Theorems · Theorem · convex and discrete geometry
Set.Subsingleton.convex
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : Module 𝕜 E] {s : Set E}, s.Subsingleton → Convex 𝕜 s- Defined in
- Mathlib.Analysis.Convex.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 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
- Convexstatement · cited by 551
- Set.Subsingletonstatement and proof · cited by 276
- Set.Subsingleton.pairwiseproof · cited by 13
- convex_iff_pairwise_posproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- convex_singletonproof · cited by 13