EuclideanGeometry.inversion_eq_center
∀ {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 x : P} {R : ℝ}, R ≠ 0 → (EuclideanGeometry.inversion c R x = c ↔ x = c)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- EuclideanGeometry.inversionstatement · cited by 47
- EuclideanGeometry.inversion_selfproof · cited by 6
- EuclideanGeometry.inversion_injectiveproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanGeometry.center_eq_inversionproof · cited by 0