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[Merged by Bors] - fix: Incorrect integral curve existence theorem for vector fields #6875

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[Merged by Bors] - fix: Incorrect integral curve existence theorem for vector fields #6875

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@winstonyin winstonyin commented Aug 30, 2023 •
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exists_isPicardLindelof_const_of_contDiffOn_nhds had unnecessarily specific assumptions.

ContDiffOn assumption is replaced with ContDiffAt.

ProperSpace E assumption is removed.

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@winstonyin winstonyin added awaiting-review The author would like community review of the PR t-analysis Analysis (normed *, calculus) labels Aug 31, 2023
@winstonyin winstonyin changed the title feat: Improve integral curve existence theorem for vector fields fix: Incorrect integral curve existence theorem for vector fields Sep 1, 2023
mcdoll
mcdoll reviewed Sep 3, 2023
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Mathlib/Analysis/ODE/PicardLindelof.lean Outdated Show resolved Hide resolved
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Mathlib/Analysis/ODE/PicardLindelof.lean
split_ifs with h
· rwa [← h] at hr'
· exact (mul_div_cancel' (r / 2) h).le }
#align exists_is_picard_lindelof_const_of_cont_diff_on_nhds exists_isPicardLindelof_const_of_contDiffOn_nhds
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You should not delete #aligns (same below)

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What if the theorem name and statement have changed?

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I would still keep the #align.

Mathlib/Analysis/ODE/PicardLindelof.lean
Comment on lines -440 to -441
∃ f : ℝ → E, f t₀ = x₀ ∧ ∀ t ∈ Ioo (t₀ - ε) (t₀ + ε), f t ∈ s ∧ HasDerivAt f (v (f t)) t := by
obtain ⟨ε, hε, L, R, C, hpl⟩ := exists_isPicardLindelof_const_of_contDiffOn_nhds t₀ x₀ hv hs
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I might be very stupid here, but it seems to me that your version is less strong in the sense that you don't have control over the image of f?

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I think it's my original statement of the theorem that was a bit stupid. Since f is differentiable at t₀, you can just shrink ε until f t ∈ s for any s ∈ nhds x₀.

@mcdoll mcdoll added awaiting-author A reviewer has asked the author a question or requested changes and removed awaiting-review The author would like community review of the PR labels Sep 3, 2023
@bors bors bot changed the base branch from master to ScottCarnahan/BinomialRing2 September 17, 2023 03:26
@semorrison semorrison changed the base branch from ScottCarnahan/BinomialRing2 to master September 17, 2023 12:06
@winstonyin winstonyin added awaiting-review The author would like community review of the PR and removed awaiting-author A reviewer has asked the author a question or requested changes labels Oct 20, 2023
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Update Mathlib/Analysis/ODE/PicardLindelof.lean
00b3005 
Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
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The new statements are a lot nicer!

Please add back the #align.

bors d+

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bors bot commented Oct 23, 2023

✌️ winstonyin 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 and removed awaiting-review The author would like community review of the PR labels Oct 23, 2023
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bors r+

bors bot pushed a commit that referenced this pull request Oct 24, 2023
@winstonyin
fix: Incorrect integral curve existence theorem for vector fields (#6875
f201111 
)

`exists_isPicardLindelof_const_of_contDiffOn_nhds` had unnecessarily specific assumptions.

`ContDiffOn` assumption is replaced with `ContDiffAt`.

`ProperSpace E` assumption is removed.
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@bors bors bot changed the title fix: Incorrect integral curve existence theorem for vector fields [Merged by Bors] - fix: Incorrect integral curve existence theorem for vector fields Oct 24, 2023
@bors bors bot closed this Oct 24, 2023
@bors bors bot deleted the picardlindeloffix branch October 24, 2023 08:20
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