Theorems · Definition · geometry
AffineSubspace.perpBisector
{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] → P → P → AffineSubspace ℝ PPerpendicular bisector of a segment in a Euclidean affine space.
- Defined in
- Mathlib.Geometry.Euclidean.PerpBisector
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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
- AffineSubspacestatement · cited by 871
- LinearMap.kerproof · cited by 848
- VSub.vsubproof · cited by 817
- midpointproof · cited by 123
- AffineSubspace.mk'proof · cited by 33
- innerₛₗproof · cited by 28
Cited by28
Results whose statement or proof uses this declaration.
- AffineSubspace.mem_perpBisector_iff_inner_eq_zerostatement · cited by 6
- EuclideanGeometry.inversion_mem_perpBisector_inversion_iffstatement · cited by 2
- AffineSubspace.perpBisector_commstatement · cited by 1
- AffineSubspace.perpBisector_nonemptystatement · cited by 1
- AffineSubspace.perpBisector_selfstatement · cited by 1
- AffineSubspace.right_mem_perpBisectorstatement · cited by 1
- EuclideanGeometry.preimage_inversion_perpBisectorstatement and proof · cited by 1
- EuclideanGeometry.preimage_inversion_perpBisector_inversionstatement · cited by 1
- EuclideanGeometry.preimage_inversion_sphere_dist_centerstatement and proof · cited by 1
- Isometry.preimage_perpBisectorstatement · cited by 1
- EuclideanGeometry.inversion_mem_perpBisector_inversion_iff'statement and proof · cited by 1
- AffineSubspace.left_mem_perpBisectorstatement · cited by 1