--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Unification/Swap.thy	Sun Apr 29 11:29:56 2012 +0100
@@ -0,0 +1,55 @@
+
+theory Swap = Main:
+
+consts 
+  swapa   :: "(string \<times> string) \<Rightarrow> string \<Rightarrow> string"
+  swapas  :: "(string \<times> string)list \<Rightarrow> string \<Rightarrow> string"
+primrec
+  "swapa (b,c) a = (if b = a then c else (if c = a then b else a))"
+
+primrec
+  "swapas []     a = a"
+  "swapas (x#pi) a = swapa x (swapas pi a)"
+
+lemma [simp]: 
+  "swapas [(a,a)] b=b"
+apply(auto)
+done
+
+lemma swapas_append: 
+  "swapas (pi1@pi2) a = swapas pi1 (swapas pi2 a)"
+apply(induct_tac pi1, auto)
+done 
+
+lemma [simp]: 
+  "swapas (rev pi) (swapas pi a) = a"
+apply(induct_tac pi)
+apply(simp_all add: swapas_append, auto)
+done
+
+lemma swapas_rev_pi_a: 
+  "swapas pi a = b \<Longrightarrow> swapas (rev pi) b = a"
+apply(auto)
+done
+
+lemma [simp]: 
+  "swapas pi (swapas (rev pi) a) = a"
+apply(rule swapas_rev_pi_a[of "(rev pi)" _ _,simplified])
+apply(simp)
+done
+
+lemma swapas_rev_pi_b: 
+  "swapas (rev pi) a = b \<Longrightarrow> swapas pi b = a"
+apply(auto)
+done
+
+lemma swapas_comm: 
+  "(swapas (pi@[(a,b)]) c) = (swapas ([(swapas pi a,swapas pi b)]@pi) c)"
+apply(auto)
+apply(simp_all only: swapas_append)
+apply(auto)
+apply(drule swapas_rev_pi_a, simp)
+apply(drule swapas_rev_pi_a, simp)
+done
+
+end
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