Theorems · Theorem · complex analysis
Complex.ofReal_cos_ofReal_re
∀ (x : ℝ), ↑(Complex.cos ↑x).re = Complex.cos ↑x
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Complexstatement and proof · cited by 5,565
- Complex.ofRealstatement and proof · cited by 1,654
- Complex.restatement · cited by 882
- Complex.cosstatement and proof · cited by 279
- Complex.conj_ofRealproof · cited by 41
- Complex.conj_eq_iff_reproof · cited by 12
- Complex.cos_conjproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Complex.ofReal_cosproof · cited by 43
- Complex.cos_ofReal_improof · cited by 8
- Complex.cpow_ofReal_reproof · cited by 1