Theorems · Theorem · complex analysis
Real.tanh_eq_sinh_div_cosh
∀ (x : ℝ), Real.tanh x = Real.sinh x / Real.cosh x
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Complex.ofRealproof · cited by 1,654
- Real.sinhstatement and proof · cited by 142
- Real.coshstatement and proof · cited by 119
- Complex.coshproof · cited by 118
- Complex.sinhproof · cited by 113
- Complex.ofReal_divproof · cited by 83
- Complex.ofReal_injproof · cited by 38
- Real.tanhstatement · cited by 19
- Complex.ofReal_coshproof · cited by 12
- Complex.ofReal_sinhproof · cited by 12
- Complex.ofReal_tanhproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Real.tanh_eqproof · cited by 3
- Real.tanh_arsinhproof · cited by 0
- Real.logDeriv_coshproof · cited by 0
- UpperHalfPlane.tanh_half_distproof · cited by 0
- Real.tanh_arcoshproof · cited by 0