equal
deleted
inserted
replaced
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] |