equal
deleted
inserted
replaced
44 unfolding compact_take_def |
44 unfolding compact_take_def |
45 by (simp add: Abs_compact_basis_inverse) |
45 by (simp add: Abs_compact_basis_inverse) |
46 |
46 |
47 lemmas approx_Rep_compact_basis = Rep_compact_take [symmetric] |
47 lemmas approx_Rep_compact_basis = Rep_compact_take [symmetric] |
48 |
48 |
49 interpretation compact_basis!: |
49 interpretation compact_basis: |
50 basis_take sq_le compact_take |
50 basis_take sq_le compact_take |
51 proof |
51 proof |
52 fix n :: nat and a :: "'a compact_basis" |
52 fix n :: nat and a :: "'a compact_basis" |
53 show "compact_take n a \<sqsubseteq> a" |
53 show "compact_take n a \<sqsubseteq> a" |
54 unfolding compact_le_def |
54 unfolding compact_le_def |
90 |
90 |
91 definition |
91 definition |
92 approximants :: "'a \<Rightarrow> 'a compact_basis set" where |
92 approximants :: "'a \<Rightarrow> 'a compact_basis set" where |
93 "approximants = (\<lambda>x. {a. Rep_compact_basis a \<sqsubseteq> x})" |
93 "approximants = (\<lambda>x. {a. Rep_compact_basis a \<sqsubseteq> x})" |
94 |
94 |
95 interpretation compact_basis!: |
95 interpretation compact_basis: |
96 ideal_completion sq_le compact_take Rep_compact_basis approximants |
96 ideal_completion sq_le compact_take Rep_compact_basis approximants |
97 proof |
97 proof |
98 fix w :: 'a |
98 fix w :: 'a |
99 show "preorder.ideal sq_le (approximants w)" |
99 show "preorder.ideal sq_le (approximants w)" |
100 proof (rule sq_le.idealI) |
100 proof (rule sq_le.idealI) |