src/HOL/List.thy
changeset 72302 d7d90ed4c74e
parent 72184 881bd98bddee
child 72555 653ac845b466
equal deleted inserted replaced
72301:c5d1a01d2d6c 72302:d7d90ed4c74e
  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)