Theorems · Theorem · geometry

EuclideanGeometry.orthogonalProjection_affineSpan_singleton

∀ {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] (p₁ p₂ : P),
  ↑((EuclideanGeometry.orthogonalProjection (affineSpan 𝕜 {p₁})) p₂) = p₁

Defined in

Mathlib.Geometry.Euclidean.Projection

Cited by

2 results in Mathlib

Foundations

Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor