Theorems · Theorem · real analysis
Complex.norm_cpow_eq_rpow_re_of_nonneg
∀ {x : ℝ}, 0 ≤ x → ∀ {y : ℂ}, y.re ≠ 0 → ‖↑x ^ y‖ = x ^ y.re- Cited by
- 4 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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 and proof · cited by 5,565
- Norm.normstatement · cited by 5,413
- Complex.ofRealstatement · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- Complex.restatement and proof · cited by 882
- Real.expproof · cited by 871
- div_oneproof · cited by 629
- Complex.improof · cited by 591
- abs_of_nonnegproof · cited by 279
- Complex.norm_realproof · cited by 105
- Real.exp_zeroproof · cited by 81
Cited by4
Results whose statement or proof uses this declaration.
- summable_riemannZetaSummandproof · cited by 4
- Complex.norm_natCast_cpow_of_re_ne_zeroproof · cited by 2
- Complex.HadamardThreeLines.norm_le_interpStrip_of_mem_verticalStrip_zeroproof · cited by 1
- DirichletCharacter.eulerProduct_log_eq_LSeriesproof · cited by 1