Theorems · Theorem · geometry

EuclideanGeometry.reflection_mem_of_le_of_mem

∀ {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] {s₁ s₂ : AffineSubspace 𝕜 P}
  [inst_5 : Nonempty ↥s₁] [inst_6 : s₁.direction.HasOrthogonalProjection],
  s₁ ≤ s₂ → ∀ {p : P}, p ∈ s₂ → (EuclideanGeometry.reflection s₁) p ∈ s₂

The reflection of a point in a subspace is contained in any larger subspace containing both the point and the subspace reflected in.

Defined in

Mathlib.Geometry.Euclidean.Projection

Cited by

1 results in Mathlib

Foundations

Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNonemptySubmodule.HasOrthogonalProjection