Theorems · Theorem · real analysis
Real.sqrt_prod
∀ {ι : Type u_1} (s : Finset ι) {x : ι → ℝ}, (∀ i ∈ s, 0 ≤ x i) → √(∏ i ∈ s, x i) = ∏ i ∈ s, √(x i)- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Finsetstatement and proof · cited by 13,712
- Finset.prodstatement and proof · cited by 2,356
- NNReal.toRealproof · cited by 1,260
- Finset.prod_congrproof · cited by 646
- Real.sqrtstatement and proof · cited by 545
- Real.toNNRealproof · cited by 267
- sup_of_le_leftproof · cited by 218
- map_prodproof · cited by 108
- NNReal.sqrtproof · cited by 91
- Real.coe_sqrtproof · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.PosSemidef.det_sqrtproof · cited by 0