Theorems · Theorem · geometry

EuclideanGeometry.orthogonalProjection_congr

∀ {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}
  {p₁ p₂ : P} [inst_5 : Nonempty ↥s₁] [inst_6 : s₁.direction.HasOrthogonalProjection] (h : s₁ = s₂),
  p₁ = p₂ → ↑((EuclideanGeometry.orthogonalProjection s₁) p₁) = ↑((EuclideanGeometry.orthogonalProjection s₂) p₂)

Since both instance arguments are propositions, allow simp to rewrite them alongside the s argument. Note that without the coercion to P, the LHS and RHS would have different types.

Defined in

Mathlib.Geometry.Euclidean.Projection

Cited by

8 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNonemptySubmodule.HasOrthogonalProjection