Theorems · Theorem · convex and discrete geometry
Set.OrdConnected.convex
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : LinearOrder E] [IsOrderedAddMonoid E] [inst_5 : Module 𝕜 E] [PosSMulMono 𝕜 E] {s : Set E},
s.OrdConnected → Convex 𝕜 s- Defined in
- Mathlib.Analysis.Convex.Basic
- Cited by
- 4 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.
Cites12
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
- LinearOrderstatement and proof · cited by 8,572
- PartialOrderstatement and proof · cited by 6,410
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Convexstatement · cited by 551
- PosSMulMonostatement and proof · cited by 188
- Set.OrdConnectedstatement and proof · cited by 161
- isChain_of_trichotomousproof · cited by 4
- Set.OrdConnected.convex_of_chainproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Metric.exists_forall_closedEBall_subset_aux₂proof · cited by 3
- Convex.image_derivproof · cited by 0
- Convex.image_derivWithinproof · cited by 0
- Convex.image_hasDerivWithinAtproof · cited by 0