Theorems · Theorem · convex and discrete geometry

StrictConvex.add_smul_sub_mem

∀ {𝕜 : Type u_1} {E : Type u_3} [inst : Ring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : TopologicalSpace E]
  [inst_3 : AddCommGroup E] [inst_4 : Module 𝕜 E] {s : Set E} {x y : E} [AddRightMono 𝕜],
  StrictConvex 𝕜 s → x ∈ s → y ∈ s → x ≠ y → ∀ {t : 𝕜}, 0 < t → t < 1 → x + t • (y - x) ∈ interior s

Defined in

Mathlib.Analysis.Convex.Strict

Cited by

0 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Quot.sound

Assumes

RingPartialOrderTopologicalSpaceAddCommGroupModuleAddRightMono