Theorems · Theorem · convex and discrete geometry

StarConvex.add_smul_mem

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Ring 𝕜] [inst_1 : PartialOrder 𝕜] [AddRightMono 𝕜] [inst_3 : AddCommGroup E]
  [inst_4 : Module 𝕜 E] {x y : E} {s : Set E}, StarConvex 𝕜 x s → x + y ∈ s → ∀ {t : 𝕜}, 0 ≤ t → t ≤ 1 → x + t • y ∈ s

Defined in

Mathlib.Analysis.Convex.Star

Cited by

4 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext

Assumes

RingPartialOrderAddRightMonoAddCommGroupModule