EuclideanGeometry.Sphere.IsDiameter.dist_left_right_div_two
∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : NormedSpace ℝ V] [inst_2 : MetricSpace P]
[inst_3 : NormedAddTorsor V P] {s : EuclideanGeometry.Sphere P} {p₁ p₂ : P},
s.IsDiameter p₁ p₂ → dist p₁ p₂ / 2 = s.radius- Defined in
- Mathlib.Geometry.Euclidean.Sphere.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- NormedSpacestatement and proof · cited by 12,499
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- EuclideanGeometry.Spherestatement and proof · cited by 233
- EuclideanGeometry.Sphere.radiusstatement and proof · cited by 123
- mul_div_cancel_left₀proof · cited by 111
- EuclideanGeometry.Sphere.IsDiameterstatement and proof · cited by 31
- EuclideanGeometry.Sphere.IsDiameter.dist_left_rightproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanGeometry.Sphere.IsDiameter.ofDiameter_eqproof · cited by 1