[Merged by Bors] - feat(ENNReal): liminf/limsup/iInf/iSup and multiplication#17656
Closed
[Merged by Bors] - feat(ENNReal): liminf/limsup/iInf/iSup and multiplication#17656
Conversation
PR summary 6afef36680Import changes for modified filesNo significant changes to the import graph Import changes for all files
|
YaelDillies
reviewed
Oct 11, 2024
YaelDillies
reviewed
Oct 15, 2024
Contributor
YaelDillies
left a comment
There was a problem hiding this comment.
I could shave 49 lines off. If you are happy with the changes, then LGTM.
Collaborator
Author
|
@YaelDillies : I am more than happy with your changes ; you did an excellent job! I've got a few ideas to improve this aspect of mathlib, but I'll write a separate PR for that -- it'll be much easier with this part done. |
YaelDillies
reviewed
Oct 20, 2024
|
🚀 Pull request has been placed on the maintainer queue by YaelDillies. |
Contributor
|
bors r+ |
mathlib-bors bot
pushed a commit
that referenced
this pull request
Oct 21, 2024
This PR adds a few lemmas about multiplication and liminf/limsup/iInf/iSup: `mul_iInf_le_iInf_mul`, `iSup_mul_le_mul_iSup`, `mul_liminf_le_liminf_mul` and three avatars of the latter. The strategy adopted is the same as for similar lemmas in EReal (`EReal.add_iInf_le_iInf_add`...): we suffer to prove the key result `mul_le_of_forall_mul_le`, and everything is deduced from there. Note that `ENNReal.mul_le_of_forall_mul_le` could be deduced much faster from `EReal.add_le_of_forall_add_le` using the exp (both as an order isomorphism and as a "group" morphism). However, I wanted to avoid importing special functions, which unfortunately leads to a much longer and painful proof. This also generalizes some lemmas in #15373 : `limsup_mul_le'` therein can be replaced by `limsup_mul_le_mul_limsup` with some easy plug-and-play; if `_root_.Real.limsup_mul_le` is still needed, I can write another PR to deal with it (most of the work is already done anyways -- I think I can prove `mul_le_of_forall_mul_le` in NNReal, and leverage it to simplify the proof in ENNReal). Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
Contributor
|
Pull request successfully merged into master. Build succeeded: |
1 task
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
3 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
This PR adds a few lemmas about multiplication and liminf/limsup/iInf/iSup:
mul_iInf_le_iInf_mul,iSup_mul_le_mul_iSup,mul_liminf_le_liminf_muland three avatars of the latter.The strategy adopted is the same as for similar lemmas in EReal (
EReal.add_iInf_le_iInf_add...): we suffer to prove the key resultmul_le_of_forall_mul_le, and everything is deduced from there.Note that
ENNReal.mul_le_of_forall_mul_lecould be deduced much faster fromEReal.add_le_of_forall_add_leusing the exp (both as an order isomorphism and as a "group" morphism). However, I wanted to avoid importing special functions, which unfortunately leads to a much longer and painful proof.This also generalizes some lemmas in #15373 :
limsup_mul_le'therein can be replaced bylimsup_mul_le_mul_limsupwith some easy plug-and-play; if_root_.Real.limsup_mul_leis still needed, I can write another PR to deal with it (most of the work is already done anyways -- I think I can provemul_le_of_forall_mul_lein NNReal, and leverage it to simplify the proof in ENNReal).Paging @mariainesdff (for #15373).