Theorems · Theorem · convex and discrete geometry
affineSpan_convexHull
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Ring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommGroup E]
[inst_3 : Module 𝕜 E] (s : Set E), affineSpan 𝕜 ((convexHull 𝕜) s) = affineSpan 𝕜 s- Defined in
- Mathlib.Analysis.Convex.Hull
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- 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
- le_antisymmproof · cited by 2,068
- AffineSubspacestatement · cited by 871
- affineSpanstatement · cited by 417
- ClosureOperatorstatement · cited by 371
- convexHullstatement · cited by 163
- subset_convexHullproof · cited by 36
Cited by2
Results whose statement or proof uses this declaration.
- affineSpan_eq_top_of_nonempty_interiorproof · cited by 1
- vectorSpan_segmentproof · cited by 1