Theorems · Theorem · complex analysis
Real.cosh_sub_sinh
∀ (x : ℝ), Real.cosh x - Real.sinh x = Real.exp (-x)
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 2 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.
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
- Complex.ofRealproof · cited by 1,654
- Real.expstatement · cited by 871
- Complex.expproof · cited by 612
- Real.sinhstatement and proof · cited by 142
- Complex.ofReal_negproof · cited by 130
- Real.coshstatement and proof · cited by 119
- Complex.ofReal_subproof · cited by 63
- Complex.ofReal_expproof · cited by 44
- Complex.ofReal_injproof · cited by 38
- Complex.ofReal_coshproof · cited by 12
- Complex.ofReal_sinhproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- UpperHalfPlane.le_dist_coeproof · cited by 0
- Real.sinh_sub_coshproof · cited by 0