Theorems · Theorem · complex analysis
RCLike.sqrt_of_nonneg
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {a : 𝕜}, 0 ≤ a → RCLike.sqrt a = ↑√(RCLike.re a)- Defined in
- Mathlib.Analysis.RCLike.Sqrt
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 204 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.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- Complexproof · cited by 5,565
- mul_oneproof · cited by 3,885
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- add_zeroproof · cited by 2,707
- MulZeroClass.mul_zeroproof · cited by 2,091
- Complex.ofRealproof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- map_zeroproof · cited by 1,614
- sub_selfproof · cited by 996
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.PosSemidef.det_sqrtproof · cited by 0