Theorems · Theorem · convex and discrete geometry

image_openSegment

∀ (𝕜 : Type u_1) {E : Type u_2} {F : Type u_3} [inst : Ring 𝕜] [inst_1 : PartialOrder 𝕜] [AddRightMono 𝕜]
  [inst_3 : AddCommGroup E] [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 E] [inst_6 : Module 𝕜 F] (f : E →ᵃ[𝕜] F)
  (a b : E), ⇑f '' openSegment 𝕜 a b = openSegment 𝕜 (f a) (f b)

Defined in

Mathlib.Analysis.Convex.Segment

Cited by

5 results in Mathlib

Foundations

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

Assumes

RingPartialOrderAddRightMonoAddCommGroupAddCommGroupModuleModule