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ball_filter can be generalized #1042

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affeldt-aist opened this issue Oct 3, 2023 · 0 comments · Fixed by #1043
Closed

ball_filter can be generalized #1042

affeldt-aist opened this issue Oct 3, 2023 · 0 comments · Fixed by #1043
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enhancement ✨ This issue/PR is about adding new features enhancing the library
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@affeldt-aist
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from realFieldType to realDomainType (that does not seem to open any new perspective though):

Global Instance ball_filter (R : realDomainType) (t : R) : Filter
  [set P | exists2 i : R, 0 < i & ball_ Num.norm t i `<=` P].
Proof.
apply: Build_Filter; [by exists 1 | move=> P Q | move=> P Q PQ]; rewrite /mkset.
- move=> -[x x0 xP] [y ? yQ]; exists (Num.min x y); first by rewrite lt_minr x0.
  move=> z tz; split.
  by apply: xP; rewrite /= (lt_le_trans tz) // le_minl lexx.
  by apply: yQ; rewrite /= (lt_le_trans tz) // le_minl lexx orbT.
- by move=> -[x ? xP]; exists x => //; apply: (subset_trans xP).
Qed.

#[global] Hint Extern 0
    (Filter [set P | exists2 i, _ & ball_ _ _ i `<=` P]) =>
  (apply: ball_filter) : typeclass_instances.
@affeldt-aist affeldt-aist added the enhancement ✨ This issue/PR is about adding new features enhancing the library label Oct 3, 2023
@affeldt-aist affeldt-aist added this to the 0.6.6 milestone Oct 3, 2023
affeldt-aist added a commit to affeldt-aist/analysis that referenced this issue Oct 3, 2023
affeldt-aist added a commit to affeldt-aist/analysis that referenced this issue Oct 5, 2023
proux01 pushed a commit that referenced this issue Oct 9, 2023
affeldt-aist added a commit to affeldt-aist/analysis that referenced this issue Oct 10, 2023
affeldt-aist added a commit that referenced this issue Oct 11, 2023
IshiguroYoshihiro pushed a commit to IshiguroYoshihiro/analysis that referenced this issue Oct 24, 2023
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