equal
deleted
inserted
replaced
424 apply (case_tac "\<not> stable r step ss p") |
424 apply (case_tac "\<not> stable r step ss p") |
425 apply simp_all |
425 apply simp_all |
426 done |
426 done |
427 also have "\<And>f. (UN p:{..<size ss}. f p) = \<Union>(set (map f [0..<size ss]))" by auto |
427 also have "\<And>f. (UN p:{..<size ss}. f p) = \<Union>(set (map f [0..<size ss]))" by auto |
428 also note Sup_set_fold also note fold_map |
428 also note Sup_set_fold also note fold_map |
429 also have "op \<union> \<circ> (\<lambda>p. if \<not> stable r step ss p then {p} else {}) = |
429 also have "(\<union>) \<circ> (\<lambda>p. if \<not> stable r step ss p then {p} else {}) = |
430 (\<lambda>p A. if \<not>stable r step ss p then insert p A else A)" |
430 (\<lambda>p A. if \<not>stable r step ss p then insert p A else A)" |
431 by(auto simp add: fun_eq_iff) |
431 by(auto simp add: fun_eq_iff) |
432 finally show ?thesis . |
432 finally show ?thesis . |
433 qed |
433 qed |
434 |
434 |