Theorems · Theorem · convex and discrete geometry

midpoint_mem_openSegment

∀ {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] [inst_5 : Invertible 2] (x y : E), midpoint 𝕜 x y ∈ openSegment 𝕜 x y

Defined in

Mathlib.Analysis.Convex.Segment

Cited by

3 results in Mathlib

Foundations

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

Assumes

RingLinearOrderIsStrictOrderedRingAddCommGroupModuleInvertible