EuclideanGeometry.Sphere.isDiameter_ofDiameter
∀ {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] (p₁ p₂ : P), (EuclideanGeometry.Sphere.ofDiameter p₁ p₂).IsDiameter p₁ p₂- Defined in
- Mathlib.Geometry.Euclidean.Sphere.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 159 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.distproof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- EuclideanGeometry.Sphere.IsDiameterstatement · cited by 31
- inv_mul_eq_divproof · cited by 26
- Real.norm_ofNatproof · cited by 23
- dist_left_midpointproof · cited by 7
- EuclideanGeometry.Sphere.ofDiameterstatement · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- EuclideanGeometry.Sphere.angle_eq_pi_div_two_iff_mem_sphere_ofDiameterproof · cited by 1
- EuclideanGeometry.Sphere.isDiameter_of_angle_eq_pi_div_twoproof · cited by 0
- EuclideanGeometry.Sphere.isDiameter_iff_ofDiameter_eqproof · cited by 0