Theorems · Theorem · complex analysis
Complex.norm_real
∀ (r : ℝ), ‖↑r‖ = ‖r‖
- Defined in
- Mathlib.Analysis.Complex.Norm
- Cited by
- 105 results in Mathlib
- Foundations
- Depth 130 from the axioms, rests on 3,520 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 5,565
- Norm.normstatement · cited by 5,413
- absproof · cited by 1,814
- Complex.ofRealstatement and proof · cited by 1,654
- Real.sqrtproof · cited by 545
- Complex.norm_defproof · cited by 18
- Complex.normSq_ofRealproof · cited by 10
- Real.sqrt_mul_self_eq_absproof · cited by 4
Cited by106
Results whose statement or proof uses this declaration.
- norm_circleMap_zeroproof · cited by 21
- Complex.norm_of_nonnegproof · cited by 20
- Complex.arg_ofReal_of_nonnegproof · cited by 16
- Complex.norm_intCastproof · cited by 12
- NumberField.InfinitePlace.prod_eq_abs_normproof · cited by 8
- Real.rpow_def_of_negproof · cited by 7
- Complex.ofRealLIproof · cited by 7
- Complex.isTheta_ofRealproof · cited by 6
- Complex.canonicalFactor_ne_zeroproof · cited by 6
- Complex.nnnorm_realproof · cited by 6
- NumberField.mixedEmbedding.normAtPlace_smulproof · cited by 5
- Complex.norm_cpow_eq_rpow_re_of_nonnegproof · cited by 4