Theorems · Theorem · complex analysis
RCLike.sqrt_neg_of_nonneg
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {a : 𝕜}, 0 ≤ a → RCLike.sqrt (-a) = RCLike.I * RCLike.sqrt a- Defined in
- Mathlib.Analysis.RCLike.Sqrt
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites43
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realproof · cited by 25,697
- Complexproof · cited by 5,565
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- RCLikestatement and proof · cited by 2,829
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- Complex.ofRealproof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
Cited by1
Results whose statement or proof uses this declaration.
- RCLike.sqrt_neg_oneproof · cited by 0