src/HOL/Finite_Set.thy
changeset 35416 d8d7d1b785af
parent 35267 8dfd816713c6
child 35577 43b93e294522
equal deleted inserted replaced
35342:4dc65845eab3 35416:d8d7d1b785af
  2526   for f :: "'a => 'a => 'a"
  2526   for f :: "'a => 'a => 'a"
  2527 where
  2527 where
  2528   fold1Set_insertI [intro]:
  2528   fold1Set_insertI [intro]:
  2529    "\<lbrakk> fold_graph f a A x; a \<notin> A \<rbrakk> \<Longrightarrow> fold1Set f (insert a A) x"
  2529    "\<lbrakk> fold_graph f a A x; a \<notin> A \<rbrakk> \<Longrightarrow> fold1Set f (insert a A) x"
  2530 
  2530 
  2531 constdefs
  2531 definition fold1 :: "('a => 'a => 'a) => 'a set => 'a" where
  2532   fold1 :: "('a => 'a => 'a) => 'a set => 'a"
       
  2533   "fold1 f A == THE x. fold1Set f A x"
  2532   "fold1 f A == THE x. fold1Set f A x"
  2534 
  2533 
  2535 lemma fold1Set_nonempty:
  2534 lemma fold1Set_nonempty:
  2536   "fold1Set f A x \<Longrightarrow> A \<noteq> {}"
  2535   "fold1Set f A x \<Longrightarrow> A \<noteq> {}"
  2537 by(erule fold1Set.cases, simp_all)
  2536 by(erule fold1Set.cases, simp_all)