Theorems · Theorem · complex analysis
Real.sin_add
∀ (x y : ℝ), Real.sin (x + y) = Real.sin x * Real.cos y + Real.cos x * Real.sin y
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complex.ofRealproof · cited by 1,654
- Real.cosstatement and proof · cited by 424
- Real.sinstatement and proof · cited by 389
- Complex.cosproof · cited by 279
- Complex.sinproof · cited by 258
- Complex.ofReal_mulproof · cited by 180
- Complex.ofReal_addproof · cited by 94
- Complex.ofReal_cosproof · cited by 43
- Complex.ofReal_sinproof · cited by 40
- Complex.ofReal_injectiveproof · cited by 23
- Complex.sin_addproof · cited by 12
Cited by12
Results whose statement or proof uses this declaration.
- Real.sin_piproof · cited by 14
- Real.sin_antiperiodicproof · cited by 14
- Real.sin_pi_div_two_subproof · cited by 6
- Real.sin_eq_zero_iffproof · cited by 5
- Real.sin_add_pi_div_twoproof · cited by 5
- Complex.sin_argproof · cited by 4
- Real.quadratic_root_cos_pi_div_fiveproof · cited by 2
- Real.Angle.sin_addproof · cited by 2
- Real.sin_subproof · cited by 2
- Real.sin_sub_pi_div_twoproof · cited by 1
- Real.sin_two_piproof · cited by 0
- Real.two_mul_sin_mul_cosproof · cited by 0