Theorems · Theorem · convex and discrete geometry

Set.OrdConnected.convex_of_chain

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
  [inst_3 : PartialOrder E] [IsOrderedAddMonoid E] [inst_5 : Module 𝕜 E] [PosSMulMono 𝕜 E] {s : Set E},
  s.OrdConnected → IsChain (fun x1 x2 => x1 ≤ x2) s → Convex 𝕜 s

Defined in

Mathlib.Analysis.Convex.Basic

Cited by

1 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderAddCommMonoidPartialOrderIsOrderedAddMonoidModulePosSMulMono