Theorems · Theorem · real analysis
Real.sqrt_mul
∀ {x : ℝ}, 0 ≤ x → ∀ (y : ℝ), √(x * y) = √x * √y- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 32 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.
Cites7
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.sqrtproof · cited by 91
- NNReal.sqrt_mulproof · cited by 6
- Real.toNNReal_mulproof · cited by 6
Cited by32
Results whose statement or proof uses this declaration.
- Complex.norm_mulproof · cited by 59
- inner_self_eq_norm_mul_normproof · cited by 9
- Real.sqrt_mul'proof · cited by 8
- Complex.cpow_inv_two_reproof · cited by 6
- Complex.cpow_inv_two_im_eq_sqrtproof · cited by 4
- Real.sqrt_divproof · cited by 4
- InnerProductGeometry.angle_add_eq_arctan_of_inner_eq_zeroproof · cited by 4
- ContinuousLinearMap.norm_adjoint_comp_selfproof · cited by 3
- Complex.cpow_inv_two_im_eq_neg_sqrtproof · cited by 2
- ProbabilityTheory.lintegral_gaussianPDFReal_eq_oneproof · cited by 2
- Complex.norm_le_sqrt_two_mul_maxproof · cited by 2
- ProbabilityTheory.gaussianPDFReal_inv_mulproof · cited by 2