Theorems · Theorem · convex and discrete geometry

Convex.mem_extremePoints_iff_convex_sdiff

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Ring 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜]
  [inst_3 : AddCommGroup E] [inst_4 : Module 𝕜 E] [DenselyOrdered 𝕜] [Module.IsTorsionFree 𝕜 E] {A : Set E} {x : E},
  Convex 𝕜 A → (x ∈ Set.extremePoints 𝕜 A ↔ x ∈ A ∧ Convex 𝕜 (A \ {x}))

Defined in

Mathlib.Analysis.Convex.Extreme

Cited by

3 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingLinearOrderIsStrictOrderedRingAddCommGroupModuleDenselyOrderedModule.IsTorsionFree