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[Merged by Bors] - feat(analysis/convex/function): helper lemmas and general cleanup #9438

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@YaelDillies YaelDillies commented Sep 28, 2021

This adds

  • convex_iff_pairwise_on_pos
  • convex_on_iff_forall_pos, concave_on_iff_forall_pos,
  • convex_on_iff_forall_pos_ne, concave_on_iff_forall_pos_ne
  • convex_on.convex_strict_epigraph, concave_on.convex_strict_hypograph

generalizes some instance assumptions:

  • convex_on.translate_ didn't need module π•œ Ξ² but has_scalar π•œ Ξ².
  • some proofs in analysis.convex.exposed were vestigially using ℝ.

and golfs proofs.


This is preparatory work for #9437.

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@YaelDillies YaelDillies added the awaiting-review The author would like community review of the PR label Sep 28, 2021
@eric-wieser
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Can you summarize what the generalizations to the instances are in the PR description?

@@ -423,6 +423,21 @@ begin
exact h hx hy ha hb hab
end

lemma convex_iff_forall_pos_ne :
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Is there any point keeping convex_iff_forall_pos around? Either you need the strong forward direction, which is just rw convex, or you need the strong backwards direction, which is rw <-convex_iff_forall_pos_ne. I think having an intermediate strength version is unecessary.

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I think it's fine to keep? We can nuke it later if we want to.

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
@github-actions github-actions bot added the merge-conflict Please `git merge origin/master` then a bot will remove this label. label Sep 29, 2021
@github-actions github-actions bot removed the merge-conflict Please `git merge origin/master` then a bot will remove this label. label Sep 30, 2021
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Thanks πŸŽ‰

bors d+

(Please merge after updating the PR description following Eric's remark.)

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bors bot commented Sep 30, 2021

✌️ YaelDillies can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

@github-actions github-actions bot added delegated The PR author may merge after reviewing final suggestions. and removed awaiting-review The author would like community review of the PR labels Sep 30, 2021
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bors merge

bors bot pushed a commit that referenced this pull request Oct 1, 2021
)

This adds
* `convex_iff_pairwise_on_pos`
* `convex_on_iff_forall_pos`, `concave_on_iff_forall_pos`,
* `convex_on_iff_forall_pos_ne`, `concave_on_iff_forall_pos_ne`
* `convex_on.convex_strict_epigraph`, `concave_on.convex_strict_hypograph`

generalizes some instance assumptions:
* `convex_on.translate_` didn't need `module π•œ Ξ²` but `has_scalar π•œ Ξ²`.
* some proofs in `analysis.convex.exposed` were vestigially using `ℝ`.
 
and golfs proofs.
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bors bot commented Oct 1, 2021

Build failed (retrying...):

bors bot pushed a commit that referenced this pull request Oct 1, 2021
)

This adds
* `convex_iff_pairwise_on_pos`
* `convex_on_iff_forall_pos`, `concave_on_iff_forall_pos`,
* `convex_on_iff_forall_pos_ne`, `concave_on_iff_forall_pos_ne`
* `convex_on.convex_strict_epigraph`, `concave_on.convex_strict_hypograph`

generalizes some instance assumptions:
* `convex_on.translate_` didn't need `module π•œ Ξ²` but `has_scalar π•œ Ξ²`.
* some proofs in `analysis.convex.exposed` were vestigially using `ℝ`.
 
and golfs proofs.
@bors
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bors bot commented Oct 1, 2021

Build failed (retrying...):

bors bot pushed a commit that referenced this pull request Oct 1, 2021
)

This adds
* `convex_iff_pairwise_on_pos`
* `convex_on_iff_forall_pos`, `concave_on_iff_forall_pos`,
* `convex_on_iff_forall_pos_ne`, `concave_on_iff_forall_pos_ne`
* `convex_on.convex_strict_epigraph`, `concave_on.convex_strict_hypograph`

generalizes some instance assumptions:
* `convex_on.translate_` didn't need `module π•œ Ξ²` but `has_scalar π•œ Ξ²`.
* some proofs in `analysis.convex.exposed` were vestigially using `ℝ`.
 
and golfs proofs.
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bors bot commented Oct 1, 2021

Build failed (retrying...):

@sgouezel
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sgouezel commented Oct 1, 2021

bors r-
Can you merge master, fix the errors if any, and put it back on the queue?
bors d+

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bors bot commented Oct 1, 2021

✌️ YaelDillies can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

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bors bot commented Oct 1, 2021

Canceled.

@jcommelin jcommelin added the awaiting-CI The author would like to see what CI has to say before doing more work. label Oct 1, 2021
@sgouezel sgouezel added awaiting-author A reviewer has asked the author a question or requested changes and removed awaiting-CI The author would like to see what CI has to say before doing more work. labels Oct 1, 2021
@YaelDillies
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bors merge

bors bot pushed a commit that referenced this pull request Oct 2, 2021
)

This adds
* `convex_iff_pairwise_on_pos`
* `convex_on_iff_forall_pos`, `concave_on_iff_forall_pos`,
* `convex_on_iff_forall_pos_ne`, `concave_on_iff_forall_pos_ne`
* `convex_on.convex_strict_epigraph`, `concave_on.convex_strict_hypograph`

generalizes some instance assumptions:
* `convex_on.translate_` didn't need `module π•œ Ξ²` but `has_scalar π•œ Ξ²`.
* some proofs in `analysis.convex.exposed` were vestigially using `ℝ`.
 
and golfs proofs.
@bors
Copy link

bors bot commented Oct 2, 2021

Build failed (retrying...):

bors bot pushed a commit that referenced this pull request Oct 3, 2021
)

This adds
* `convex_iff_pairwise_on_pos`
* `convex_on_iff_forall_pos`, `concave_on_iff_forall_pos`,
* `convex_on_iff_forall_pos_ne`, `concave_on_iff_forall_pos_ne`
* `convex_on.convex_strict_epigraph`, `concave_on.convex_strict_hypograph`

generalizes some instance assumptions:
* `convex_on.translate_` didn't need `module π•œ Ξ²` but `has_scalar π•œ Ξ²`.
* some proofs in `analysis.convex.exposed` were vestigially using `ℝ`.
 
and golfs proofs.
@bors
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bors bot commented Oct 3, 2021

Pull request successfully merged into master.

Build succeeded:

@bors bors bot changed the title feat(analysis/convex/function): helper lemmas and general cleanup [Merged by Bors] - feat(analysis/convex/function): helper lemmas and general cleanup Oct 3, 2021
@bors bors bot closed this Oct 3, 2021
@bors bors bot deleted the convex_on_cleanup branch October 3, 2021 02:48
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4 participants