Theorems · Theorem · complex analysis
Complex.norm_def
∀ (z : ℂ), ‖z‖ = √(Complex.normSq z)
- Defined in
- Mathlib.Analysis.Complex.Norm
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normstatement · cited by 5,413
- MonoidWithZeroHomstatement · cited by 704
- Real.sqrtstatement · cited by 545
- Complex.normSqstatement · cited by 103
Cited by18
Results whose statement or proof uses this declaration.
- Complex.norm_realproof · cited by 105
- Complex.norm_mulproof · cited by 59
- Complex.norm_divproof · cited by 15
- Complex.normSq_eq_norm_sqproof · cited by 14
- Complex.norm_conjproof · cited by 8
- Complex.norm_cos_add_sin_mul_Iproof · cited by 6
- AnalyticAt.harmonicAt_log_normproof · cited by 4
- Complex.norm_eq_sqrt_sq_add_sqproof · cited by 2
- Complex.abs_re_lt_normproof · cited by 2
- Complex.norm_le_sqrt_two_mul_maxproof · cited by 2
- circleAverage_log_norm_sub_const₁proof · cited by 1
- EisensteinSeries.auxbound1proof · cited by 1