Theorems · Theorem · complex analysis
Complex.ofReal_sin
∀ (x : ℝ), ↑(Real.sin x) = Complex.sin ↑x
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 40 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 · cited by 5,565
- Complex.ofRealstatement · cited by 1,654
- Real.sinstatement · cited by 389
- Complex.sinstatement · cited by 258
- Complex.ofReal_sin_ofReal_reproof · cited by 3
Cited by40
Results whose statement or proof uses this declaration.
- Real.tan_eq_sin_div_cosproof · cited by 15
- Complex.exp_logproof · cited by 14
- Real.sin_addproof · cited by 12
- Real.sin_sq_add_cos_sqproof · cited by 12
- Complex.sin_pi_div_twoproof · cited by 10
- Real.cos_addproof · cited by 8
- Complex.sin_piproof · cited by 8
- Real.rpow_def_of_negproof · cited by 7
- Complex.arg_mul_coe_angleproof · cited by 6
- Real.sin_two_mulproof · cited by 4
- PhragmenLindelof.quadrant_Iproof · cited by 4
- Complex.polarCoord_symm_applyproof · cited by 3