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   150 declare ex2seq_UU [simp] ex2seq_nil [simp] ex2seq_cons [simp]  | 
   150 declare ex2seq_UU [simp] ex2seq_nil [simp] ex2seq_cons [simp]  | 
   151   | 
   151   | 
   152   | 
   152   | 
   153 lemma ex2seq_nUUnnil: "ex2seq exec ~= UU & ex2seq exec ~= nil"  | 
   153 lemma ex2seq_nUUnnil: "ex2seq exec ~= UU & ex2seq exec ~= nil"  | 
   154 apply (tactic {* pair_tac @{context} "exec" 1 *}) | 
   154 apply (tactic {* pair_tac @{context} "exec" 1 *}) | 
   155 apply (tactic {* Seq_case_simp_tac @{context} "y" 1 *}) | 
   155 apply (tactic {* Seq_case_simp_tac @{context} "x2" 1 *}) | 
   156 apply (tactic {* pair_tac @{context} "a" 1 *}) | 
   156 apply (tactic {* pair_tac @{context} "a" 1 *}) | 
   157 done  | 
   157 done  | 
   158   | 
   158   | 
   159   | 
   159   | 
   160 subsection {* Interface TL -- TLS *} | 
   160 subsection {* Interface TL -- TLS *} | 
   171 apply clarify  | 
   171 apply clarify  | 
   172 apply (simp split add: split_if)  | 
   172 apply (simp split add: split_if)  | 
   173 (* TL = UU *)  | 
   173 (* TL = UU *)  | 
   174 apply (rule conjI)  | 
   174 apply (rule conjI)  | 
   175 apply (tactic {* pair_tac @{context} "ex" 1 *}) | 
   175 apply (tactic {* pair_tac @{context} "ex" 1 *}) | 
   176 apply (tactic {* Seq_case_simp_tac @{context} "y" 1 *}) | 
   176 apply (tactic {* Seq_case_simp_tac @{context} "x2" 1 *}) | 
   177 apply (tactic {* pair_tac @{context} "a" 1 *}) | 
   177 apply (tactic {* pair_tac @{context} "a" 1 *}) | 
   178 apply (tactic {* Seq_case_simp_tac @{context} "s" 1 *}) | 
   178 apply (tactic {* Seq_case_simp_tac @{context} "s" 1 *}) | 
   179 apply (tactic {* pair_tac @{context} "a" 1 *}) | 
   179 apply (tactic {* pair_tac @{context} "a" 1 *}) | 
   180 (* TL = nil *)  | 
   180 (* TL = nil *)  | 
   181 apply (rule conjI)  | 
   181 apply (rule conjI)  | 
   182 apply (tactic {* pair_tac @{context} "ex" 1 *}) | 
   182 apply (tactic {* pair_tac @{context} "ex" 1 *}) | 
   183 apply (tactic {* Seq_case_tac @{context} "y" 1 *}) | 
   183 apply (tactic {* Seq_case_tac @{context} "x2" 1 *}) | 
   184 apply (simp add: unlift_def)  | 
   184 apply (simp add: unlift_def)  | 
   185 apply fast  | 
   185 apply fast  | 
   186 apply (simp add: unlift_def)  | 
   186 apply (simp add: unlift_def)  | 
   187 apply fast  | 
   187 apply fast  | 
   188 apply (simp add: unlift_def)  | 
   188 apply (simp add: unlift_def)  | 
   191 apply (tactic {* pair_tac @{context} "a" 1 *}) | 
   191 apply (tactic {* pair_tac @{context} "a" 1 *}) | 
   192 (* TL =cons *)  | 
   192 (* TL =cons *)  | 
   193 apply (simp add: unlift_def)  | 
   193 apply (simp add: unlift_def)  | 
   194   | 
   194   | 
   195 apply (tactic {* pair_tac @{context} "ex" 1 *}) | 
   195 apply (tactic {* pair_tac @{context} "ex" 1 *}) | 
   196 apply (tactic {* Seq_case_simp_tac @{context} "y" 1 *}) | 
   196 apply (tactic {* Seq_case_simp_tac @{context} "x2" 1 *}) | 
   197 apply (tactic {* pair_tac @{context} "a" 1 *}) | 
   197 apply (tactic {* pair_tac @{context} "a" 1 *}) | 
   198 apply (tactic {* Seq_case_simp_tac @{context} "s" 1 *}) | 
   198 apply (tactic {* Seq_case_simp_tac @{context} "s" 1 *}) | 
   199 apply (tactic {* pair_tac @{context} "a" 1 *}) | 
   199 apply (tactic {* pair_tac @{context} "a" 1 *}) | 
   200 done  | 
   200 done  | 
   201   | 
   201   |