Theorems · Theorem · complex analysis
Complex.cosh_mul_I
∀ (x : ℂ), Complex.cosh (x * Complex.I) = Complex.cos x
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 11 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.
Cites10
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
- Complex.Istatement and proof · cited by 866
- Complex.expproof · cited by 612
- Complex.cosstatement and proof · cited by 279
- Complex.coshstatement · cited by 118
- mul_right_inj'proof · cited by 56
- two_ne_zero'proof · cited by 38
- neg_mul_eq_neg_mulproof · cited by 20
- Complex.two_coshproof · cited by 5
- Complex.two_cosproof · cited by 2
Cited by11
Results whose statement or proof uses this declaration.
- Complex.sin_addproof · cited by 12
- Complex.sin_sq_add_cos_sqproof · cited by 11
- Complex.cos_addproof · cited by 11
- Complex.cos_mul_Iproof · cited by 6
- Complex.cos_add_sin_Iproof · cited by 4
- Complex.cos_conjproof · cited by 3
- Complex.cosh_antiperiodicproof · cited by 3
- Complex.sinh_antiperiodicproof · cited by 3
- Complex.cos_three_mulproof · cited by 1
- Complex.cos_sub_sin_Iproof · cited by 0
- Complex.tanh_mul_Iproof · cited by 0