equal
deleted
inserted
replaced
185 apply (rule finite_subset [where B="insert 0 {x. P x}"]) |
185 apply (rule finite_subset [where B="insert 0 {x. P x}"]) |
186 apply (clarsimp simp add: ubasis_until') |
186 apply (clarsimp simp add: ubasis_until') |
187 apply simp |
187 apply simp |
188 done |
188 done |
189 |
189 |
190 subsubsection {* Take function for @{typ ubasis} *} |
190 subsubsection {* Take function for \emph{ubasis} *} |
191 |
191 |
192 definition |
192 definition |
193 ubasis_take :: "nat \<Rightarrow> ubasis \<Rightarrow> ubasis" |
193 ubasis_take :: "nat \<Rightarrow> ubasis \<Rightarrow> ubasis" |
194 where |
194 where |
195 "ubasis_take n = ubasis_until (\<lambda>x. x \<le> n)" |
195 "ubasis_take n = ubasis_until (\<lambda>x. x \<le> n)" |
336 "\<exists>a\<in>Rep_udom x. approx n\<cdot>x = udom_principal (ubasis_take n a)" |
336 "\<exists>a\<in>Rep_udom x. approx n\<cdot>x = udom_principal (ubasis_take n a)" |
337 unfolding approx_udom_def |
337 unfolding approx_udom_def |
338 by (rule udom.completion_approx_eq_principal) |
338 by (rule udom.completion_approx_eq_principal) |
339 |
339 |
340 |
340 |
341 subsection {* Universality of @{typ udom} *} |
341 subsection {* Universality of \emph{udom} *} |
342 |
342 |
343 defaultsort bifinite |
343 defaultsort bifinite |
344 |
344 |
345 subsubsection {* Choosing a maximal element from a finite set *} |
345 subsubsection {* Choosing a maximal element from a finite set *} |
346 |
346 |
814 choose |
814 choose |
815 choose_pos |
815 choose_pos |
816 place |
816 place |
817 sub |
817 sub |
818 |
818 |
819 subsubsection {* EP-pair from any bifinite domain into @{typ udom} *} |
819 subsubsection {* EP-pair from any bifinite domain into \emph{udom} *} |
820 |
820 |
821 definition |
821 definition |
822 udom_emb :: "'a::bifinite \<rightarrow> udom" |
822 udom_emb :: "'a::bifinite \<rightarrow> udom" |
823 where |
823 where |
824 "udom_emb = compact_basis.basis_fun (\<lambda>x. udom_principal (basis_emb x))" |
824 "udom_emb = compact_basis.basis_fun (\<lambda>x. udom_principal (basis_emb x))" |