[Merged by Bors] - chore(analysis/convex/strict_convex_space): generalize/add strict_convex_space.of_* lemmas
#17206
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urkud
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Oct 27, 2022
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urkud
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- depends on: [Merged by Bors] - refactor(analysis/convex/strict): rename, golf, generalize #17464
It suffices to verify `∥x + y∥ = ∥x∥ + ∥y∥ → same_ray ℝ x y` for nonzero vectors.
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src/analysis/convex/segment.lean
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| lemma open_segment_subset_union (c : 𝕜) (x y : E) : | ||
| open_segment 𝕜 x y ⊆ insert (line_map x y c) (open_segment 𝕜 x (line_map x y c) ∪ | ||
| open_segment 𝕜 (line_map x y c) y) := |
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This statement could do with a docstring explanation.
EDIT: If you modify it according to my next comment, maybe not.
| rcases lt_trichotomy a c with hac|rfl|hca, | ||
| { right, left, | ||
| have hc : 0 < c, from h₀.trans hac, | ||
| refine ⟨a / c, ⟨div_pos h₀ hc, (div_lt_one hc).2 hac⟩, _⟩, |
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| refine ⟨a / c, ⟨div_pos h₀ hc, (div_lt_one hc).2 hac⟩, _⟩, | |
| refine ⟨a / c, ⟨by positivity, (div_lt_one hc).2 hac⟩, _⟩, |
and in other places.
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What's wrong with short *_pos proofs?
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Not much, but I thought I would showcase positivity!
src/analysis/convex/topology.lean
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| /-- A convex set `s` is strictly convex provided that for any two distinct points of | ||
| `s \ interior s`, the line passing through these points has nonempty intersection with | ||
| `interior s`. -/ | ||
| lemma convex.to_strict_convex' {s : set E} (hs : convex 𝕜 s) |
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| lemma convex.to_strict_convex' {s : set E} (hs : convex 𝕜 s) | |
| lemma convex.strict_convex' {s : set E} (hs : convex 𝕜 s) |
The to_ convention is reserved for instance names.
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We already had convex.strict_convex. I renamed the old lemma to convex.strict_convex_of_open and golfed lemmas about strict_convex_Ixx.
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🔒 Permission denied Existing reviewers: click here to make YaelDillies a reviewer |
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@YaelDillies Did you mean |
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Uh yeah sorry. maintainer merge |
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🚀 Pull request has been placed on the maintainer queue by YaelDillies. |
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bors merge |
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Nov 12, 2022
…nvex_space.of_*` lemmas (#17206)
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Pull request successfully merged into master. Build succeeded: |
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