--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Unification/Atoms.thy	Sun Apr 29 11:29:56 2012 +0100
@@ -0,0 +1,46 @@
+
+theory Atoms = Main + Swap + Terms:
+
+consts atms   :: "(string \<times> string) list \<Rightarrow> string set"
+primrec
+"atms [] = {}"
+"atms (x#xs) = ((atms xs) \<union>  {fst(x),snd(x)})"
+
+lemma [simp]: 
+  "atms (xs@ys) = atms xs \<union> atms ys"
+apply(induct_tac xs, auto)
+done
+
+lemma [simp]: 
+  "atms (rev pi) = atms pi"
+apply(induct_tac pi, simp_all)
+done
+
+lemma a_not_in_atms: 
+  "a\<notin>atms pi \<longrightarrow> a = swapas pi a" 
+apply(induct_tac pi, auto)
+done
+
+lemma swapas_pi_ineq_a: 
+  "swapas pi a \<noteq> a \<longrightarrow> a\<in>atms pi"
+apply(case_tac "a\<in>atms pi")
+apply(simp)+
+apply(drule a_not_in_atms[THEN mp])
+apply(simp)
+done
+
+lemma a_ineq_swapas_pi: 
+  "a \<noteq> swapas pi a \<longrightarrow> a\<in>atms pi"
+apply(case_tac "a\<in>atms pi")
+apply(simp_all add: a_not_in_atms)
+done
+
+lemma swapas_pi_in_atms[THEN mp]: 
+  "a\<in>atms pi \<longrightarrow> swapas pi a\<in>atms pi"
+apply(subgoal_tac "\<forall>pi1. (a\<in>atms pi1) \<longrightarrow> swapas pi a\<in>(atms pi1 \<union> atms pi)")
+apply(force)
+apply(induct_tac pi)
+apply(auto)
+done
+
+end
\ No newline at end of file