Theorems · Theorem · complex analysis
Complex.sqrt_of_nonneg
∀ {a : ℂ}, 0 ≤ a → a.sqrt = ↑√a.re- Defined in
- Mathlib.Analysis.RCLike.Sqrt
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- add_zeroproof · cited by 2,707
- Complex.ofRealstatement and proof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- sub_selfproof · cited by 996
- Complex.restatement · cited by 882
- Complex.Iproof · cited by 866
- Complex.improof · cited by 591
- Real.sqrtstatement and proof · cited by 545
- RCLike.ofRealproof · cited by 350
- abs_of_nonnegproof · cited by 279
Cited by2
Results whose statement or proof uses this declaration.
- Complex.sqrt_neg_of_nonnegproof · cited by 2
- RCLike.sqrt_of_nonnegproof · cited by 1