equal
deleted
inserted
replaced
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" |