equal
deleted
inserted
replaced
213 by (rule typedef_po [OF type_definition_fin_defl sq_le_fin_defl_def]) |
213 by (rule typedef_po [OF type_definition_fin_defl sq_le_fin_defl_def]) |
214 |
214 |
215 lemma finite_deflation_Rep_fin_defl: "finite_deflation (Rep_fin_defl d)" |
215 lemma finite_deflation_Rep_fin_defl: "finite_deflation (Rep_fin_defl d)" |
216 using Rep_fin_defl by simp |
216 using Rep_fin_defl by simp |
217 |
217 |
218 interpretation Rep_fin_defl!: finite_deflation "Rep_fin_defl d" |
218 interpretation Rep_fin_defl: finite_deflation "Rep_fin_defl d" |
219 by (rule finite_deflation_Rep_fin_defl) |
219 by (rule finite_deflation_Rep_fin_defl) |
220 |
220 |
221 lemma fin_defl_lessI: |
221 lemma fin_defl_lessI: |
222 "(\<And>x. Rep_fin_defl a\<cdot>x = x \<Longrightarrow> Rep_fin_defl b\<cdot>x = x) \<Longrightarrow> a \<sqsubseteq> b" |
222 "(\<And>x. Rep_fin_defl a\<cdot>x = x \<Longrightarrow> Rep_fin_defl b\<cdot>x = x) \<Longrightarrow> a \<sqsubseteq> b" |
223 unfolding sq_le_fin_defl_def |
223 unfolding sq_le_fin_defl_def |
318 apply (rule profinite_compact_eq_approx) |
318 apply (rule profinite_compact_eq_approx) |
319 apply (erule subst) |
319 apply (erule subst) |
320 apply (rule Rep_fin_defl.compact) |
320 apply (rule Rep_fin_defl.compact) |
321 done |
321 done |
322 |
322 |
323 interpretation fin_defl!: basis_take sq_le fd_take |
323 interpretation fin_defl: basis_take sq_le fd_take |
324 apply default |
324 apply default |
325 apply (rule fd_take_less) |
325 apply (rule fd_take_less) |
326 apply (rule fd_take_idem) |
326 apply (rule fd_take_idem) |
327 apply (erule fd_take_mono) |
327 apply (erule fd_take_mono) |
328 apply (rule fd_take_chain, simp) |
328 apply (rule fd_take_chain, simp) |
368 lemma Rep_alg_defl_principal: |
368 lemma Rep_alg_defl_principal: |
369 "Rep_alg_defl (alg_defl_principal t) = {u. u \<sqsubseteq> t}" |
369 "Rep_alg_defl (alg_defl_principal t) = {u. u \<sqsubseteq> t}" |
370 unfolding alg_defl_principal_def |
370 unfolding alg_defl_principal_def |
371 by (simp add: Abs_alg_defl_inverse sq_le.ideal_principal) |
371 by (simp add: Abs_alg_defl_inverse sq_le.ideal_principal) |
372 |
372 |
373 interpretation alg_defl!: |
373 interpretation alg_defl: |
374 ideal_completion sq_le fd_take alg_defl_principal Rep_alg_defl |
374 ideal_completion sq_le fd_take alg_defl_principal Rep_alg_defl |
375 apply default |
375 apply default |
376 apply (rule ideal_Rep_alg_defl) |
376 apply (rule ideal_Rep_alg_defl) |
377 apply (erule Rep_alg_defl_lub) |
377 apply (erule Rep_alg_defl_lub) |
378 apply (rule Rep_alg_defl_principal) |
378 apply (rule Rep_alg_defl_principal) |
459 apply (drule alg_defl.compact_imp_principal, clarify) |
459 apply (drule alg_defl.compact_imp_principal, clarify) |
460 apply (simp add: cast_alg_defl_principal) |
460 apply (simp add: cast_alg_defl_principal) |
461 apply (rule finite_deflation_Rep_fin_defl) |
461 apply (rule finite_deflation_Rep_fin_defl) |
462 done |
462 done |
463 |
463 |
464 interpretation cast!: deflation "cast\<cdot>d" |
464 interpretation cast: deflation "cast\<cdot>d" |
465 by (rule deflation_cast) |
465 by (rule deflation_cast) |
466 |
466 |
467 lemma "cast\<cdot>(\<Squnion>i. alg_defl_principal (Abs_fin_defl (approx i)))\<cdot>x = x" |
467 lemma "cast\<cdot>(\<Squnion>i. alg_defl_principal (Abs_fin_defl (approx i)))\<cdot>x = x" |
468 apply (subst contlub_cfun_arg) |
468 apply (subst contlub_cfun_arg) |
469 apply (rule chainI) |
469 apply (rule chainI) |