Theorems · Theorem · geometry

EuclideanGeometry.orthogonalProjection_map

∀ {𝕜 : Type u_1} {V : Type u_2} {P : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup V]
  [inst_2 : InnerProductSpace 𝕜 V] {V₂ : Type u_4} {P₂ : Type u_5} [inst_3 : NormedAddCommGroup V₂]
  [inst_4 : InnerProductSpace 𝕜 V₂] [inst_5 : MetricSpace P] [inst_6 : NormedAddTorsor V P] [inst_7 : MetricSpace P₂]
  [inst_8 : NormedAddTorsor V₂ P₂] (s : AffineSubspace 𝕜 P) [inst_9 : Nonempty ↥s]
  [inst_10 : s.direction.HasOrthogonalProjection] (f : P →ᵃⁱ[𝕜] P₂)
  [inst_11 : (AffineSubspace.map f.toAffineMap s).direction.HasOrthogonalProjection] (p : P),
  ↑((EuclideanGeometry.orthogonalProjection (AffineSubspace.map f.toAffineMap s)) (f p)) =
    f ↑((EuclideanGeometry.orthogonalProjection s) p)

Defined in

Mathlib.Geometry.Euclidean.Projection

Cited by

3 results in Mathlib

Foundations

Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorMetricSpaceNormedAddTorsorNonemptySubmodule.HasOrthogonalProjectionSubmodule.HasOrthogonalProjection