equal
deleted
inserted
replaced
276 by (auto simp add: orbit_def in_affected dest: range_eq_singletonD [of _ _ 1]) |
276 by (auto simp add: orbit_def in_affected dest: range_eq_singletonD [of _ _ 1]) |
277 qed |
277 qed |
278 |
278 |
279 definition order :: "'a perm \<Rightarrow> 'a \<Rightarrow> nat" |
279 definition order :: "'a perm \<Rightarrow> 'a \<Rightarrow> nat" |
280 where |
280 where |
281 "order f = card \<circ> orbit f" |
281 "order f = card \<circ> orbit f" |
282 |
282 |
283 lemma orbit_subset_eq_affected: |
283 lemma orbit_subset_eq_affected: |
284 assumes "a \<in> affected f" |
284 assumes "a \<in> affected f" |
285 shows "orbit f a \<subseteq> affected f" |
285 shows "orbit f a \<subseteq> affected f" |
286 proof (rule ccontr) |
286 proof (rule ccontr) |