Theorems · Theorem · complex analysis
Complex.sq_norm
∀ (z : ℂ), ‖z‖ ^ 2 = Complex.normSq z
- Defined in
- Mathlib.Analysis.Complex.Norm
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 129 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
- Complex.normSqstatement · cited by 103
- Complex.normSq_eq_norm_sqproof · cited by 14
Cited by7
Results whose statement or proof uses this declaration.
- UpperHalfPlane.cosh_half_distproof · cited by 3
- Complex.norm_sub_one_sq_eq_of_norm_eq_oneproof · cited by 2
- Orientation.norm_kahlerproof · cited by 2
- UpperHalfPlane.dist_coe_center_sqproof · cited by 2
- Complex.sq_norm_sub_sq_reproof · cited by 1
- UpperHalfPlane.cosh_dist'proof · cited by 1
- UpperHalfPlane.eq_of_re_of_normproof · cited by 0