Theorems · Theorem · convex and discrete geometry
convexJoin_iUnion_left
∀ {ι : Sort u_1} {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 : ι → Set E) (t : Set E), convexJoin 𝕜 (⋃ i, s i) t = ⋃ i, convexJoin 𝕜 (s i) 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.
Cites11
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.iUnionstatement and proof · cited by 2,483
- Set.iUnion_congr_Propproof · cited by 374
- segmentproof · cited by 120
- Set.iUnion_existsproof · cited by 45
- convexJoinstatement · cited by 31
- Set.iUnion_commproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- convexJoin_iUnion_rightproof · cited by 0