# HG changeset patch # User Andreas Lochbihler # Date 1447689611 -3600 # Node ID e4d7972402ed764147837796559135e9e851e403 # Parent 95a57e288fd4b6d2315385ee463b4e494ebc5194 export internal definition diff -r 95a57e288fd4 -r e4d7972402ed src/HOL/Complete_Partial_Order.thy --- a/src/HOL/Complete_Partial_Order.thy Mon Nov 16 14:27:10 2015 +0100 +++ b/src/HOL/Complete_Partial_Order.thy Mon Nov 16 17:00:11 2015 +0100 @@ -87,12 +87,16 @@ subsection \Transfinite iteration of a function\ +context notes [[inductive_defs]] begin + inductive_set iterates :: "('a \ 'a) \ 'a set" for f :: "'a \ 'a" where step: "x \ iterates f \ f x \ iterates f" | Sup: "chain (op \) M \ \x\M. x \ iterates f \ Sup M \ iterates f" +end + lemma iterates_le_f: "x \ iterates f \ monotone (op \) (op \) f \ x \ f x" by (induct x rule: iterates.induct)