Theorems · Theorem · geometry

EuclideanGeometry.orthogonalProjection_subtype

∀ {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] (s : AffineSubspace 𝕜 P)
  [inst_5 : Nonempty ↥s] (s' : AffineSubspace 𝕜 ↥s) [inst_6 : Nonempty ↥s']
  [inst_7 : s'.direction.HasOrthogonalProjection]
  [inst_8 : (AffineSubspace.map s.subtype s').direction.HasOrthogonalProjection] (p : ↥s),
  ↑↑((EuclideanGeometry.orthogonalProjection s') p) =
    ↑((EuclideanGeometry.orthogonalProjection (AffineSubspace.map s.subtype s')) ↑p)

Defined in

Mathlib.Geometry.Euclidean.Projection

Cited by

1 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNonemptyNonemptySubmodule.HasOrthogonalProjectionSubmodule.HasOrthogonalProjection