Theorems · Theorem · number theory
UpperHalfPlane.moebius_im
∀ (g : GL (Fin 2) ℝ) (z : ℂ),
(UpperHalfPlane.num g z / UpperHalfPlane.denom g z).im =
↑(Matrix.GeneralLinearGroup.det g) * z.im / Complex.normSq (UpperHalfPlane.denom g z)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Matrixstatement · cited by 4,303
- MonoidHomstatement · cited by 3,629
- Unitsstatement · cited by 2,804
- add_zeroproof · cited by 2,707
- Units.valstatement and proof · cited by 1,966
- Complex.ofRealproof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- sub_zeroproof · cited by 938
- Complex.reproof · cited by 882
Cited by3
Results whose statement or proof uses this declaration.
- UpperHalfPlane.mul_smul'proof · cited by 1
- UpperHalfPlane.im_smulproof · cited by 1
- UpperHalfPlane.smulAux'_improof · cited by 1