Theorems · Theorem · convex and discrete geometry
segment_subset_convexJoin
∀ {𝕜 : Type u_2} {E : Type u_3} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : Module 𝕜 E] {s t : Set E} {x y : E}, x ∈ s → y ∈ t → segment 𝕜 x y ⊆ convexJoin 𝕜 s t- Defined in
- Mathlib.Analysis.Convex.Join
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- segmentstatement · cited by 120
- convexJoinstatement · cited by 31
- Set.subset_iUnion₂proof · cited by 13
- Set.subset_iUnion₂_of_subsetproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- subset_convexJoin_leftproof · cited by 2