Theorems · Theorem · convex and discrete geometry

sameRay_of_mem_segment

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : CommRing 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : IsStrictOrderedRing 𝕜]
  [inst_3 : AddCommGroup E] [inst_4 : Module 𝕜 E] {x y z : E}, x ∈ segment 𝕜 y z → SameRay 𝕜 (x - y) (z - x)

Defined in

Mathlib.Analysis.Convex.Segment

Cited by

2 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingPartialOrderIsStrictOrderedRingAddCommGroupModule