UpperHalfPlane.sinh_half_dist
∀ (z w : UpperHalfPlane), Real.sinh (dist z w / 2) = dist ↑z ↑w / (2 * √(z.im * w.im))
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Dist.diststatement and proof · cited by 1,539
- UpperHalfPlanestatement and proof · cited by 626
- Real.sqrtstatement and proof · cited by 545
- UpperHalfPlane.coestatement and proof · cited by 288
- two_ne_zeroproof · cited by 251
- Real.sinhstatement and proof · cited by 142
- UpperHalfPlane.imstatement and proof · cited by 128
- mul_div_cancel_left₀proof · cited by 111
- Real.arsinhproof · cited by 55
- Real.sinh_arsinhproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- UpperHalfPlane.cosh_half_distproof · cited by 3
- UpperHalfPlane.dist_le_iff_le_sinhproof · cited by 2
- UpperHalfPlane.sinh_half_dist_add_distproof · cited by 1
- UpperHalfPlane.dist_eq_iff_eq_sinhproof · cited by 1
- UpperHalfPlane.exp_half_distproof · cited by 0
- UpperHalfPlane.tanh_half_distproof · cited by 0