Theorems · Theorem · field theory
Complex.ofReal_re
∀ (r : ℝ), (↑r).re = r
- Defined in
- Mathlib.Data.Complex.Basic
- Cited by
- 34 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.restatement · cited by 882
Cited by34
Results whose statement or proof uses this declaration.
- Complex.ofReal_logproof · cited by 14
- LSeriesSummable_of_abscissaOfAbsConv_lt_reproof · cited by 9
- Real.rpow_def_of_negproof · cited by 7
- intervalIntegral.intervalIntegrable_cpow'proof · cited by 7
- Real.Gamma_nat_eq_factorialproof · cited by 5
- zeta_nat_eq_tsum_of_gt_oneproof · cited by 4
- Real.Gamma_eq_integralproof · cited by 4
- integral_rpowproof · cited by 4
- IsSelfAdjoint.mem_spectrum_eq_reproof · cited by 3
- LSeries.abscissaOfAbsConv_binop_leproof · cited by 3
- Real.integral_rpow_mul_exp_neg_mul_Ioiproof · cited by 3
- PhragmenLindelof.horizontal_stripproof · cited by 3