--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Attic/ProofAutomation.thy	Fri Feb 05 10:16:10 2016 +0000
@@ -0,0 +1,36 @@
+theory ProofAutomation
+imports Main
+begin
+
+lemma "\<forall>x. \<exists>y. x = y"
+by auto
+
+lemma "A \<subseteq> B \<inter> C \<Longrightarrow> A \<subseteq> B \<union> C"
+by auto
+
+lemma "\<lbrakk> \<forall> xs \<in> A. \<exists> ys. xs = ys @ ys; us \<in> A \<rbrakk> \<Longrightarrow> \<exists>n. length us = n+n"
+by fastforce
+
+lemma "\<lbrakk>xs @ ys = ys @ xs; length xs = length ys \<rbrakk> \<Longrightarrow> xs = ys"
+by auto
+
+lemma "\<lbrakk> (a::nat) \<le> x + b; 2*x < c\<rbrakk> \<Longrightarrow> 2*a + 1 \<le> 2*b + c"
+by arith
+
+lemma "\<lbrakk> (a::nat) \<le> b; b \<le> c; c \<le> d; d \<le> e \<rbrakk> \<Longrightarrow> a \<le> e"
+by (blast intro: le_trans)
+
+lemma "Suc(Suc(Suc a)) \<le> b \<Longrightarrow> a \<le> b"
+by(blast dest: Suc_leD)
+
+inductive ev :: "nat \<Rightarrow> bool" where
+ev0: "ev 0" |
+evSS: "ev n \<Longrightarrow> ev (n + 2)"
+
+fun even :: "nat \<Rightarrow> bool" where
+"even 0 = True" |
+"even (Suc 0) = False" |
+"even (Suc(Suc n)) = even n"
+
+lemma "ev m \<Longrightarrow> even m"
+