Theorems · Theorem · real analysis
Real.coe_sqrt
∀ {x : NNReal}, ↑(NNReal.sqrt x) = √↑x- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 and proof · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- NNReal.toRealstatement and proof · cited by 1,260
- OrderIsostatement · cited by 874
- Real.sqrtstatement · cited by 545
- NNReal.sqrtstatement and proof · cited by 91
- Real.toNNReal_coeproof · cited by 36
Cited by15
Results whose statement or proof uses this declaration.
- EuclideanSpace.norm_eqproof · cited by 8
- NNReal.sqrt_eq_rpowproof · cited by 7
- PiLp.nnnorm_eq_of_L2proof · cited by 5
- NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discrproof · cited by 2
- Complex.antilipschitz_equivRealProdproof · cited by 2
- Real.sqrt_prodproof · cited by 1
- NumberField.mixedEmbedding.covolume_idealLatticeproof · cited by 1
- NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplexproof · cited by 1
- ProbabilityTheory.Kernel.HasSubgaussianMGF.addproof · cited by 1
- WithLp.prod_nnnorm_eq_of_L2proof · cited by 1
- PiLp.nndist_eq_of_L2proof · cited by 1
- CFC.norm_sqrtproof · cited by 0