<commit_before>(*  Title:      HOLCF/Adm.thy
    ID:         $Id$
    Author:     <NAME> and <NAME>
*)

header {* Admissibility and compactness *}

theory Adm
imports Cont
begin

defaultsort cpo

subsection {* Definitions *}

definition
  adm :: "('a::cpo \<Rightarrow> bool) \<Rightarrow> bool" where
  "adm P = (\<forall>Y. chain Y \<longrightarrow> (\<forall>i. P (Y i)) \<longrightarrow> P (\<Squnion>i. Y i))"

lemma admI:
   "(\<And>Y. \<lbrakk>chain Y; \<forall>i. P (Y i)\<rbrakk> \<Longrightarrow> P (\<Squnion>i. Y i)) \<Longrightarrow> adm P"
unfolding adm_def by fast

lemma admD: "\<lbrakk>adm P; chain Y; \<And>i. P (Y i)\<rbrakk> \<Longrightarrow> P (\<Squnion>i. Y i)"
unfolding adm_def by fast

lemma triv_admI: "\<forall>x. P x \<Longrightarrow> adm P"
by (rule admI, erule spec)

text {* improved admissibility introduction *}

lemma admI2:
  "(\<And>Y. \<lbrakk>chain Y; \<forall>i. P (Y i); \<forall>i. \<exists>j>i. Y i \<noteq> Y j \<and> Y i \<sqsubseteq> Y j\<rbrakk> 
    \<Longrightarrow> P (\<Squnion>i. Y i)) \<Longrightarrow> adm P"<commit_msg>Adm now imports Ffun rather than Cont, because SetPcpo, which imports Adm, needs functions (since sets are now just functions).<commit_after>(*  Title:      HOLCF/Adm.thy
    ID:         $Id$
    Author:     <NAME> and <NAME>
*)

header {* Admissibility and compactness *}

theory Adm
imports Ffun
begin

defaultsort cpo

subsection {* Definitions *}

definition
  adm :: "('a::cpo \<Rightarrow> bool) \<Rightarrow> bool" where
  "adm P = (\<forall>Y. chain Y \<longrightarrow> (\<forall>i. P (Y i)) \<longrightarrow> P (\<Squnion>i. Y i))"

lemma admI:
   "(\<And>Y. \<lbrakk>chain Y; \<forall>i. P (Y i)\<rbrakk> \<Longrightarrow> P (\<Squnion>i. Y i)) \<Longrightarrow> adm P"
unfolding adm_def by fast

lemma admD: "\<lbrakk>adm P; chain Y; \<And>i. P (Y i)\<rbrakk> \<Longrightarrow> P (\<Squnion>i. Y i)"
unfolding adm_def by fast

lemma triv_admI: "\<forall>x. P x \<Longrightarrow> adm P"
by (rule admI, erule spec)

text {* improved admissibility introduction *}

lemma admI2:
  "(\<And>Y. \<lbrakk>chain Y; \<forall>i. P (Y i); \<forall>i. \<exists>j>i. Y i \<noteq> Y j \<and> Y i \<sqsubseteq> Y j\<rbrakk> 
    \<Longrightarrow> P (\<Squnion>i. Y i)) \<Longrightarrow> adm P"
{'fraction_non_alphanumeric': 0.1794871794871795, 'fraction_numerical': 0.0008841732979664014, 'mean_word_length': 3.535070140280561, 'pattern_counts': {'":': 0, '<': 73, '<?xml version=': 0, '>': 75, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
{'dir': 'git-commits-cleaned', 'id': '5958373', 'n_tokens_mistral': 949, 'n_tokens_neox': 846, 'n_words': 282}