equal
deleted
inserted
replaced
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" |