Theorems · Theorem · complex analysis
Real.cos_add
∀ (x y : ℝ), Real.cos (x + y) = Real.cos x * Real.cos y - Real.sin x * Real.sin y
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 8 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.
Cites13
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_subproof · cited by 63
- Complex.ofReal_cosproof · cited by 43
- Complex.ofReal_sinproof · cited by 40
- Complex.ofReal_injectiveproof · cited by 23
Cited by8
Results whose statement or proof uses this declaration.
- Real.cos_antiperiodicproof · cited by 16
- Real.cos_sub_pi_div_twoproof · cited by 3
- Real.cos_add_pi_div_twoproof · cited by 2
- Real.cos_subproof · cited by 2
- Real.Angle.cos_addproof · cited by 1
- Real.cos_two_piproof · cited by 0
- Real.two_mul_cos_mul_cosproof · cited by 0
- Real.two_mul_sin_mul_sinproof · cited by 0