Theorems · Theorem · real analysis
NNReal.sqrt_mul
∀ (x y : NNReal), NNReal.sqrt (x * y) = NNReal.sqrt x * NNReal.sqrt y
- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 6 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.
Cites7
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
- NNRealstatement and proof · cited by 4,310
- OrderIsostatement · cited by 874
- mul_powproof · cited by 220
- NNReal.sqrtstatement and proof · cited by 91
- NNReal.sq_sqrtproof · cited by 9
- NNReal.sqrt_eq_iff_eq_sqproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- Real.sqrt_mulproof · cited by 32
- NNReal.sqrtHomproof · cited by 3
- DoubleCentralizer.norm_fst_eq_sndproof · cited by 3
- NNReal.agmSequences_fst_lt_agm_of_pos_of_neproof · cited by 1
- Real.sqrt_prodproof · cited by 1
- NNReal.sum_mul_le_sqrt_mul_sqrtproof · cited by 1
- NNReal.agm_mul_distribproof · cited by 0