Affine.Triangle.orthocenter_mem_altitude
∀ {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) {i₁ : Fin 3}, t.orthocenter ∈ Affine.Simplex.altitude t i₁The orthocenter lies in the altitudes.
- Defined in
- Mathlib.Geometry.Euclidean.MongePoint
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineSubspacestatement and proof · cited by 871
- Affine.Trianglestatement and proof · cited by 75
- Affine.Triangle.orthocenterstatement · cited by 23
- Affine.Simplex.mongePointproof · cited by 20
- Affine.Simplex.altitudestatement and proof · cited by 17
- Affine.Triangle.orthocenter_eq_mongePointproof · cited by 7
- Affine.Simplex.mongePoint_mem_mongePlaneproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Affine.Triangle.affineSpan_orthocenter_point_le_altitudeproof · cited by 1
- Affine.Triangle.altitudeFoot_mem_ninePointCircleproof · cited by 0