src/HOL/Nat.thy
changeset 52729 412c9e0381a1
parent 52435 6646bb548c6b
child 53374 a14d2a854c02
     1.1 --- a/src/HOL/Nat.thy	Wed Jul 24 17:15:59 2013 +0200
     1.2 +++ b/src/HOL/Nat.thy	Thu Jul 25 08:57:16 2013 +0200
     1.3 @@ -444,7 +444,7 @@
     1.4  
     1.5  end
     1.6  
     1.7 -instantiation nat :: bot
     1.8 +instantiation nat :: order_bot
     1.9  begin
    1.10  
    1.11  definition bot_nat :: nat where
    1.12 @@ -1318,7 +1318,8 @@
    1.13  
    1.14  subsection {* Kleene iteration *}
    1.15  
    1.16 -lemma Kleene_iter_lpfp: assumes "mono f" and "f p \<le> p" shows "(f^^k) bot \<le> p"
    1.17 +lemma Kleene_iter_lpfp:
    1.18 +assumes "mono f" and "f p \<le> p" shows "(f^^k) (bot::'a::order_bot) \<le> p"
    1.19  proof(induction k)
    1.20    case 0 show ?case by simp
    1.21  next