src/HOL/Library/Infinite_Set.thy
changeset 44890 22f665a2e91c
parent 44454 6f28f96a09bf
child 46783 3e89a5cab8d7
equal deleted inserted replaced
44889:340df9f3491f 44890:22f665a2e91c
   542     "enumerate S (Suc n) = enumerate (S - {enumerate S 0}) n"
   542     "enumerate S (Suc n) = enumerate (S - {enumerate S 0}) n"
   543   by simp
   543   by simp
   544 
   544 
   545 lemma enumerate_in_set: "infinite S \<Longrightarrow> enumerate S n : S"
   545 lemma enumerate_in_set: "infinite S \<Longrightarrow> enumerate S n : S"
   546 apply (induct n arbitrary: S)
   546 apply (induct n arbitrary: S)
   547  apply (fastsimp intro: LeastI dest!: infinite_imp_nonempty)
   547  apply (fastforce intro: LeastI dest!: infinite_imp_nonempty)
   548 apply simp
   548 apply simp
   549 apply (metis DiffE infinite_remove)
   549 apply (metis DiffE infinite_remove)
   550 done
   550 done
   551 
   551 
   552 declare enumerate_0 [simp del] enumerate_Suc [simp del]
   552 declare enumerate_0 [simp del] enumerate_Suc [simp del]