cases: fixes a1 :: "nat \<Rightarrow> 'd"   and a2 :: "'e net_state"   and a3 :: "'f node_action"   and a4 :: "nat \<Rightarrow> 'd"   and a5 :: "'e net_state"   and S :: "(((nat \<Rightarrow> 'd) \<times> 'e net_state) \<times> 'f node_action \<times> (nat \<Rightarrow> 'd) \<times> 'e net_state) set"   and T :: "(((nat \<Rightarrow> 'd) \<times> 'e net_state) \<times> 'f node_action \<times> (nat \<Rightarrow> 'd) \<times> 'e net_state) set" assumes "((a1, a2), a3, a4, a5) \<in> opnet_sos S T" obtains \<sigma> :: "nat \<Rightarrow> 'd" and s :: "'e net_state" and R :: "nat set" and m :: "'f" and \<sigma>' :: "nat \<Rightarrow> 'd" and s' :: "'e net_state" and t :: "'e net_state" and H :: "nat set" and K :: "nat set" and t' :: "'e net_state" where "a1 = \<sigma>'__" and "a2 = SubnetS s__ t__" and "a3 = R__:*cast(m__)" and "a4 = \<sigma>''__" and "a5 = SubnetS s'__ t'__" and "((\<sigma>'__, s__), R__:*cast(m__), \<sigma>''__, s'__) \<in> S" and "((\<sigma>'__, t__), H__\<not>K__:arrive(m__), \<sigma>''__, t'__) \<in> T" and "H__ \<subseteq> R__" and "K__ \<inter> R__ = {}"   | \<sigma> :: "nat \<Rightarrow> 'd" and s :: "'e net_state" and H :: "nat set" and K :: "nat set" and m :: "'f" and \<sigma>' :: "nat \<Rightarrow> 'd" and s' :: "'e net_state" and t :: "'e net_state" and R :: "nat set" and t' :: "'e net_state" where "a1 = \<sigma>'''__" and "a2 = SubnetS sa__ ta__" and "a3 = R:*cast(ma__)" and "a4 = \<sigma>''''__" and "a5 = SubnetS s'a__ t'a__" and "((\<sigma>'''__, sa__), Ha__\<not>Ka__:arrive(ma__), \<sigma>''''__, s'a__) \<in> S" and "((\<sigma>'''__, ta__), R:*cast(ma__), \<sigma>''''__, t'a__) \<in> T" and "Ha__ \<subseteq> R" and "Ka__ \<inter> R = {}"   | \<sigma> :: "nat \<Rightarrow> 'd" and s :: "'e net_state" and H :: "nat set" and K :: "nat set" and m :: "'f" and \<sigma>' :: "nat \<Rightarrow> 'd" and s' :: "'e net_state" and t :: "'e net_state" and H' :: "nat set" and K' :: "nat set" and t' :: "'e net_state" where "a1 = \<sigma>'''''__" and "a2 = SubnetS sb__ tb__" and "a3 = (H \<union> H')\<not>(K \<union> K'):arrive(m)" and "a4 = \<sigma>''''''__" and "a5 = SubnetS s'b__ t'b__" and "((\<sigma>'''''__, sb__), H\<not>K:arrive(m), \<sigma>''''''__, s'b__) \<in> S" and "((\<sigma>'''''__, tb__), H'\<not>K':arrive(m), \<sigma>''''''__, t'b__) \<in> T"   | \<sigma> :: "nat \<Rightarrow> 'd" and s :: "'e net_state" and i :: "nat" and d :: "nat" and \<sigma>' :: "nat \<Rightarrow> 'd" and s' :: "'e net_state" and t :: "'e net_state" where "a1 = \<sigma>'''''''__" and "a2 = SubnetS sc__ tc__" and "a3 = i__:deliver(d__)" and "a4 = \<sigma>''''''''__" and "a5 = SubnetS s'c__ tc__" and "((\<sigma>'''''''__, sc__), i__:deliver(d__), \<sigma>''''''''__, s'c__) \<in> S"   | \<sigma> :: "nat \<Rightarrow> 'd" and t :: "'e net_state" and i :: "nat" and d :: "nat" and \<sigma>' :: "nat \<Rightarrow> 'd" and t' :: "'e net_state" and s :: "'e net_state" where "a1 = \<sigma>'''''''''__" and "a2 = SubnetS sd__ td__" and "a3 = ia__:deliver(d)" and "a4 = \<sigma>''''''''''__" and "a5 = SubnetS sd__ t'c__" and "((\<sigma>'''''''''__, td__), ia__:deliver(d), \<sigma>''''''''''__, t'c__) \<in> T"   | \<sigma> :: "nat \<Rightarrow> 'd" and s :: "'e net_state" and \<sigma>' :: "nat \<Rightarrow> 'd" and s' :: "'e net_state" and t :: "'e net_state" where "a1 = \<sigma>'''''''''''__" and "a2 = SubnetS se__ te__" and "a3 = \<tau>" and "a4 = \<sigma>''''''''''''__" and "a5 = SubnetS s'd__ te__" and "((\<sigma>'''''''''''__, se__), \<tau>, \<sigma>''''''''''''__, s'd__) \<in> S"   | \<sigma> :: "nat \<Rightarrow> 'd" and t :: "'e net_state" and \<sigma>' :: "nat \<Rightarrow> 'd" and t' :: "'e net_state" and s :: "'e net_state" where "a1 = \<sigma>'''''''''''''__" and "a2 = SubnetS sf__ tf__" and "a3 = \<tau>" and "a4 = \<sigma>''''''''''''''__" and "a5 = SubnetS sf__ t'd__" and "((\<sigma>'''''''''''''__, tf__), \<tau>, \<sigma>''''''''''''''__, t'd__) \<in> T"   | \<sigma> :: "nat \<Rightarrow> 'd" and s :: "'e net_state" and i :: "nat" and i' :: "nat" and \<sigma>' :: "nat \<Rightarrow> 'd" and s' :: "'e net_state" and t :: "'e net_state" and t' :: "'e net_state" where "a1 = \<sigma>'''''''''''''''__" and "a2 = SubnetS sg__ tg__" and "a3 = connect(ib__, i'__)" and "a4 = \<sigma>''''''''''''''''__" and "a5 = SubnetS s'e__ t'e__" and "((\<sigma>'''''''''''''''__, sg__), connect(ib__, i'__), \<sigma>''''''''''''''''__, s'e__) \<in> S" and "((\<sigma>'''''''''''''''__, tg__), connect(ib__, i'__), \<sigma>''''''''''''''''__, t'e__) \<in> T"   | \<sigma> :: "nat \<Rightarrow> 'd" and s :: "'e net_state" and i :: "nat" and i' :: "nat" and \<sigma>' :: "nat \<Rightarrow> 'd" and s' :: "'e net_state" and t :: "'e net_state" and t' :: "'e net_state" where "a1 = \<sigma>" and "a2 = SubnetS s t" and "a3 = disconnect(i, i')" and "a4 = \<sigma>'" and "a5 = SubnetS s' t'" and "((\<sigma>, s), disconnect(i, i'), \<sigma>', s') \<in> S" and "((\<sigma>, t), disconnect(i, i'), \<sigma>', t') \<in> T"