Theorems · Theorem · geometry

Affine.Simplex.altitudeFoot_restrict

∀ {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) (S : AffineSubspace ℝ P)
  (hS : affineSpan ℝ (Set.range s.points) ≤ S) (i : Fin (n + 1)), ↑((s.restrict S hS).altitudeFoot i) = s.altitudeFoot i

Defined in

Mathlib.Geometry.Euclidean.Altitude

Cited by

0 results in Mathlib

Foundations

Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNeZero