Theorems · Theorem · complex analysis
Complex.cosh_sub_sinh
∀ (x : ℂ), Complex.cosh x - Complex.sinh x = Complex.exp (-x)
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 4 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.
Cites11
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.expstatement and proof · cited by 612
- two_mulproof · cited by 232
- mul_subproof · cited by 201
- Complex.coshstatement and proof · cited by 118
- Complex.sinhstatement and proof · cited by 113
- mul_right_inj'proof · cited by 56
- two_ne_zero'proof · cited by 38
- add_sub_sub_cancelproof · cited by 14
- Complex.two_coshproof · cited by 5
- Complex.two_sinhproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Complex.cosh_sq_sub_sinh_sqproof · cited by 4
- Real.cosh_sub_sinhproof · cited by 2
- Complex.cos_sub_sin_Iproof · cited by 0
- Complex.sinh_sub_coshproof · cited by 0