Theorems · Theorem · convex and discrete geometry

convex_halfSpace_lt

∀ {𝕜 : Type u_1} {E : Type u_2} {β : Type u_4} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
  [inst_3 : Module 𝕜 E] [inst_4 : AddCommMonoid β] [inst_5 : PartialOrder β] [IsOrderedCancelAddMonoid β]
  [inst_7 : Module 𝕜 β] [PosSMulStrictMono 𝕜 β] {f : E → β}, IsLinearMap 𝕜 f → ∀ (r : β), Convex 𝕜 {w | f w < r}

Defined in

Mathlib.Analysis.Convex.Basic

Cited by

2 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderAddCommMonoidModuleAddCommMonoidPartialOrderIsOrderedCancelAddMonoidModulePosSMulStrictMono