--- a/src/HOLCF/Representable.thy Fri Mar 05 13:55:36 2010 -0800
+++ b/src/HOLCF/Representable.thy Fri Mar 05 13:56:04 2010 -0800
@@ -12,6 +12,38 @@
("Tools/Domain/domain_isomorphism.ML")
begin
+subsection {* Preliminaries: Take proofs *}
+
+lemma deflation_abs_rep:
+ fixes abs and rep and d
+ assumes abs_iso: "\<And>x. rep\<cdot>(abs\<cdot>x) = x"
+ assumes rep_iso: "\<And>y. abs\<cdot>(rep\<cdot>y) = y"
+ shows "deflation d \<Longrightarrow> deflation (abs oo d oo rep)"
+by (rule ep_pair.deflation_e_d_p) (simp add: ep_pair.intro assms)
+
+lemma deflation_chain_min:
+ assumes chain: "chain d"
+ assumes defl: "\<And>n. deflation (d n)"
+ shows "d m\<cdot>(d n\<cdot>x) = d (min m n)\<cdot>x"
+proof (rule linorder_le_cases)
+ assume "m \<le> n"
+ with chain have "d m \<sqsubseteq> d n" by (rule chain_mono)
+ then have "d m\<cdot>(d n\<cdot>x) = d m\<cdot>x"
+ by (rule deflation_below_comp1 [OF defl defl])
+ moreover from `m \<le> n` have "min m n = m" by simp
+ ultimately show ?thesis by simp
+next
+ assume "n \<le> m"
+ with chain have "d n \<sqsubseteq> d m" by (rule chain_mono)
+ then have "d m\<cdot>(d n\<cdot>x) = d n\<cdot>x"
+ by (rule deflation_below_comp2 [OF defl defl])
+ moreover from `n \<le> m` have "min m n = n" by simp
+ ultimately show ?thesis by simp
+qed
+
+use "Tools/Domain/domain_take_proofs.ML"
+
+
subsection {* Class of representable types *}
text "Overloaded embedding and projection functions between
@@ -180,33 +212,6 @@
shows "abs\<cdot>(rep\<cdot>x) = x"
unfolding abs_def rep_def by (simp add: REP [symmetric])
-lemma deflation_abs_rep:
- fixes abs and rep and d
- assumes abs_iso: "\<And>x. rep\<cdot>(abs\<cdot>x) = x"
- assumes rep_iso: "\<And>y. abs\<cdot>(rep\<cdot>y) = y"
- shows "deflation d \<Longrightarrow> deflation (abs oo d oo rep)"
-by (rule ep_pair.deflation_e_d_p) (simp add: ep_pair.intro assms)
-
-lemma deflation_chain_min:
- assumes chain: "chain d"
- assumes defl: "\<And>n. deflation (d n)"
- shows "d m\<cdot>(d n\<cdot>x) = d (min m n)\<cdot>x"
-proof (rule linorder_le_cases)
- assume "m \<le> n"
- with chain have "d m \<sqsubseteq> d n" by (rule chain_mono)
- then have "d m\<cdot>(d n\<cdot>x) = d m\<cdot>x"
- by (rule deflation_below_comp1 [OF defl defl])
- moreover from `m \<le> n` have "min m n = m" by simp
- ultimately show ?thesis by simp
-next
- assume "n \<le> m"
- with chain have "d n \<sqsubseteq> d m" by (rule chain_mono)
- then have "d m\<cdot>(d n\<cdot>x) = d n\<cdot>x"
- by (rule deflation_below_comp2 [OF defl defl])
- moreover from `n \<le> m` have "min m n = n" by simp
- ultimately show ?thesis by simp
-qed
-
subsection {* Proving a subtype is representable *}
@@ -777,7 +782,6 @@
subsection {* Constructing Domain Isomorphisms *}
-use "Tools/Domain/domain_take_proofs.ML"
use "Tools/Domain/domain_isomorphism.ML"
setup {*