cases: fixes a1 :: "'c constr list \<times> nat \<times> 'c TESL_atomic list \<times> 'c TESL_atomic list"   and a2 :: "'c constr list \<times> nat \<times> 'c TESL_atomic list \<times> 'c TESL_atomic list" assumes "a1 \<hookrightarrow>\<^sub>e a2" obtains \<Gamma> :: "'c constr list" and n :: "nat" and K\<^sub>1 :: "clock" and \<tau> :: "'c tag_const" and K\<^sub>2 :: "clock" and \<Psi> :: "'c TESL_atomic list" and \<Phi> :: "'c TESL_atomic list" where "a1 = \<Gamma>__, n__ \<turnstile> (K\<^sub>1__ sporadic \<tau>__ on K\<^sub>2__) # \<Psi>__ \<triangleright> \<Phi>__" and "a2 = \<Gamma>__, n__ \<turnstile> \<Psi>__ \<triangleright> (K\<^sub>1__ sporadic \<tau>__ on K\<^sub>2__) # \<Phi>__"   | \<Gamma> :: "'c constr list" and n :: "nat" and K\<^sub>1 :: "clock" and \<tau> :: "'c tag_const" and K\<^sub>2 :: "clock" and \<Psi> :: "'c TESL_atomic list" and \<Phi> :: "'c TESL_atomic list" where "a1 = \<Gamma>'__, na__ \<turnstile> (K\<^sub>1'__ sporadic \<tau> on K\<^sub>2'__) # \<Psi>'__ \<triangleright> \<Phi>'__" and "a2 = K\<^sub>1'__ \<Up> na__ # K\<^sub>2'__ \<Down> na__ @ \<tau> # \<Gamma>'__, na__ \<turnstile> \<Psi>'__ \<triangleright> \<Phi>'__"   | \<Gamma> :: "'c constr list" and n :: "nat" and K\<^sub>1 :: "clock" and K\<^sub>2 :: "clock" and R :: "'c tag_const \<times> 'c tag_const \<Rightarrow> bool" and \<Psi> :: "'c TESL_atomic list" and \<Phi> :: "'c TESL_atomic list" where "a1 = \<Gamma>''__, nb__ \<turnstile> (time-relation \<lfloor>K\<^sub>1''__, K\<^sub>2''__\<rfloor> \<in> R) # \<Psi>''__ \<triangleright> \<Phi>''__" and "a2 = \<lfloor>\<tau>\<^sub>v\<^sub>a\<^sub>r (K\<^sub>1''__, nb__), \<tau>\<^sub>v\<^sub>a\<^sub>r (K\<^sub>2''__, nb__)\<rfloor> \<in> R # \<Gamma>''__, nb__ \<turnstile> \<Psi>''__ \<triangleright> (time-relation \<lfloor>K\<^sub>1''__, K\<^sub>2''__\<rfloor> \<in> R) # \<Phi>''__"   | \<Gamma> :: "'c constr list" and n :: "nat" and K\<^sub>1 :: "clock" and K\<^sub>2 :: "clock" and \<Psi> :: "'c TESL_atomic list" and \<Phi> :: "'c TESL_atomic list" where "a1 = \<Gamma>'''__, nc__ \<turnstile> (K\<^sub>1'''__ implies K\<^sub>2'''__) # \<Psi>'''__ \<triangleright> \<Phi>'''__" and "a2 = K\<^sub>1'''__ \<not>\<Up> nc__ # \<Gamma>'''__, nc__ \<turnstile> \<Psi>'''__ \<triangleright> (K\<^sub>1'''__ implies K\<^sub>2'''__) # \<Phi>'''__"   | \<Gamma> :: "'c constr list" and n :: "nat" and K\<^sub>1 :: "clock" and K\<^sub>2 :: "clock" and \<Psi> :: "'c TESL_atomic list" and \<Phi> :: "'c TESL_atomic list" where "a1 = \<Gamma>''''__, nd__ \<turnstile> (K\<^sub>1''''__ implies K\<^sub>2''''__) # \<Psi>''''__ \<triangleright> \<Phi>''''__" and "a2 = K\<^sub>1''''__ \<Up> nd__ # K\<^sub>2''''__ \<Up> nd__ # \<Gamma>''''__, nd__ \<turnstile> \<Psi>''''__ \<triangleright> (K\<^sub>1''''__ implies K\<^sub>2''''__) # \<Phi>''''__"   | \<Gamma> :: "'c constr list" and n :: "nat" and K\<^sub>1 :: "clock" and K\<^sub>2 :: "clock" and \<Psi> :: "'c TESL_atomic list" and \<Phi> :: "'c TESL_atomic list" where "a1 = \<Gamma>'''''__, ne__ \<turnstile> (K\<^sub>1'''''__ implies not K\<^sub>2'''''__) # \<Psi>'''''__ \<triangleright> \<Phi>'''''__" and "a2 = K\<^sub>1'''''__ \<not>\<Up> ne__ # \<Gamma>'''''__, ne__ \<turnstile> \<Psi>'''''__ \<triangleright> (K\<^sub>1'''''__ implies not K\<^sub>2'''''__) # \<Phi>'''''__"   | \<Gamma> :: "'c constr list" and n :: "nat" and K\<^sub>1 :: "clock" and K\<^sub>2 :: "clock" and \<Psi> :: "'c TESL_atomic list" and \<Phi> :: "'c TESL_atomic list" where "a1 = \<Gamma>''''''__, nf__ \<turnstile> (K\<^sub>1''''''__ implies not K\<^sub>2''''''__) # \<Psi>''''''__ \<triangleright> \<Phi>''''''__" and "a2 = K\<^sub>1''''''__ \<Up> nf__ # K\<^sub>2''''''__ \<not>\<Up> nf__ # \<Gamma>''''''__, nf__ \<turnstile> \<Psi>''''''__ \<triangleright> (K\<^sub>1''''''__ implies not K\<^sub>2''''''__) # \<Phi>''''''__"   | \<Gamma> :: "'c constr list" and n :: "nat" and K\<^sub>1 :: "clock" and \<delta>\<tau> :: "'c tag_const" and K\<^sub>2 :: "clock" and K\<^sub>3 :: "clock" and \<Psi> :: "'c TESL_atomic list" and \<Phi> :: "'c TESL_atomic list" where "a1 = \<Gamma>'''''''__, ng__ \<turnstile> (K\<^sub>1'''''''__ time-delayed by \<delta>\<tau>__ on K\<^sub>2'''''''__ implies K\<^sub>3__) # \<Psi>'''''''__ \<triangleright> \<Phi>'''''''__" and "a2 = K\<^sub>1'''''''__ \<not>\<Up> ng__ # \<Gamma>'''''''__, ng__ \<turnstile> \<Psi>'''''''__ \<triangleright> (K\<^sub>1'''''''__ time-delayed by \<delta>\<tau>__ on K\<^sub>2'''''''__ implies K\<^sub>3__) # \<Phi>'''''''__"   | \<Gamma> :: "'c constr list" and n :: "nat" and K\<^sub>1 :: "clock" and \<delta>\<tau> :: "'c tag_const" and K\<^sub>2 :: "clock" and K\<^sub>3 :: "clock" and \<Psi> :: "'c TESL_atomic list" and \<Phi> :: "'c TESL_atomic list" where "a1 = \<Gamma>''''''''__, nh__ \<turnstile> (K\<^sub>1''''''''__ time-delayed by \<delta>\<tau> on K\<^sub>2''''''''__ implies K\<^sub>3) # \<Psi>''''''''__ \<triangleright> \<Phi>''''''''__" and "a2 = K\<^sub>1''''''''__ \<Up> nh__ # K\<^sub>2''''''''__ @ nh__ \<oplus> \<delta>\<tau> \<Rightarrow> K\<^sub>3 # \<Gamma>''''''''__, nh__ \<turnstile> \<Psi>''''''''__ \<triangleright> (K\<^sub>1''''''''__ time-delayed by \<delta>\<tau> on K\<^sub>2''''''''__ implies K\<^sub>3) # \<Phi>''''''''__"   | \<Gamma> :: "'c constr list" and n :: "nat" and K\<^sub>1 :: "clock" and K\<^sub>2 :: "clock" and \<Psi> :: "'c TESL_atomic list" and \<Phi> :: "'c TESL_atomic list" where "a1 = \<Gamma>'''''''''__, ni__ \<turnstile> (K\<^sub>1'''''''''__ weakly precedes K\<^sub>2'''''''''__) # \<Psi>'''''''''__ \<triangleright> \<Phi>'''''''''__" and "a2 = \<lceil>#\<^sup>\<le> K\<^sub>2'''''''''__ ni__, #\<^sup>\<le> K\<^sub>1'''''''''__ ni__\<rceil> \<in> \<lambda>(x, y). x \<le> y # \<Gamma>'''''''''__, ni__ \<turnstile> \<Psi>'''''''''__ \<triangleright> (K\<^sub>1'''''''''__ weakly precedes K\<^sub>2'''''''''__) # \<Phi>'''''''''__"   | \<Gamma> :: "'c constr list" and n :: "nat" and K\<^sub>1 :: "clock" and K\<^sub>2 :: "clock" and \<Psi> :: "'c TESL_atomic list" and \<Phi> :: "'c TESL_atomic list" where "a1 = \<Gamma>''''''''''__, nj__ \<turnstile> (K\<^sub>1''''''''''__ strictly precedes K\<^sub>2''''''''''__) # \<Psi>''''''''''__ \<triangleright> \<Phi>''''''''''__" and "a2 = \<lceil>#\<^sup>\<le> K\<^sub>2''''''''''__ nj__, #\<^sup>< K\<^sub>1''''''''''__ nj__\<rceil> \<in> \<lambda>(x, y). x \<le> y # \<Gamma>''''''''''__, nj__ \<turnstile> \<Psi>''''''''''__ \<triangleright> (K\<^sub>1''''''''''__ strictly precedes K\<^sub>2''''''''''__) # \<Phi>''''''''''__"   | \<Gamma> :: "'c constr list" and n :: "nat" and K\<^sub>1 :: "clock" and K\<^sub>2 :: "clock" and \<Psi> :: "'c TESL_atomic list" and \<Phi> :: "'c TESL_atomic list" where "a1 = \<Gamma>'''''''''''__, nk__ \<turnstile> (K\<^sub>1'''''''''''__ kills K\<^sub>2'''''''''''__) # \<Psi>'''''''''''__ \<triangleright> \<Phi>'''''''''''__" and "a2 = K\<^sub>1'''''''''''__ \<not>\<Up> nk__ # \<Gamma>'''''''''''__, nk__ \<turnstile> \<Psi>'''''''''''__ \<triangleright> (K\<^sub>1'''''''''''__ kills K\<^sub>2'''''''''''__) # \<Phi>'''''''''''__"   | \<Gamma> :: "'c constr list" and n :: "nat" and K\<^sub>1 :: "clock" and K\<^sub>2 :: "clock" and \<Psi> :: "'c TESL_atomic list" and \<Phi> :: "'c TESL_atomic list" where "a1 = \<Gamma>, n \<turnstile> (K\<^sub>1 kills K\<^sub>2) # \<Psi> \<triangleright> \<Phi>" and "a2 = K\<^sub>1 \<Up> n # K\<^sub>2 \<not>\<Up> \<ge> n # \<Gamma>, n \<turnstile> \<Psi> \<triangleright> (K\<^sub>1 kills K\<^sub>2) # \<Phi>"