src/HOL/Finite_Set.thy
changeset 53374 a14d2a854c02
parent 53015 a1119cf551e8
child 53820 9c7e97d67b45
equal deleted inserted replaced
53373:3ca9e79ac926 53374:a14d2a854c02
  1101   assumes "finite A" and "x \<in> A"
  1101   assumes "finite A" and "x \<in> A"
  1102   shows "F A = f x (F (A - {x}))"
  1102   shows "F A = f x (F (A - {x}))"
  1103 proof -
  1103 proof -
  1104   from `x \<in> A` obtain B where A: "A = insert x B" and "x \<notin> B"
  1104   from `x \<in> A` obtain B where A: "A = insert x B" and "x \<notin> B"
  1105     by (auto dest: mk_disjoint_insert)
  1105     by (auto dest: mk_disjoint_insert)
  1106   moreover from `finite A` this have "finite B" by simp
  1106   moreover from `finite A` A have "finite B" by simp
  1107   ultimately show ?thesis by simp
  1107   ultimately show ?thesis by simp
  1108 qed
  1108 qed
  1109 
  1109 
  1110 lemma insert_remove:
  1110 lemma insert_remove:
  1111   assumes "finite A"
  1111   assumes "finite A"