Theorems · Theorem · complex analysis
Complex.cosh_sq_sub_sinh_sq
∀ (x : ℂ), Complex.cosh x ^ 2 - Complex.sinh x ^ 2 = 1
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 145 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.expproof · cited by 612
- add_neg_cancelproof · cited by 213
- Complex.coshstatement and proof · cited by 118
- Complex.sinhstatement and proof · cited by 113
- Complex.exp_addproof · cited by 55
- Complex.exp_zeroproof · cited by 43
- sq_sub_sqproof · cited by 12
- Complex.cosh_add_sinhproof · cited by 5
- Complex.cosh_sub_sinhproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Complex.sin_sq_add_cos_sqproof · cited by 11
- Complex.sinh_sqproof · cited by 2
- Complex.cosh_sqproof · cited by 2
- Real.cosh_sq_sub_sinh_sqproof · cited by 0