Theorems · Definition · complex analysis
Real.cos
ℝ → ℝ
The real cosine function, defined as the real part of the complex cosine
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 424 results in Mathlib
- Foundations
- Depth 143 from the axioms, rests on 3,708 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Complex.reproof · cited by 882
- Complex.cosproof · cited by 279
Cited by431
Results whose statement or proof uses this declaration.
- Complex.ofReal_cosstatement · cited by 43
- Real.cos_zerostatement · cited by 38
- Real.cos_negstatement · cited by 27
- Real.cos_pi_div_twostatement and proof · cited by 26
- polarCoordproof · cited by 25
- Real.sqrt_eq_rpowproof · cited by 25
- Real.cos_pistatement and proof · cited by 20
- Real.Angle.cos_coestatement · cited by 20
- Real.Angle.tan_coeproof · cited by 19
- Real.cos_antiperiodicstatement and proof · cited by 16
- Real.cos_periodicstatement · cited by 16
- Real.tan_eq_sin_div_cosstatement and proof · cited by 15
Showing the 200 most cited of 431.