Theorems · Theorem · complex analysis
Complex.sin_add
∀ (x y : ℂ), Complex.sin (x + y) = Complex.sin x * Complex.cos y + Complex.cos x * Complex.sin y
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 12 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.
Cites14
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.Iproof · cited by 866
- add_mulproof · cited by 363
- Complex.cosstatement and proof · cited by 279
- Complex.sinstatement and proof · cited by 258
- Complex.coshproof · cited by 118
- Complex.sinhproof · cited by 113
- mul_right_commproof · cited by 108
- mul_left_inj'proof · cited by 35
- Complex.I_ne_zeroproof · cited by 19
- Complex.cosh_mul_Iproof · cited by 11
Cited by12
Results whose statement or proof uses this declaration.
- Real.sin_addproof · cited by 12
- Complex.sin_antiperiodicproof · cited by 7
- Complex.sin_two_mulproof · cited by 5
- Complex.tan_addproof · cited by 5
- Complex.sin_sub_sinproof · cited by 3
- Complex.sin_pi_div_two_subproof · cited by 2
- Complex.sin_add_mul_Iproof · cited by 1
- Complex.sin_add_pi_div_twoproof · cited by 1
- Complex.sin_subproof · cited by 1
- Complex.sin_three_mulproof · cited by 1
- Complex.sin_sub_pi_div_twoproof · cited by 0
- Complex.sin_two_piproof · cited by 0