Affine.Simplex.orthogonalProjectionSpan_eulerPoint_mem_ninePointCircle
∀ {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) (i : Fin (n + 1)),
↑((s.faceOpposite i).orthogonalProjectionSpan (s.eulerPoint i)) ∈ s.ninePointCircle- Cited by
- 1 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement · cited by 7,192
- Set.rangestatement and proof · cited by 4,705
- InnerProductSpacestatement and proof · cited by 3,523
- Real.piproof · cited by 1,774
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineSubspacestatement · cited by 871
- Affine.Simplexstatement and proof · cited by 471
- affineSpanstatement and proof · cited by 417
Cited by1
Results whose statement or proof uses this declaration.
- Affine.Triangle.altitudeFoot_mem_ninePointCircleproof · cited by 0