[Merged by Bors] - refactor(analysis/convex/basic): rewrite a few proofs #13658
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Apr 25, 2022
* prove that a closed segment is the union of the corresponding open segment and the endpoints; * use this lemma to golf some proofs; * make the "field" argument of `mem_open_segment_of_ne_left_right` implicit. * use section variables.
YaelDillies
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Apr 25, 2022
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| refine and_congr_right (λ hxA, forall₄_congr $ λ x₁ h₁ x₂ h₂, _), | ||
| split, |
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| refine and_congr_right (λ hxA, forall₄_congr $ λ x₁ h₁ x₂ h₂, _), | |
| split, | |
| refine and_congr_right (λ hxA, forall₄_congr $ λ x₁ h₁ x₂ h₂, ⟨_, λ H hx, _⟩), |
| lemma mem_open_segment_of_ne_left_right {x y z : E} (hx : x ≠ z) (hy : y ≠ z) | ||
| (hz : z ∈ [x -[𝕜] y]) : | ||
| z ∈ open_segment 𝕜 x y := | ||
| lemma insert_endpoints_open_segment (x y : E) : |
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Not sure about the name of that one. I think it's okay, but I would have expected some thing like _left_right instead of _endpoints.
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mem_open_segment_of_ne_left_rightimplicit.