Theorems · Theorem · geometry

Affine.Simplex.orthogonalProjectionSpan_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] {m n : ℕ}
  {s₁ : Affine.Simplex 𝕜 P m} {s₂ : Affine.Simplex 𝕜 P n} {p₁ p₂ : P},
  Set.range s₁.points = Set.range s₂.points →
    p₁ = p₂ → ↑(s₁.orthogonalProjectionSpan p₁) = ↑(s₂.orthogonalProjectionSpan p₂)

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

RCLikeNormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor