Theorems · Theorem · functional analysis

dist_left_midpoint_eq_dist_right_midpoint

∀ {V : Type u_1} {P : Type u_2} [inst : SeminormedAddCommGroup V] [inst_1 : PseudoMetricSpace P]
  [inst_2 : NormedAddTorsor V P] {𝕜 : Type u_5} [inst_3 : NormedField 𝕜] [inst_4 : NormedSpace 𝕜 V]
  [inst_5 : Invertible 2] (p₁ p₂ : P), dist p₁ (midpoint 𝕜 p₁ p₂) = dist p₂ (midpoint 𝕜 p₁ p₂)

The midpoint of the segment AB is the same distance from A as it is from B.

Defined in

Mathlib.Analysis.Normed.Affine.AddTorsor

Cited by

2 results in Mathlib

Foundations

Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedAddCommGroupPseudoMetricSpaceNormedAddTorsorNormedFieldNormedSpaceInvertible