Theorems · Theorem · convex and discrete geometry

left_mem_openSegment_iff

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Ring 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜]
  [inst_3 : AddCommGroup E] [inst_4 : Module 𝕜 E] {x y : E} [DenselyOrdered 𝕜] [Module.IsTorsionFree 𝕜 E],
  x ∈ openSegment 𝕜 x y ↔ x = y

Defined in

Mathlib.Analysis.Convex.Segment

Cited by

2 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingLinearOrderIsStrictOrderedRingAddCommGroupModuleDenselyOrderedModule.IsTorsionFree