Affine.Simplex.points_vsub_eulerPoint
∀ {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} (s : Affine.Simplex ℝ P n) (i : Fin (n + 1)),
s.points i -ᵥ s.eulerPoint i = ((↑n - 1) / ↑n) • (s.points i -ᵥ s.mongePoint)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Set.rangeproof · cited by 4,705
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- one_smulproof · cited by 1,374
- NormedAddTorsorstatement and proof · cited by 1,325
- sub_selfproof · cited by 996
- VSub.vsubstatement and proof · cited by 817
- smul_zeroproof · cited by 665
- one_divproof · cited by 624
Cited by2
Results whose statement or proof uses this declaration.
- Affine.Triangle.altitudeFoot_mem_ninePointCircleproof · cited by 0
- Affine.Triangle.eulerPoint_eq_midpointproof · cited by 0