Theorems · Theorem · convex and discrete geometry
StarConvex.add_smul_sub_mem
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Ring 𝕜] [inst_1 : PartialOrder 𝕜] [AddRightMono 𝕜] [inst_3 : AddCommGroup E]
[inst_4 : Module 𝕜 E] {x y : E} {s : Set E}, StarConvex 𝕜 x s → y ∈ s → ∀ {t : 𝕜}, 0 ≤ t → t ≤ 1 → x + t • (y - x) ∈ s- Defined in
- Mathlib.Analysis.Convex.Star
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- Set.mem_image_of_memproof · cited by 371
- AddRightMonostatement and proof · cited by 367
- StarConvexstatement and proof · cited by 62
- StarConvex.segment_subsetproof · cited by 4
- segment_eq_image'proof · cited by 3
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