equal
deleted
inserted
replaced
5324 |
5324 |
5325 lemma card_lists_distinct_length_eq': |
5325 lemma card_lists_distinct_length_eq': |
5326 assumes "k < card A" |
5326 assumes "k < card A" |
5327 shows "card {xs. length xs = k \<and> distinct xs \<and> set xs \<subseteq> A} = \<Prod>{card A - k + 1 .. card A}" |
5327 shows "card {xs. length xs = k \<and> distinct xs \<and> set xs \<subseteq> A} = \<Prod>{card A - k + 1 .. card A}" |
5328 proof - |
5328 proof - |
5329 from \<open>k < card A\<close> have "finite A" and "k \<le> card A" using card_infinite by force+ |
5329 from \<open>k < card A\<close> have "finite A" and "k \<le> card A" using card.infinite by force+ |
5330 from this show ?thesis by (rule card_lists_distinct_length_eq) |
5330 from this show ?thesis by (rule card_lists_distinct_length_eq) |
5331 qed |
5331 qed |
5332 |
5332 |
5333 lemma infinite_UNIV_listI: "\<not> finite(UNIV::'a list set)" |
5333 lemma infinite_UNIV_listI: "\<not> finite(UNIV::'a list set)" |
5334 by (metis UNIV_I finite_maxlen length_replicate less_irrefl) |
5334 by (metis UNIV_I finite_maxlen length_replicate less_irrefl) |