# HG changeset patch # User Andreas Lochbihler # Date 1499077189 -7200 # Node ID 4c999b5d78e24137b6f4ea71a750ff4ef0358ebb # Parent 453f9cabddb5a13f9151de350dd53e39cb953f22 qualify Complete_Partial_Order2.compact diff -r 453f9cabddb5 -r 4c999b5d78e2 src/HOL/Library/Complete_Partial_Order2.thy --- a/src/HOL/Library/Complete_Partial_Order2.thy Sat Jul 01 16:39:56 2017 +0200 +++ b/src/HOL/Library/Complete_Partial_Order2.thy Mon Jul 03 12:19:49 2017 +0200 @@ -904,6 +904,7 @@ end +setup \Sign.map_naming (Name_Space.mandatory_path "ccpo")\ inductive compact :: "('a set \ 'a) \ ('a \ 'a \ bool) \ 'a \ bool" for lub ord x @@ -912,15 +913,15 @@ ccpo.admissible lub ord (\y. x \ y) \ \ compact lub ord x" -hide_fact (open) compact +setup \Sign.map_naming Name_Space.parent_path\ context ccpo begin lemma compactI: assumes "ccpo.admissible Sup op \ (\y. \ x \ y)" - shows "compact Sup op \ x" + shows "ccpo.compact Sup op \ x" using assms -proof(rule compact.intros) +proof(rule ccpo.compact.intros) have neq: "(\y. x \ y) = (\y. \ x \ y \ \ y \ x)" by(auto) show "ccpo.admissible Sup op \ (\y. x \ y)" by(subst neq)(rule admissible_disj admissible_not_below assms)+ @@ -928,7 +929,7 @@ lemma compact_bot: assumes "x = Sup {}" - shows "compact Sup op \ x" + shows "ccpo.compact Sup op \ x" proof(rule compactI) show "ccpo.admissible Sup op \ (\y. \ x \ y)" using assms by(auto intro!: ccpo.admissibleI intro: ccpo_Sup_least chain_empty) @@ -937,11 +938,11 @@ end lemma admissible_compact_neq' [THEN admissible_subst, cont_intro, simp]: - shows admissible_compact_neq: "compact lub ord k \ ccpo.admissible lub ord (\x. k \ x)" -by(simp add: compact.simps) + shows admissible_compact_neq: "ccpo.compact lub ord k \ ccpo.admissible lub ord (\x. k \ x)" +by(simp add: ccpo.compact.simps) lemma admissible_neq_compact' [THEN admissible_subst, cont_intro, simp]: - shows admissible_neq_compact: "compact lub ord k \ ccpo.admissible lub ord (\x. x \ k)" + shows admissible_neq_compact: "ccpo.compact lub ord k \ ccpo.admissible lub ord (\x. x \ k)" by(subst eq_commute)(rule admissible_compact_neq) context partial_function_definitions begin @@ -1728,7 +1729,7 @@ "mono_option B \ mono_option (\f. map_option g (B f))" unfolding map_conv_bind_option by(rule bind_mono) simp_all -lemma compact_flat_lub [cont_intro]: "compact (flat_lub x) (flat_ord x) y" +lemma compact_flat_lub [cont_intro]: "ccpo.compact (flat_lub x) (flat_ord x) y" using flat_interpretation[THEN ccpo] proof(rule ccpo.compactI[OF _ ccpo.admissibleI]) fix A