Theorems · Theorem · complex analysis
Complex.cosh_add
∀ (x y : ℂ), Complex.cosh (x + y) = Complex.cosh x * Complex.cosh y + Complex.sinh x * Complex.sinh y
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 144 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.
- Complexstatement and proof · cited by 5,565
- mul_assocproof · cited by 1,667
- Complex.expproof · cited by 612
- mul_addproof · cited by 413
- mul_left_commproof · cited by 184
- Complex.coshstatement and proof · cited by 118
- Complex.sinhstatement and proof · cited by 113
- neg_addproof · cited by 69
- mul_right_inj'proof · cited by 56
- Complex.exp_addproof · cited by 55
- two_ne_zero'proof · cited by 38
- Complex.two_coshproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- Complex.cos_addproof · cited by 11
- Complex.cosh_two_mulproof · cited by 3
- Complex.cosh_antiperiodicproof · cited by 3
- Complex.cosh_three_mulproof · cited by 2
- Real.cosh_addproof · cited by 1
- Complex.cosh_subproof · cited by 0