Theorems · Theorem · convex and discrete geometry

mem_openSegment_of_ne_left_right

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
  [ZeroLEOneClass 𝕜] [inst_4 : Module 𝕜 E] {x y z : E}, x ≠ z → y ≠ z → z ∈ segment 𝕜 x y → z ∈ openSegment 𝕜 x y

Defined in

Mathlib.Analysis.Convex.Segment

Cited by

1 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderAddCommMonoidZeroLEOneClassModule