Theorems · Theorem · real analysis
Real.sqrt_nonneg
∀ (x : ℝ), 0 ≤ √x
- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Real.sqrtstatement · cited by 545
- Real.toNNRealproof · cited by 267
- NNReal.coe_nonnegproof · cited by 130
- NNReal.sqrtproof · cited by 91
Cited by35
Results whose statement or proof uses this declaration.
- Real.sqrt_eq_rpowproof · cited by 25
- Real.sqrt_mul_selfproof · cited by 14
- ProbabilityTheory.gaussianPDFReal_nonnegproof · cited by 6
- Real.cosh_arcoshproof · cited by 3
- LinearMap.singularValues_nonnegproof · cited by 3
- CFC.exists_sqrt_of_isSelfAdjoint_of_quasispectrumRestrictsproof · cited by 3
- ContinuousLinearMap.norm_adjoint_comp_selfproof · cited by 3
- Real.strictMonoOn_arcoshproof · cited by 2
- Real.sinh_arcoshproof · cited by 2
- CFC.sqrt_eq_real_sqrtproof · cited by 2
- Complex.norm_nonnegproof · cited by 2
- Real.sqrt_le_iffproof · cited by 2