--- a/src/HOL/Library/Permutations.thy Fri Sep 25 14:12:01 2020 +0100
+++ b/src/HOL/Library/Permutations.thy Fri Sep 25 14:54:52 2020 +0100
@@ -334,14 +334,14 @@
case (insert x F)
{
fix n
- assume card.insert_remove: "card (insert x F) = n"
+ assume card_insert: "card (insert x F) = n"
let ?xF = "{p. p permutes insert x F}"
let ?pF = "{p. p permutes F}"
let ?pF' = "{(b, p). b \<in> insert x F \<and> p \<in> ?pF}"
let ?g = "(\<lambda>(b, p). Fun.swap x b id \<circ> p)"
have xfgpF': "?xF = ?g ` ?pF'"
by (rule permutes_insert[of x F])
- from \<open>x \<notin> F\<close> \<open>finite F\<close> card.insert_remove have Fs: "card F = n - 1"
+ from \<open>x \<notin> F\<close> \<open>finite F\<close> card_insert have Fs: "card F = n - 1"
by auto
from \<open>finite F\<close> insert.hyps Fs have pFs: "card ?pF = fact (n - 1)"
by auto
@@ -383,13 +383,13 @@
then show ?thesis
unfolding inj_on_def by blast
qed
- from \<open>x \<notin> F\<close> \<open>finite F\<close> card.insert_remove have "n \<noteq> 0"
+ from \<open>x \<notin> F\<close> \<open>finite F\<close> card_insert have "n \<noteq> 0"
by auto
then have "\<exists>m. n = Suc m"
by presburger
then obtain m where n: "n = Suc m"
by blast
- from pFs card.insert_remove have *: "card ?xF = fact n"
+ from pFs card_insert have *: "card ?xF = fact n"
unfolding xfgpF' card_image[OF ginj]
using \<open>finite F\<close> \<open>finite ?pF\<close>
by (simp only: Collect_case_prod Collect_mem_eq card_cartesian_product) (simp add: n)