Theorems · Theorem · field theory
Complex.normSq_nonneg
∀ (z : ℂ), 0 ≤ Complex.normSq z
- Defined in
- Mathlib.Data.Complex.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 106 from the axioms · 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.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Complex.reproof · cited by 882
- MonoidWithZeroHomstatement · cited by 704
- Complex.improof · cited by 591
- add_nonnegproof · cited by 104
- Complex.normSqstatement · cited by 103
- mul_self_nonnegproof · cited by 35
Cited by14
Results whose statement or proof uses this declaration.
- Complex.norm_mulproof · cited by 59
- Complex.norm_divproof · cited by 15
- Complex.normSq_eq_norm_sqproof · cited by 14
- Complex.normSq_posproof · cited by 7
- Complex.norm_mul_self_eq_normSqproof · cited by 5
- AnalyticAt.harmonicAt_log_normproof · cited by 4
- jacobiTheta₂_functional_equationproof · cited by 3
- circleAverage_log_norm_sub_const₁proof · cited by 1
- LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_reproof · cited by 1
- UpperHalfPlane.im_smulproof · cited by 1
- Complex.norm_eq_zero_iffproof · cited by 1
- jacobiTheta₂'_functional_equationproof · cited by 1