Theorems · Theorem · complex analysis
Real.sinh_eq
∀ (x : ℝ), Real.sinh x = (Real.exp x - Real.exp (-x)) / 2
The definition of sinh in terms of exp.
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.expstatement and proof · cited by 871
- Complex.expproof · cited by 612
- Real.sinhstatement and proof · cited by 142
- Complex.ofReal_negproof · cited by 130
- Complex.ofReal_divproof · cited by 83
- Complex.ofReal_subproof · cited by 63
- Complex.ofReal_expproof · cited by 44
- Complex.ofReal_injectiveproof · cited by 23
- Complex.ofReal_sinhproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- Real.sinh_arsinhproof · cited by 8
- Real.tanh_eqproof · cited by 3
- Real.sinh_arcoshproof · cited by 2
- Real.sinh_logproof · cited by 1
- Real.exp_mul_le_cosh_add_mul_sinhproof · cited by 0