Theorems · Theorem · complex analysis
Complex.norm_natCast
∀ (n : ℕ), ‖↑n‖ = ↑n
- Defined in
- Mathlib.Analysis.Complex.Norm
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Complexstatement · cited by 5,565
- Norm.normstatement · cited by 5,413
- Nat.cast_nonnegproof · cited by 109
- Complex.norm_of_nonnegproof · cited by 20
Cited by12
Results whose statement or proof uses this declaration.
- Complex.norm_ofNatproof · cited by 19
- Complex.exp_boundproof · cited by 6
- Complex.isCauSeq_norm_expproof · cited by 2
- EisensteinSeries.summable_sigma_mul_cexp_powproof · cited by 2
- Complex.hasSum_taylorSeries_logproof · cited by 2
- Complex.nnnorm_natCastproof · cited by 2
- LSeries.tendsto_cpow_mul_atTopproof · cited by 2
- summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexpproof · cited by 2
- Complex.norm_exp_sub_sum_le_exp_norm_sub_sumproof · cited by 1
- LindemannWeierstrass.exp_polynomial_approxproof · cited by 0
- Complex.norm_exp_sub_sum_le_norm_mul_expproof · cited by 0
- Complex.exp_bound'proof · cited by 0