Theorems · Theorem · geometry

EuclideanGeometry.OrthocentricSystem.eq_insert_orthocenter

∀ {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 →
    ∀ {t : Affine.Triangle ℝ P}, Set.range t.points ⊆ s → s = insert t.orthocenter (Set.range t.points)

Given any triangle in an orthocentric system, the fourth point is its orthocenter.

Defined in

Mathlib.Geometry.Euclidean.MongePoint

Cited by

0 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor