differentiation under integral #1435
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affeldt-aist
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CohenCyril
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Dec 17, 2024
theories/normedtype.v
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| @@ -2651,6 +2660,12 @@ Qed. | |||
| Lemma cvg_zero f a : (f - cst a) @ F --> (0 : V) -> f @ F --> a. | |||
| Proof. by move=> Cfa; apply: cvg_sub0 Cfa (cvg_cst _). Qed. | |||
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| Lemma cvgr_sub0 f a : (fun x => f x - a) @ F --> 0 <-> f @ F --> a. | |||
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I don't understand the naming of this lemma.
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I think that it was named after:
cvge_sub0 : forall {I : Type} {F : set_system I}, Filter F ->
forall {R : realFieldType} (f : I -> \bar R) [k : \bar R],
k \is a fin_num -> (f x - k)%E @[x --> F] --> 0 <-> f x @[x --> F] --> kWhat about cvg_zeroP? Since it is like cvg_zero but going in both directions.
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Following the convention of subr_eq0 the latter should be sube_cvg0, and the former subr_cvg0
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I have added the gauss integral as an application of differentiation under integral |
Co-authored-by: IshiguroYoshihiro <jb.15r.1213@s.thers.ac.jp>
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Motivation for this change
this can certainly be generalized but this version has already been used to prove the Gauss integral so it is maybe worth having anyway
Checklist
CHANGELOG_UNRELEASED.md- [ ] added corresponding documentation in the headersReference: How to document
Reminder to reviewers