EuclideanGeometry.Sphere.IsDiameter.right_mem
∀ {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 → p₂ ∈ s- Defined in
- Mathlib.Geometry.Euclidean.Sphere.Basic
- Cited by
- 7 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.
Cites14
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.Spherestatement and proof · cited by 233
- EuclideanGeometry.Sphere.centerproof · cited by 181
- midpointproof · cited by 123
- EuclideanGeometry.Sphere.IsDiameterstatement and proof · cited by 31
- EuclideanGeometry.mem_sphereproof · cited by 22
- EuclideanGeometry.Sphere.IsDiameter.midpoint_eq_centerproof · cited by 11
Cited by7
Results whose statement or proof uses this declaration.
- EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_wbtwproof · cited by 2
- EuclideanGeometry.Sphere.IsDiameter.symmproof · cited by 2
- EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_distproof · cited by 1
- EuclideanGeometry.Sphere.isDiameter_of_angle_eq_pi_div_twoproof · cited by 0
- Affine.Simplex.eulerPoint_mem_ninePointCircleproof · cited by 0
- EuclideanGeometry.Sphere.isDiameter_iff_right_mem_and_midpoint_eq_centerproof · cited by 0