AffineSubspace.perpBisector_nonempty
∀ {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] {p₁ p₂ : P}, (↑(AffineSubspace.perpBisector p₁ p₂)).Nonempty- Defined in
- Mathlib.Geometry.Euclidean.PerpBisector
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- SetLike.coestatement · cited by 8,199
- InnerProductSpacestatement and proof · cited by 3,523
- Set.Nonemptystatement · cited by 2,627
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineSubspacestatement · cited by 871
- midpointproof · cited by 123
- AffineSubspace.perpBisectorstatement · cited by 28
- AffineSubspace.midpoint_mem_perpBisectorproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AffineSubspace.perpBisector_ne_botproof · cited by 0