src/HOL/Auth/Yahalom2.thy

 apply (intro exI bexI)
 apply (rule_tac [2] yahalom.Nil
                     [THEN yahalom.YM1, THEN yahalom.Reception,
                      THEN yahalom.YM2, THEN yahalom.Reception,
                      THEN yahalom.YM3, THEN yahalom.Reception,
-                     THEN yahalom.YM4])
-apply possibility
+                     THEN yahalom.YM4], possibility)
 done
 
 lemma Gets_imp_Says:
      "[| Gets B X \<in> set evs; evs \<in> yahalom |] ==> \<exists>A. Says A B X \<in> set evs"
 by (erule rev_mp, erule yahalom.induct, auto)

 
 (*Spy never sees a good agent's shared key!*)
 lemma Spy_see_shrK [simp]:
      "evs \<in> yahalom ==> (Key (shrK A) \<in> parts (knows Spy evs)) = (A \<in> bad)"
 apply (erule yahalom.induct, force,
-       drule_tac [6] YM4_parts_knows_Spy, simp_all)
-apply blast+
+       drule_tac [6] YM4_parts_knows_Spy, simp_all, blast+)
 done
 
 lemma Spy_analz_shrK [simp]:
      "evs \<in> yahalom ==> (Key (shrK A) \<in> analz (knows Spy evs)) = (A \<in> bad)"
 by auto

  "evs \<in> yahalom ==>
    \<forall>K KK. KK <= - (range shrK) -->
           (Key K \<in> analz (Key`KK Un (knows Spy evs))) =
           (K \<in> KK | Key K \<in> analz (knows Spy evs))"
 apply (erule yahalom.induct, force, frule_tac [7] Says_Server_message_form,
-       drule_tac [6] YM4_analz_knows_Spy)
-apply analz_freshK
-apply spy_analz
+       drule_tac [6] YM4_analz_knows_Spy, analz_freshK, spy_analz)
 done
 
 lemma analz_insert_freshK:
      "[| evs \<in> yahalom;  KAB \<notin> range shrK |] ==>
       (Key K \<in> analz (insert (Key KAB) (knows Spy evs))) =

            \<in> set evs -->
           Notes Spy {|na, nb, Key K|} \<notin> set evs -->
           Key K \<notin> analz (knows Spy evs)"
 apply (erule yahalom.induct, force, frule_tac [7] Says_Server_message_form,
        drule_tac [6] YM4_analz_knows_Spy)
-apply (simp_all add: pushes analz_insert_eq analz_insert_freshK)
-apply spy_analz  (*Fake*)
+apply (simp_all add: pushes analz_insert_eq analz_insert_freshK, spy_analz)  (*Fake*)
 apply (blast dest: unique_session_keys)+  (*YM3, Oops*)
 done
 
 
 (*Final version*)