EuclideanGeometry.Sphere.IsDiameter.left_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 → p₁ ∈ s- Defined in
- Mathlib.Geometry.Euclidean.Sphere.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- NormedAddTorsorstatement and proof · cited by 1,325
- EuclideanGeometry.Spherestatement and proof · cited by 233
- EuclideanGeometry.Sphere.IsDiameterstatement and proof · cited by 31
Cited by8
Results whose statement or proof uses this declaration.
- EuclideanGeometry.Sphere.IsDiameter.right_memproof · cited by 7
- EuclideanGeometry.Sphere.IsDiameter.dist_left_rightproof · cited by 3
- EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_wbtwproof · cited by 2
- EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_distproof · cited by 1
- EuclideanGeometry.Sphere.isDiameter_iff_left_mem_and_midpoint_eq_centerproof · cited by 0
- EuclideanGeometry.Sphere.IsDiameter.left_ne_right_iff_radius_posproof · cited by 0
- EuclideanGeometry.Sphere.isDiameter_of_angle_eq_pi_div_twoproof · cited by 0