src/HOL/Library/Multiset.thy
changeset 42809 5b45125b15ba
parent 41505 6d19301074cf
child 42871 1c0b99f950d9
equal deleted inserted replaced
42798:02c88bdabe75 42809:5b45125b15ba
  1597 
  1597 
  1598 definition image_mset :: "('a \<Rightarrow> 'b) \<Rightarrow> 'a multiset \<Rightarrow> 'b multiset" where
  1598 definition image_mset :: "('a \<Rightarrow> 'b) \<Rightarrow> 'a multiset \<Rightarrow> 'b multiset" where
  1599   "image_mset f = fold_mset (op + o single o f) {#}"
  1599   "image_mset f = fold_mset (op + o single o f) {#}"
  1600 
  1600 
  1601 interpretation image_left_comm: fun_left_comm "op + o single o f"
  1601 interpretation image_left_comm: fun_left_comm "op + o single o f"
  1602 proof qed (simp add: add_ac)
  1602 proof qed (simp add: add_ac fun_eq_iff)
  1603 
  1603 
  1604 lemma image_mset_empty [simp]: "image_mset f {#} = {#}"
  1604 lemma image_mset_empty [simp]: "image_mset f {#} = {#}"
  1605 by (simp add: image_mset_def)
  1605 by (simp add: image_mset_def)
  1606 
  1606 
  1607 lemma image_mset_single [simp]: "image_mset f {#x#} = {#f x#}"
  1607 lemma image_mset_single [simp]: "image_mset f {#x#} = {#f x#}"