UpperHalfPlane.dist_coe_center_sq
∀ (z w : UpperHalfPlane) (r : ℝ), dist ↑z ↑(w.center r) ^ 2 = 2 * z.im * w.im * (Real.cosh (dist z w) - Real.cosh r) + (w.im * Real.sinh r) ^ 2
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- Complexstatement · cited by 5,565
- Nat.cast_oneproof · cited by 2,501
- Dist.diststatement · cited by 1,539
- ne_of_gtproof · cited by 637
- UpperHalfPlanestatement and proof · cited by 626
- mul_posproof · cited by 374
- UpperHalfPlane.coestatement and proof · cited by 288
- mul_powproof · cited by 220
- mul_subproof · cited by 201
- Real.sinhstatement and proof · cited by 142
- UpperHalfPlane.imstatement and proof · cited by 128
Cited by2
Results whose statement or proof uses this declaration.
- UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_centerproof · cited by 5
- UpperHalfPlane.dist_coe_centerproof · cited by 0