Theorems · Theorem · field theory
Complex.ofReal_im
∀ (r : ℝ), (↑r).im = 0
- Defined in
- Mathlib.Data.Complex.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.ofRealstatement · cited by 1,654
- Complex.imstatement · cited by 591
Cited by16
Results whose statement or proof uses this declaration.
- Complex.ofReal_logproof · cited by 14
- Complex.sin_ofReal_improof · cited by 9
- Complex.cos_ofReal_improof · cited by 8
- Real.rpow_def_of_negproof · cited by 7
- Complex.Gamma_ne_zeroproof · cited by 6
- Complex.exp_ofReal_improof · cited by 3
- Complex.cpow_mul_ofReal_nonnegproof · cited by 2
- Complex.eq_re_of_ofReal_leproof · cited by 2
- integral_gaussian_complexproof · cited by 2
- IsSelfAdjoint.im_eq_zero_of_mem_spectrumproof · cited by 1
- NumberField.ComplexEmbedding.IsReal.coe_embedding_applyproof · cited by 1
- ModularGroup.tendsto_normSq_coprime_pairproof · cited by 1