src/HOL/MicroJava/BV/Convert.thy
changeset 9906 5c027cca6262
parent 9757 1024a2d80ac0
child 9941 fe05af7ec816
equal deleted inserted replaced
9905:14a71104a498 9906:5c027cca6262
   381 
   381 
   382   thus ?thesis by blast
   382   thus ?thesis by blast
   383 qed
   383 qed
   384 
   384 
   385 
   385 
   386 theorem sup_loc_update [rulify]:
   386 theorem sup_loc_update [rulified]:
   387   "\<forall> n y. (G \<turnstile> a <=o b) \<longrightarrow> n < length y \<longrightarrow> (G \<turnstile> x <=l y) \<longrightarrow> 
   387   "\<forall> n y. (G \<turnstile> a <=o b) \<longrightarrow> n < length y \<longrightarrow> (G \<turnstile> x <=l y) \<longrightarrow> 
   388           (G \<turnstile> x[n := a] <=l y[n := b])" (is "?P x")
   388           (G \<turnstile> x[n := a] <=l y[n := b])" (is "?P x")
   389 proof (induct x)
   389 proof (induct x)
   390   show "?P []" by simp
   390   show "?P []" by simp
   391 
   391 
   483     show "G \<turnstile> (a!n) <=o (c!n)" .
   483     show "G \<turnstile> (a!n) <=o (c!n)" .
   484   qed
   484   qed
   485 
   485 
   486   with G
   486   with G
   487   show ?thesis 
   487   show ?thesis 
   488     by (auto intro!: all_nth_sup_loc [rulify] dest!: sup_loc_length) 
   488     by (auto intro!: all_nth_sup_loc [rulified] dest!: sup_loc_length) 
   489 qed
   489 qed
   490   
   490   
   491 
   491 
   492 theorem sup_state_trans [trans]:
   492 theorem sup_state_trans [trans]:
   493   "\<lbrakk>G \<turnstile> a <=s b; G \<turnstile> b <=s c\<rbrakk> \<Longrightarrow> G \<turnstile> a <=s c"
   493   "\<lbrakk>G \<turnstile> a <=s b; G \<turnstile> b <=s c\<rbrakk> \<Longrightarrow> G \<turnstile> a <=s c"