Theorems · Theorem · convex and discrete geometry

lineMap_mem_openSegment

∀ (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] (a b : E) {t : 𝕜}, t ∈ Set.Ioo 0 1 → (AffineMap.lineMap a b) t ∈ openSegment 𝕜 a b

Defined in

Mathlib.Analysis.Convex.Segment

Cited by

1 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Quot.sound

Assumes

RingPartialOrderAddRightMonoAddCommGroupModule