Theorems · Theorem · convex and discrete geometry

convex_Ioc

∀ {𝕜 : Type u_1} {β : Type u_4} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid β]
  [inst_3 : PartialOrder β] [IsOrderedCancelAddMonoid β] [inst_5 : Module 𝕜 β] [PosSMulStrictMono 𝕜 β] (r s : β),
  Convex 𝕜 (Set.Ioc r s)

Defined in

Mathlib.Analysis.Convex.Basic

Cited by

8 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderAddCommMonoidPartialOrderIsOrderedCancelAddMonoidModulePosSMulStrictMono