Theorems · Theorem · convex and discrete geometry
subset_convexJoin_left
∀ {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} [IsOrderedRing 𝕜], t.Nonempty → s ⊆ convexJoin 𝕜 s t- Defined in
- Mathlib.Analysis.Convex.Join
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Set.Nonemptystatement and proof · cited by 2,627
- IsOrderedRingstatement and proof · cited by 777
- convexJoinstatement and proof · cited by 31
- left_mem_segmentproof · cited by 8
- segment_subset_convexJoinproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Convex.convexHull_unionproof · cited by 1
- subset_convexJoin_rightproof · cited by 1