Theorems · Theorem · convex and discrete geometry
convexHull_singleton
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : Module 𝕜 E] (x : E), (convexHull 𝕜) {x} = {x}- Defined in
- Mathlib.Analysis.Convex.Hull
- Cited by
- 7 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.
Cites10
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 · 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
- ClosureOperatorstatement · cited by 371
- convexHullstatement · cited by 163
- convex_singletonproof · cited by 13
- Convex.convexHull_eqproof · cited by 8
Cited by7
Results whose statement or proof uses this declaration.
- convexHull_insertproof · cited by 2
- convexJoin_segmentsproof · cited by 2
- convexHull_eq_singletonproof · cited by 1
- Geometry.SimplicialComplex.vertex_mem_convexHull_iffproof · cited by 1
- ConvexIndependent.injectiveproof · cited by 0
- convexHull_zeroproof · cited by 0
- convexIndependent_iff_finsetproof · cited by 0