AffineSubspace.mem_perpBisector_iff_dist_eq
∀ {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] {c p₁ p₂ : P}, c ∈ AffineSubspace.perpBisector p₁ p₂ ↔ dist c p₁ = dist c p₂- Defined in
- Mathlib.Geometry.Euclidean.PerpBisector
- Cited by
- 1 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.
Cites19
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
- Norm.normproof · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement and proof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- Inner.innerproof · cited by 1,089
- AffineSubspacestatement · cited by 871
- VSub.vsubproof · cited by 817
- neg_vsub_eq_vsub_revproof · cited by 87
- dist_eq_norm_vsubproof · cited by 76
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanGeometry.inversion_mem_perpBisector_inversion_iffproof · cited by 2