Affine.Triangle.orthocenter_mem_affineSpan
∀ {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] (t : Affine.Triangle ℝ P), t.orthocenter ∈ affineSpan ℝ (Set.range t.points)The orthocenter lies in the affine span.
- Defined in
- Mathlib.Geometry.Euclidean.MongePoint
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Set.rangestatement · cited by 4,705
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineSubspacestatement · cited by 871
- affineSpanstatement · cited by 417
- Affine.Simplex.pointsstatement · cited by 391
- Affine.Trianglestatement and proof · cited by 75
- Affine.Triangle.orthocenterstatement · cited by 23
- Affine.Simplex.mongePoint_mem_affineSpanproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Affine.Triangle.altitude_replace_orthocenter_eq_affineSpanproof · cited by 1
- EuclideanGeometry.affineSpan_of_orthocentricSystemproof · cited by 1