Theorems · Theorem · complex analysis
Complex.ofReal_cosh
∀ (x : ℝ), ↑(Real.cosh x) = Complex.cosh ↑x
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Complex.ofRealstatement · cited by 1,654
- Real.coshstatement · cited by 119
- Complex.coshstatement · cited by 118
- Complex.ofReal_cosh_ofReal_reproof · cited by 2
Cited by12
Results whose statement or proof uses this declaration.
- Real.tanh_eq_sinh_div_coshproof · cited by 5
- Real.cosh_negproof · cited by 3
- Real.cosh_sqproof · cited by 3
- Real.cosh_add_sinhproof · cited by 2
- Real.cosh_sub_sinhproof · cited by 2
- Real.sinh_addproof · cited by 2
- Real.cosh_addproof · cited by 1
- Real.sinh_sqproof · cited by 1
- Real.cosh_two_mulproof · cited by 1
- Real.cosh_sq_sub_sinh_sqproof · cited by 0
- Real.cosh_three_mulproof · cited by 0
- Real.sinh_two_mulproof · cited by 0