Theorems · Theorem · geometry

Affine.Simplex.altitudeFoot_mem_affineSpan_image_compl

∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] {n : ℕ} [inst_4 : NeZero n] (s : Affine.Simplex ℝ P n) (i : Fin (n + 1)),
  s.altitudeFoot i ∈ affineSpan ℝ (s.points '' {i}ᶜ)

Defined in

Mathlib.Geometry.Euclidean.Altitude

Cited by

1 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNeZero