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author | huffman |

Fri, 05 Mar 2010 13:56:04 -0800 | |

changeset 35595 | 1785d387627a |

parent 35594 | 47d68e33ca29 |

child 35596 | 49a02dab35ed |

move take_proofs-related stuff to a new section

--- 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 {*