Theorems · Theorem · geometry

EuclideanGeometry.affineSpan_of_orthocentricSystem

∀ {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] {s : Set P},
  EuclideanGeometry.OrthocentricSystem s →
    ∀ {p : Fin 3 → P}, Set.range p ⊆ s → Function.Injective p → affineSpan ℝ (Set.range p) = affineSpan ℝ s

Any three points in an orthocentric system span the same subspace as the whole orthocentric system.

Defined in

Mathlib.Geometry.Euclidean.MongePoint

Cited by

1 results in Mathlib

Foundations

Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor