Theorems · Theorem · geometry

inner_vsub_right_eq_zero_symm

∀ {𝕜 : Type u_1} {V : Type u_2} {P : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup V]
  [inst_2 : InnerProductSpace 𝕜 V] [inst_3 : MetricSpace P] [inst_4 : NormedAddTorsor V P] {v : V} {a b : P},
  inner 𝕜 v (a -ᵥ b) = 0 ↔ inner 𝕜 v (b -ᵥ a) = 0

Defined in

Mathlib.Analysis.InnerProductSpace.Affine

Cited by

2 results in Mathlib

Foundations

Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor