
+
+  ALWAYS CLOSE LEMMAS WITH DONE, AND .thy FILES WITH END!
+
+*)
+theory Homework01
+  imports Main
+begin
+fun listsum :: "int list \<Rightarrow> int" where
+  "listsum [] = 0"
+| "listsum (x#xs) = x + listsum xs"
+
+value "listsum [1,2,3] = 6"
+value "listsum [] = 0"
+value "listsum [1,-2,3] = 2"
+
+lemma listsumfilter_z: "listsum (filter (\<lambda>x. x\<noteq>0) l) = listsum l"
+  apply (induction l)
+   apply auto
+  done
+lemma listsumlist: "listsum (xs@ys) =(listsum xs) + (listsum ys)"
+  apply (induction xs)
+   apply auto
+  done
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+  apply (induction xs)
+   apply (auto simp: listsumlist)
+  done
+
+lemma listsumfilter_n: "listsum (filter(\<lambda>x. x>0) l) \<ge> listsum l"
+  apply(induction l)
+   apply auto
+  done
+
+fun flatten :: "'a list list \<Rightarrow>'a list" where
+  "flatten [] = []"
+| "flatten (l#ls) = l@flatten ls"
+
+value "flatten [[1,2,3],[2]] = [1,2,3,2::int]"
+value "flatten [[1,2,3],[],[2]] = [1,2,3,2::int]"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply(induction xs)
+  apply (auto simp:listsumlist)
+  done (** Close a lemma with a done! *)
+  
+end  
+   
+  
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/ge69kel@mytum.de/msg-30498-14.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,9 @@
+Dear Dr. Lammich
+
+
+Please find attached my .thy file for the week 1 homework for Functional Data Structures.
+
+
+Thank You
+
+Arun S
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/ge69kel@mytum.de/msg-30498-15.html	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,18 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" style="font-size: 12pt; color: rgb(0, 0, 0); font-family: Calibri, Helvetica, sans-serif, EmojiFont, &quot;Apple Color Emoji&quot;, &quot;Segoe UI Emoji&quot;, NotoColorEmoji, &quot;Segoe UI Symbol&quot;, &quot;Android Emoji&quot;, EmojiSymbols;" dir="ltr">
+<p>Dear Dr. Lammich</p>
+<p><br>
+</p>
+<p>Please find attached my .thy file for the week 1 homework for Functional Data Structures.</p>
+<p><br>
+</p>
+<p>Thank You</p>
+<p>Arun S</p>
+</div>
+</body>
+</html>
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/ge72lic@mytum.de/ex01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,45 @@
+(** Score: 10/10
+*)
+theory ex01
+imports Main
+begin
+ fun listsum :: "int list \<Rightarrow> int" where
+    "listsum [] = 0"
+  | "listsum (x#xs) = x + listsum xs"
+
+ value "(listsum [1 ,2 ,3 ]) = 6"
+ value "listsum [] = 0"
+ value "listsum [1 ,-2 ,3 ] = 2"
+ value "len([1, 2, 3])"
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x . x \<noteq> 0 ) l ) = listsum l"
+  apply(induction l) by auto
+
+lemma aux : "listsum(xs@ys) = listsum xs + listsum ys"
+  apply(induction xs) by auto
+
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+  apply(induction xs)
+   apply(auto simp: aux)
+  done
+
+lemma listsum_non_decr: "listsum (filter (\<lambda>x . x \<ge> 0) l) \<ge> listsum l"
+  apply(induction l) by auto
+
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+  "flatten [] = []"
+| "flatten (l#ls) = l@ flatten ls "
+
+value "flatten [[1 ,2 ,3 ],[2 ]] = [1 ,2 ,3 ,2 ::int]"
+value "flatten [[1 ,2 ,3 ],[],[2 ]] = [1 ,2 ,3 ,2 ::int]"
+
+
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply(induction xs)
+  apply(auto simp: aux)
+  done
+
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/ge72lic@mytum.de/msg-30498-16.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,1 @@
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/ge72lic@mytum.de/msg-30498-17.html	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,10 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" style="font-size:12pt;color:#000000;font-family:Calibri,Helvetica,sans-serif;" dir="ltr">
+</div>
+</body>
+</html>
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/j.gottfriedsen@tum.de/ex01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,37 @@
+(** Score: 10/10
+*)
+theory ex01
+  imports Main
+begin
+
+fun listsum :: "int list \<Rightarrow> int" where
+  "listsum [] = 0" |
+  "listsum (x # xs) = x + listsum xs"
+
+value "listsum[1, 2, 3] = 6"
+value "listsum[] = 0"
+value "listsum[1, -2, 3] = 2"
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x. x \<noteq> 0) l) = listsum l"
+  by (induction l) auto
+
+lemma listsum_app: "listsum (xs @ ys) = listsum xs + listsum ys"
+  by (induction xs) auto
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+  by (induction xs) (auto simp add: listsum_app)
+
+lemma listsum_filter_neg: "listsum l \<le> listsum (filter (\<lambda>x. x \<ge> 0) l)"
+  by (induction l) auto
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+  "flatten [] = []" |
+  "flatten (l # ls) = l @ flatten ls"
+
+value "flatten [[1, 2, 3], [2]] = [1, 2, 3, 2::int]"
+value "flatten [[1, 2, 3], [], [2]] = [1, 2, 3, 2::int]"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  by (induction xs) (auto simp add: listsum_app)
+
+end
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/j.gottfriedsen@tum.de/msg-30498-18.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,9 @@
+Hello,
+
+
+As the submission system is still not available, my solution to sheet 1 is attached to this mail.
+
+
+Name:
+
+Jakob Gottfriedsen
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/j.gottfriedsen@tum.de/msg-30498-19.html	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,19 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" dir="ltr" style="font-size: 12pt; color: rgb(0, 0, 0); font-family: Calibri, Helvetica, sans-serif, &quot;EmojiFont&quot;, &quot;Apple Color Emoji&quot;, &quot;Segoe UI Emoji&quot;, NotoColorEmoji, &quot;Segoe UI Symbol&quot;, &quot;Android Emoji&quot;, EmojiSymbols;">
+<p>Hello,</p>
+<p><br>
+</p>
+<p>As the submission system is still not available, my solution to sheet 1 is attached to this mail.</p>
+<p><br>
+</p>
+<p>Name:</p>
+<p>Jakob Gottfriedsen<br>
+</p>
+</div>
+</body>
+</html>
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/j.v.mutius@gmail.com/hw01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,34 @@
+(** Score: 10/10
+*)
+theory hw01
+  imports Main
+begin
+
+fun listsum :: "int list \<Rightarrow> int" where
+"listsum [] = 0" |
+"listsum (x#xs) = x + listsum xs"
+
+value "listsum [1,2,3] = 6"
+value "listsum [] = 0"
+value "listsum [1,-2,3] = 2"
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x. x \<noteq>  0) l) = listsum l"
+  apply(induction l) by auto
+
+lemma listsum_app: "listsum (xs @ ys) = listsum xs + listsum ys"
+  apply(induction xs) by auto
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+  apply(induction xs) by (auto simp: listsum_app)
+
+lemma listsum_filt_neg_smalleq: "listsum (filter (\<lambda>x. x \<ge> 0) xs) \<ge> listsum xs"
+  apply(induction xs) by auto
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+"flatten [] = []" |
+"flatten (l#ls) = l @ flatten ls"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply(induction xs) by (auto simp: listsum_app)
+
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/j.v.mutius@gmail.com/msg-30498-22.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,6 @@
+Hello Mr. Lammich,
+
+attached to this email one can find my theory file for 
+the homework.
+
+Joshua von Mutius
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/jonatan.juhas@tum.de/ha01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,58 @@
+(** Score: 10/10
+*)
+theory ha01
+  imports Main
+begin
+
+(* Implementation *)
+fun listsum :: "int list \<Rightarrow> int" where
+  "listsum [] = 0" |
+  "listsum (x#xs) = x + listsum xs"
+
+(* Brute testing *)
+(* I'm not sure yet what's the difference between value but I think lemma is better here *)
+(** Value actually evaluates by compiling your expression to ML.
+  Lemma proves the lemma by auto, which happens to work in this case, 
+  but will not always work without unfolding definitions, splitting cases, etc.
+*)
+lemma "listsum [1,2,3] = 6" by auto
+lemma "listsum [] = 0" by auto
+lemma "listsum [1,-2,3] = 2" by auto
+
+(* First condition: Filtering zeroes doesn't change result *)
+lemma listsum_filter_zero: "listsum (filter (\<lambda>x. x \<noteq> 0) l) = listsum l"
+  apply (induction l)
+  apply auto
+  done
+
+(* Second condition: Reversing list doesn't change result *)
+lemma aux: "listsum (xs@ys) = listsum xs +  listsum ys" 
+  apply (induction xs) by auto
+
+lemma listsum_reverse: "listsum (rev l) = listsum l"
+  apply (induction l)
+  apply (auto simp: aux)
+  done
+
+(* Third condition: Filtering out negative numbers results in a result equal or greater than original *)
+lemma listsum_filter_negative: "listsum l \<ge> listsum (filter (\<lambda>x. x < 0) l)"
+  apply (induction l)
+  apply (auto simp: aux)
+  done
+(* Note: Took a while until I figured it can actually be greater *)
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+  "flatten [] = []" |
+  "flatten (l#ls) = l @ flatten ls"
+
+(* Brute testing *)
+lemma "flatten [[1,2,3], [2]] = [1,2,3,2::int]" by auto
+lemma "flatten [[1,2,3],[],[2]] = [1,2,3,2::int]" by auto
+
+(* First condition: Sum of the flattened list is equal to the sum of all it's elements *)
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply (induction xs)
+  apply (auto simp: aux)
+  done
+
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/jonatan.juhas@tum.de/msg-30498-20.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,7 @@
+Dear Peter,
+
+I was unable to attend classes today nor the last week. I presume the submission via E-Mail deadline was the same as the one for the submission system.
+Since I don't know if you discussed the solutions during today's lecture I wanted to try and submit my solution anyways - if for nothing else than for the sake of feedback.
+
+Thanks and have a nice weekend,
+Jonatan Juhas
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/jonatan.juhas@tum.de/msg-30498-21.html	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,1 @@
+<div>Dear Peter,</div><br><div>I was unable to attend classes today nor the last week. I presume the submission via E-Mail deadline was the same as the one for the submission system.</div><div>Since I don't know if you discussed the solutions during today's lecture I wanted to try and submit my solution anyways - if for nothing else than for the sake of feedback.</div><br><div>Thanks and have a nice weekend,</div><div>Jonatan Juhas</div><div><signature id="local-2d702942-d407"></signature></div><img class="mailspring-open" alt="Open Tracking" width="0" height="0" style="border:0; width:0; height:0;" src="https://link.getmailspring.com/open/1524256873.local-ecd65737-76e1-v1.2.1-7e7447b6@getmailspring.com?recipient=bGFtbWljaEBpbi50dW0uZGU%3D">
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/katharinaluise.schmitt@tum.de/ex01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,47 @@
+(** Score: 10/10
+*)
+theory ex01
+imports Main
+begin
+
+fun listsum :: "int list \<Rightarrow> int" where
+"listsum [] = 0" |
+"listsum (x#xs) = (listsum xs) + x"
+
+value "listsum [1,2,3]"
+value "listsum []"
+value "listsum [1,-2, 3]"
+
+lemma listsum_filter_z : "listsum (filter (\<lambda>x . x \<noteq> 0 ) l ) = listsum l"
+  apply(induction l)
+  apply(auto)
+  done
+
+lemma listsum_app : "listsum (xs @ ys) = (listsum xs) + (listsum ys)"
+  apply(induction xs)
+  apply(auto)
+  done
+
+lemma listsum_rev : "listsum (rev xs) = listsum xs"
+  apply(induction xs)
+  apply(auto simp add: listsum_app)
+  done
+
+lemma list_filter : "listsum (filter (\<lambda>x . x \<ge> 0 ) xs ) \<ge> listsum xs"
+  apply(induction xs)
+  apply(auto)
+  done
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+"flatten [] = []" |
+"flatten (l #ls) = l @ flatten ls"
+
+value "flatten [[1 ,2 ,3 ],[2 ]] = [1 ,2 ,3 ,2 ::int]"
+value "flatten [[1 ,2 ,3 ],[],[2 ]] = [1 ,2 ,3 ,2 ::int]"
+
+lemma flatten_sum : "listsum (flatten xs) = listsum (map listsum xs)"
+  apply(induction xs)
+  apply(auto simp add: listsum_app)
+  done
+
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/katharinaluise.schmitt@tum.de/msg-30498-23.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,18 @@
+Dear Dr. Lammich,
+
+
+attached please find my homework submission for the first exercise sheet.
+
+My administrative data is the following:
+
+
+Name: Katharina Schmitt
+
+Enrollment Number: 03630761
+
+TUM User ID: ga49ceq
+
+
+Best regards,
+
+Katharina Schmitt
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/katharinaluise.schmitt@tum.de/msg-30498-24.html	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,27 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" dir="ltr" style="font-size:12pt; color:rgb(0,0,0); font-family:Calibri,Helvetica,sans-serif,&quot;EmojiFont&quot;,&quot;Apple Color Emoji&quot;,&quot;Segoe UI Emoji&quot;,NotoColorEmoji,&quot;Segoe UI Symbol&quot;,&quot;Android Emoji&quot;,EmojiSymbols">
+<p>Dear Dr. Lammich,</p>
+<p><br>
+</p>
+<p>attached please find my homework submission for the first exercise sheet. <br>
+</p>
+<p>My administrative data is the following:</p>
+<p><br>
+</p>
+<p>Name: Katharina Schmitt</p>
+<p>Enrollment Number: 03630761</p>
+<p>TUM User ID: ga49ceq<br>
+</p>
+<p><br>
+</p>
+<p>Best regards,</p>
+<p>Katharina Schmitt<br>
+</p>
+</div>
+</body>
+</html>
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/m.kirchmeier@tum.de/hw01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,35 @@
+(** Score: 10/10
+*)
+theory hw01
+imports Main
+begin
+
+fun listsum :: "int list \<Rightarrow> int" where
+"listsum [] = 0" |
+"listsum (x # xs) = x + listsum xs"
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x. x \<noteq> 0) l) = listsum l"
+proof (induction l)
+qed (simp+)
+
+lemma listsum_add[simp]: "listsum (a @ b) = listsum a + listsum b"
+proof (induction a)
+qed (simp+)
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+proof (induction xs)
+qed (simp+)
+
+lemma listsum_filterneg: "listsum (filter (\<lambda>x. x > 0) l) \<ge> listsum l"
+proof (induction l)
+qed (auto+)
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+"flatten [] = []" |
+"flatten (l # ls) = l @ flatten ls"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+proof (induction xs)
+qed (simp+)
+
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/m.kirchmeier@tum.de/msg-30498-29.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,12 @@
+Hallo Peter,
+
+ich höre dieses Semester FDS (will ja nicht dass meine Isabelle Skills 
+gleich wieder einschlafen ;D).
+
+Irgendwie ist aber die offizielle Hausaufgaben-Hochlademaske für FDS 
+anscheinend noch nicht aktiviert, dort gibt's nur Info 2 und Semantics 
+zur Auswahl.
+Deshalb schicke ich Dir die erste Hausaufgabe mal auf diesem Weg.
+
+Viele Grüße
+Max
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/markuswebel@gmail.com/ex01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,41 @@
+(** Score: 10/10
+*)
+theory ex01
+imports Main
+begin
+
+fun listsum :: "int list \<Rightarrow> int" where
+  "listsum [] = 0" |
+  "listsum (x#xs) = x + listsum xs"
+
+value "listsum [1,2,3] = 6"
+value "listsum [] = 0"
+value "listsum [1,-2,3] = 2"
+
+lemma listsum_filter_z : "listsum (filter (\<lambda>x. x \<noteq> 0) l) = listsum l"
+  apply (induction l) by auto
+
+lemma listsum_app [simp] : "listsum (xs@ys) = listsum xs + listsum ys"
+  apply (induction xs) by auto
+
+lemma listsum_rev : "listsum (rev xs) = listsum xs"
+  apply (induction xs)
+  apply auto
+  done
+
+lemma listsum_filter_neg : "listsum (filter (\<lambda>x. x \<ge> 0) l) \<ge> listsum l"
+  apply (induction l) by auto
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+  "flatten [] = []" |
+  "flatten (l#ls) = l @ flatten ls"
+
+value "flatten [[1,2,3],[2]] = [1,2,3,2::int]"
+value "flatten [[1,2,3],[],[2]] = [1,2,3,2::int]"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply (induction xs) by auto
+
+(* For some reason I already proved this. Take that! *)
+
+end
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/markuswebel@gmail.com/msg-30498-25.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,8 @@
+Hello Doctor Lammich,
+
+I forgot where to turn in my homework, so I just attached it to this email
+:)
+
+Greetings,
+
+Markus Webel
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/markuswebel@gmail.com/msg-30498-26.html	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,1 @@
+<div dir="ltr">Hello Doctor Lammich,<div><br></div><div>I forgot where to turn in my homework, so I just attached it to this email :)</div><div><br></div><div>Greetings,</div><div><br></div><div>Markus Webel</div></div>
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/martin.rau@tum.de/Home01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,49 @@
+(** Score: 10/10
+*)
+theory Home01
+imports Main
+begin 
+
+text {* Homework 1 *}
+
+fun listsum :: "int list \<Rightarrow> int" where
+  "listsum [] = 0"
+| "listsum (h#t) = h + listsum t"
+
+value "listsum [1,2,3] = 6"
+value "listsum [] = 0"
+value "listsum [1,-2,3] = 2"
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x. x\<noteq>0) l) = listsum l"
+apply (induction l)
+apply (auto)
+done
+
+lemma listsum_append[simp]: "listsum (xs @ ys) = listsum xs + listsum ys"
+apply (induction xs)
+apply (auto)
+done
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+apply (induction xs)
+apply (auto)
+done
+
+lemma listsum_filter_negative: "listsum (filter (\<lambda>x. x\<ge>0) l) \<ge> listsum l"
+apply (induction l)
+apply (auto)
+done
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+  "flatten [] = []"
+| "flatten (l#ls) = l @ flatten ls"
+
+value "flatten [[1,2,3],[2]] = [1,2,3,2::int]"
+value "flatten [[1,2,3],[],[2]]= [1,2,3,2::int]"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+apply (induction xs)
+apply (auto)
+done
+
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/martin.rau@tum.de/msg-30498-27.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,5 @@
+Submission for Homework 1.
+
+Kind regards,
+
+Martin Rau
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/mitja.krebs@tum.de/hw01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,48 @@
+(** Score: 10/10
+*)
+theory hw01
+imports Main
+begin
+
+fun listsum :: "int list \<Rightarrow> int" where
+  "listsum [] = 0"
+| "listsum (x # xs) = x + listsum xs"
+
+value "listsum [1, 2, 3] = 6"
+value "listsum [] = 0"
+value "listsum [1, -2, 3] = 2"
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x. x \<noteq> 0) l) = listsum l"
+  apply (induction l)
+  apply auto
+  done
+
+lemma listsum_rev_aux[simp]: "listsum (xs @ ys) = listsum xs + listsum ys"
+  apply (induction xs)
+  apply (induction ys)
+  apply auto
+  done
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+  apply (induction xs)
+  apply auto
+  done
+
+lemma "listsum (filter (\<lambda>x. x \<ge> 0) l) \<ge> listsum l"
+  apply (induction l)
+  apply auto
+  done
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+  "flatten [] = []"
+| "flatten (l # ls) = l @ flatten ls"
+
+value "flatten [[1, 2, 3], [2]] = [1, 2, 3, 2::int]"
+value "flatten [[1, 2, 3], [], [2]] = [1, 2, 3, 2::int]"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply (induction xs)
+  apply auto
+  done
+
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/mitja.krebs@tum.de/msg-30498-28.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,6 @@
+Hallo Herr Dr. Lammich,
+
+da es im Abgabesystem auf https://vmnipkow3.in.tum.de/ noch keinen Eintrag für die Vorlesung Functional data structures gibt, lasse ich Ihnen meinen Lösungsvorschlag für die erste Hausaufgabe (siehe Anhang) per E-Mail zukommen. Ich hoffe, das passt so.
+
+Viele Grüße
+Mitja Krebs
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/odnoshivkin@me.com/hw1.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,47 @@
+(** Score: 10/10
+*)
+theory hw1
+  imports Main
+
+begin
+fun listsum :: "int list \<Rightarrow> int" where
+"listsum [] = 0"|
+"listsum (x#xs) = x + listsum xs"
+
+value "listsum [1,2,3] = 6"
+value "listsum [] = 0"
+value "listsum [1,-2,3] = 2"
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x. x \<noteq> 0) l) = listsum l"
+apply(induction l)
+apply(auto)
+  done
+
+lemma listsum_app[simp]: "listsum (xs@ys) = listsum(xs) + listsum(ys)"
+  apply(induction xs)
+   apply(auto)
+  done 
+  
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+apply(induction xs)
+apply(auto)
+done
+
+lemma listsum_filter_neg: "listsum (filter (\<lambda>x. x>0) l) \<ge> listsum l"
+  apply(induction l)
+   apply(auto)
+  done
+
+fun flatten :: " 'a list list \<Rightarrow> 'a list" where
+"flatten [] = []"
+| "flatten (l#ls) = l @ flatten ls"
+
+value "flatten [[1,2,3],[2]] = [1,2,3,2::int]"
+value "flatten [[1,2,3],[],[2]] = [1,2,3,2::int]"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply(induction xs)
+  apply (auto)
+  done
+
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/odnoshivkin@me.com/msg-30498-30.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,5 @@
+Hi,
+Here is my homework 1.
+
+Best Regards,
+Mykola
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/omar.badramany@tum.de/hw01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,44 @@
+(** Score: 10/10
+*)
+theory hw01
+imports Main
+begin
+
+fun listsum :: "int list \<Rightarrow> int" where
+  "listsum [] = (0::int)"
+| "listsum (x#xs) = x + (listsum xs)"
+
+value "listsum [1,2,3]"
+value "listsum []"
+value "listsum [1,-2,3]"
+
+lemma listsum_filter_z : "listsum (filter (\<lambda>x. x \<noteq> 0) l) = listsum l"
+  apply (induction l)
+  apply auto
+  done
+
+lemma aux : "listsum (xs@ys) = listsum xs + listsum ys"
+  apply (induction xs)
+  apply auto
+  done
+  
+lemma listsum_rev : "listsum (rev xs) = listsum xs"
+  apply (induction xs)
+  apply (auto simp: aux)
+  done
+
+lemma t : "listsum (filter (\<lambda>x. x > 0) xs) \<ge> listsum xs "
+  apply (induction xs)
+  apply auto
+  done
+
+fun flatten :: "'a list list \<Rightarrow> 'a list " where 
+  "flatten [] = []"
+| "flatten (x#xs) = x@(flatten xs)"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply (induction xs)
+  apply (auto simp : aux)
+  done
+
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/omar.badramany@tum.de/msg-30498-31.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,7 @@
+Sehr geehrter Herr Lammich,
+
+ich habe versucht die Hausaufgabe auf der gegebenen Webseite hochzuladen aber es gibt leider kein Link fr die Vorlesung Funktionale Datenstrukturen.
+Anbei finden Sie meine Lsung.
+
+Viele Gre,
+Omar
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/omar.badramany@tum.de/msg-30498-32.html	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,19 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" style="font-size:12pt;color:#000000;font-family:Calibri,Helvetica,sans-serif;" dir="ltr">
+Sehr geehrter Herr Lammich,
+<div><br>
+</div>
+<div>ich habe versucht die Hausaufgabe auf der gegebenen Webseite hochzuladen aber es gibt leider kein Link fr die Vorlesung Funktionale Datenstrukturen.</div>
+<div>Anbei finden Sie meine Lsung.</div>
+<div><br>
+</div>
+<div>Viele Gre,</div>
+<div>Omar</div>
+</div>
+</body>
+</html>
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/s.griebel@tum.de/homework_1.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,49 @@
+(** Score: 10/10
+*)
+theory homework_1
+  imports Main
+begin
+
+fun listsum :: "int list \<Rightarrow> int" where
+  "listsum [] = 0"
+| "listsum (x#xs) = x + (listsum xs)"
+
+
+value "listsum [1, 2, 3] = 6"
+value "listsum [] = 0"
+value "listsum [1, -2, 3] = 2"
+
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x. x \<noteq> 0) l) = listsum l"
+  apply(induction l)
+   apply(auto)
+  done
+
+lemma listsum_append : "listsum (xs@ys) = listsum xs + listsum ys"
+  apply(induction xs)
+   apply(auto)
+  done
+
+lemma listsum_rev: "listsum (rev xs) = listsum xs"
+  apply(induction xs)
+   apply(auto simp: listsum_append)
+  done
+  
+lemma listsum_filter_neg: "listsum (filter (\<lambda> x. x \<ge> 0) l) \<ge> listsum l"
+  apply(induction l)
+   apply(auto)
+  done
+
+fun flatten:: "'a list list \<Rightarrow> 'a list" where
+  "flatten [] = []"
+| "flatten (l#ls) = l @ flatten ls"
+
+value "flatten [[1 ,2 ,3 ],[2 ]] = [1 ,2 ,3 ,2 ::int]"
+value "flatten [[1 ,2 ,3 ],[],[2 ]] = [1 ,2 ,3 ,2 ::int]"
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply(induction xs)
+   apply(auto simp: listsum_append)
+  done
+
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/s.griebel@tum.de/msg-30498-35.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,10 @@
+Hallo Peter,
+
+anbei befindet sich meine Lsung zur ersten Hausaufgabe.
+
+
+Gre,
+
+Simon Griebel
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/s.griebel@tum.de/msg-30498-36.html	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,21 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" style="font-size:12pt;color:#000000;font-family:Calibri,Helvetica,sans-serif;" dir="ltr">
+<p>Hallo Peter,</p>
+<p>anbei befindet sich meine Lsung zur ersten Hausaufgabe.</p>
+<p><br>
+</p>
+<p>Gre,</p>
+<p>Simon Griebel<br>
+</p>
+<p><br>
+</p>
+<p><br>
+</p>
+</div>
+</body>
+</html>
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/sabine.rieder@tum.de/hw01.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,57 @@
+(** Score: 10/10
+*)
+theory hw01
+  imports Main
+
+begin
+fun listsum :: "int list => int" where
+  "listsum (Nil) = 0" |
+  "listsum (x # xs) = x + (listsum xs)"
+
+value "listsum [1 ,2 ,3 ] = 6"
+lemma "listsum [1 ,2 ,3 ] = 6" by simp
+
+value "listsum [] = 0"
+lemma "listsum [] = 0" by simp
+
+value "listsum [1 ,-2 ,3 ] = 2"
+lemma "listsum [1, -2, 3] = 2" by simp
+
+lemma listsum_filter_z: "listsum (filter (\<lambda>x. x \<noteq>0 ) l ) = listsum l"
+  apply(induction l)
+  apply auto
+  done
+
+lemma listsum_app[simp]: "listsum (xs @ ys) = listsum ys  + listsum xs"
+  apply(induction xs arbitrary: ys)
+  apply(auto)
+  done
+
+lemma listsum_rev[simp]: "listsum (rev xs) = listsum xs"
+  apply(induction xs)
+  apply(auto)
+  done
+
+lemma listsum_filter_neg : "listsum (filter (\<lambda>x. x \<ge> 0 ) l ) \<ge> listsum l"
+  apply(induction l)
+  apply(auto)
+  done
+
+fun flatten :: "'a list list \<Rightarrow>  'a list" where
+  "flatten [] = []" |
+  "flatten (l#ls) = l @ (flatten ls)"
+
+value "flatten [[1 ,2 ,3 ],[2 ]] = [1 ,2 ,3 ,2 ::int]"
+lemma "flatten [[1 ,2 ,3 ],[2 ]] = [1 ,2 ,3 ,2 ::int]" by simp
+
+value "flatten [[1 ,2 ,3 ],[],[2 ]] = [1 ,2 ,3 ,2 ::int]"
+lemma "flatten [[1 ,2 ,3 ],[],[2 ]] = [1 ,2 ,3 ,2 ::int]" by simp
+
+
+lemma "listsum (flatten xs) = listsum (map listsum xs)"
+  apply(induction xs)
+  apply(auto)
+  done
+
+
+end
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/sabine.rieder@tum.de/msg-30498-33.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,6 @@
+Dear Dr. Lammich,
+Attached you can find my homework for week 1.
+
+Best regards,
+Sabine Rieder
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/sabine.rieder@tum.de/msg-30498-34.html	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,21 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
+</head>
+<body dir="ltr">
+<div id="divtagdefaultwrapper" dir="ltr" style="font-size: 12pt; color: rgb(0, 0, 0); font-family: Calibri, Helvetica, sans-serif, &quot;EmojiFont&quot;, &quot;Apple Color Emoji&quot;, &quot;Segoe UI Emoji&quot;, NotoColorEmoji, &quot;Segoe UI Symbol&quot;, &quot;Android Emoji&quot;, EmojiSymbols;">
+<p></p>
+<div>
+<p class="MsoNormal"><span style="mso-ansi-language:EN-GB" lang="EN-GB">Dear Dr. Lammich,</span></p>
+<p class="MsoNormal"><span style="mso-ansi-language:EN-GB" lang="EN-GB">Attached you can find my homework for week 1.</span></p>
+<p class="MsoNormal"><span style="mso-ansi-language:EN-GB" lang="EN-GB"><br>
+</span></p>
+<p class="MsoNormal"><span style="mso-ansi-language:EN-GB" lang="EN-GB">Best regards,</span></p>
+<p class="MsoNormal"><span style="mso-ansi-language:EN-GB" lang="EN-GB">Sabine Rieder</span></p>
+</div>
+<p><br>
+</p>
+</div>
+</body>
+</html>
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/smith.nickh@gmail.com/HW1.thy	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,58 @@
+(** Score: 10/10
+*)
+theory HW1
+imports Main
+begin
+
+fun listsum :: "int list \<Rightarrow> int" where
+  " listsum [] = (0 :: int) " |
+  " listsum (x#xs) =  (x:: int) + (listsum xs) "
+
+(** The type-annots inside the terms are not necessary. They are inferred
+  from the type-spec of the function int list \<Rightarrow> int .
+*)
+
+value "listsum [1,2,3]"
+value "listsum []"
+value "listsum [1,-2,3]"
+value "[3::nat] @ [1,2]"
+
+lemma listsum_filter_z :"listsum (filter( \<lambda>x. x \<noteq> 0) l) = listsum l"
+  apply (induction l)    
+  apply (auto)
+  done
+
+lemma listsum_rev_AUX: "listsum(xs @ [x]) = listsum(xs) + x"
+  apply (induction xs)   
+  apply (auto)
+  done
+
+lemma listsum_rev: "listsum (rev ls) = listsum ls"
+  apply (induction ls)
+  apply (auto simp: listsum_rev_AUX)
+  done
+
+lemma negnum_filter: "listsum(filter( \<lambda>x. x < 0) l ) \<le> listsum(l)"
+  apply (induction l)
+  apply (auto)
+  done
+
+fun flatten :: "'a list list \<Rightarrow> 'a list" where
+  "flatten [] = []" |
+  "flatten (l#ls) = l @ (flatten ls) "
+
+value " flatten ([[1,2,3],[4,5]] :: nat list list)"
+value "flatten [[1,2,3],[2 ]] = [1 ,2,3,2 ::int]"
+value "map listsum [[1,2,3],[5],[6,7,8]]"
+
+lemma listsum_AUX[simp]: "listsum (xs@ys) = listsum(xs) + listsum(ys)"
+  apply (induction xs)
+  apply (auto)
+  done
+
+lemma listsum_sum: " listsum( flatten (ls) )  = listsum (map listsum(ls) )"
+  apply (induction ls)
+  apply (auto)
+  done
+
+end
\ No newline at end of file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/smith.nickh@gmail.com/msg-30498-37.txt	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,6 @@
+Attached is my homework for HW1.
+Thanks
+
+-- 
+Nicholas Smith
+(310) 291-0777
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SS18/Exercises/hwsubm/hw01/smith.nickh@gmail.com/msg-30498-38.html	Mon Apr 23 11:46:13 2018 +0200
@@ -0,0 +1,2 @@
+<div dir="ltr">Attached is my homework for HW1.<div>Thanks<br clear="all"><div><br></div>-- <br><div class="gmail_signature" data-smartmail="gmail_signature">Nicholas Smith<br>(310) 291-0777</div>
+</div></div>