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Merged
affeldt-aist merged 1 commit into from
Sep 16, 2025
Merged

littleoE0 #1707

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2 changes: 2 additions & 0 deletions CHANGELOG_UNRELEASED.md
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Expand Up @@ -33,6 +33,8 @@
+ notation `- 1` in scopes `ereal_dual_scope` and `ereal_scope`
- in `pseudometric_normed_Zmodule.v`:
+ lemma `le0_ball0`
- in `theories/landau.v`:
+ lemma `littleoE0`

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5 changes: 5 additions & 0 deletions theories/landau.v
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Expand Up @@ -390,6 +390,11 @@ Lemma littleoE (tag : unit) (F : filter_on T)
littleo_def F f h -> the_littleo tag F phF f h = f.
Proof. by move=> /asboolP?; rewrite /the_littleo /insubd insubT. Qed.

Lemma littleoE0 (tag : unit) (F : filter_on T)
(phF : phantom (set (set T)) F) f h :
~ littleo_def F f h -> the_littleo tag F phF f h = 0.
Proof. by move=> ?; rewrite /the_littleo /insubd insubN//; apply/asboolP. Qed.

Canonical the_littleo_littleo (tag : unit) (F : filter_on T)
(phF : phantom (set_system T) F) f h := [littleo of the_littleo tag F phF f h].

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