Theorems · Theorem · complex analysis
Complex.sqrt_neg_of_nonneg
∀ {a : ℂ}, 0 ≤ a → (-a).sqrt = Complex.I * a.sqrt- Defined in
- Mathlib.Analysis.RCLike.Sqrt
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- zero_addproof · cited by 2,366
- mul_commproof · cited by 2,262
- Complex.ofRealproof · cited by 1,654
- Complex.Istatement and proof · cited by 866
- Real.sqrtproof · cited by 545
- neg_zeroproof · cited by 542
- RCLike.ofRealproof · cited by 350
- abs_of_nonnegproof · cited by 279
- sub_neg_eq_addproof · cited by 264
- zero_divproof · cited by 222
Cited by2
Results whose statement or proof uses this declaration.
- RCLike.sqrt_neg_of_nonnegproof · cited by 1
- Complex.sqrt_neg_oneproof · cited by 0