equal
deleted
inserted
replaced
5623 case True thus ?thesis by(induction A) (simp_all add: distinct_insort) |
5623 case True thus ?thesis by(induction A) (simp_all add: distinct_insort) |
5624 next |
5624 next |
5625 case False thus ?thesis by simp |
5625 case False thus ?thesis by simp |
5626 qed |
5626 qed |
5627 |
5627 |
|
5628 lemmas sorted_list_of_set = set_sorted_list_of_set sorted_sorted_list_of_set distinct_sorted_list_of_set |
|
5629 |
5628 lemma sorted_list_of_set_sort_remdups [code]: |
5630 lemma sorted_list_of_set_sort_remdups [code]: |
5629 "sorted_list_of_set (set xs) = sort (remdups xs)" |
5631 "sorted_list_of_set (set xs) = sort (remdups xs)" |
5630 proof - |
5632 proof - |
5631 interpret comp_fun_commute insort by (fact comp_fun_commute_insort) |
5633 interpret comp_fun_commute insort by (fact comp_fun_commute_insort) |
5632 show ?thesis by (simp add: sorted_list_of_set.eq_fold sort_conv_fold fold_set_fold_remdups) |
5634 show ?thesis by (simp add: sorted_list_of_set.eq_fold sort_conv_fold fold_set_fold_remdups) |
6054 apply (rule allI, case_tac x, simp, simp) |
6056 apply (rule allI, case_tac x, simp, simp) |
6055 by blast |
6057 by blast |
6056 |
6058 |
6057 lemma lexord_irrefl: |
6059 lemma lexord_irrefl: |
6058 "irrefl R \<Longrightarrow> irrefl (lexord R)" |
6060 "irrefl R \<Longrightarrow> irrefl (lexord R)" |
6059 by (simp add: irrefl_def lexord_irreflexive) |
6061 by (simp add: irrefl_def lexord_irreflexive) |
6060 |
6062 |
6061 lemma lexord_asym: |
6063 lemma lexord_asym: |
6062 assumes "asym R" |
6064 assumes "asym R" |
6063 shows "asym (lexord R)" |
6065 shows "asym (lexord R)" |
6064 proof |
6066 proof |