EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_left
∀ {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] {s : EuclideanGeometry.Sphere P} {p x : P},
x ∈ s.orthRadius p ↔ inner ℝ (x -ᵥ p) (p -ᵥ s.center) = 0- Cited by
- 7 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- Inner.innerstatement and proof · cited by 1,089
- AffineSubspacestatement and proof · cited by 871
- VSub.vsubstatement and proof · cited by 817
- EuclideanGeometry.Spherestatement and proof · cited by 233
- EuclideanGeometry.Sphere.centerstatement and proof · cited by 181
- EuclideanGeometry.Sphere.orthRadiusstatement · cited by 41
- Submodule.mem_orthogonal_singleton_iff_inner_leftproof · cited by 7
Cited by7
Results whose statement or proof uses this declaration.
- EuclideanGeometry.Sphere.orthRadius_le_orthRadius_iffproof · cited by 2
- EuclideanGeometry.Sphere.IsTangentAt.inner_left_eq_zero_of_memproof · cited by 2
- EuclideanGeometry.Sphere.dist_sq_eq_iff_mem_orthRadiusproof · cited by 1
- EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_rightproof · cited by 1
- EuclideanGeometry.Sphere.center_mem_orthRadius_iffproof · cited by 1
- EuclideanGeometry.Sphere.isTangentAt_iff_dist_sq_eq_powerproof · cited by 1