Theorems · Theorem · real analysis
NNReal.mul_rpow
∀ {x y : NNReal} {z : ℝ}, (x * y) ^ z = x ^ z * y ^ z- Cited by
- 13 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- NNReal.eqproof · cited by 201
- Real.mul_rpowproof · cited by 37
Cited by14
Results whose statement or proof uses this declaration.
- ENNReal.mul_rpow_eq_iteproof · cited by 5
- PiLp.nnnorm_toLp_constproof · cited by 4
- NNReal.rpowMonoidHomproof · cited by 3
- NNReal.Lr_rpow_le_Lp_mul_Lqproof · cited by 3
- MeasureTheory.eLpNorm'_le_nnreal_smul_eLpNorm'_of_ae_le_mulproof · cited by 2
- HolderOnWith.of_leproof · cited by 2
- NNReal.inner_le_weight_mul_Lpproof · cited by 2
- FormalMultilinearSeries.radius_eq_liminfproof · cited by 2
- Matrix.frobenius_nnnorm_mulproof · cited by 1
- lp.norm_const_smul_leproof · cited by 1
- NNReal.rpow_sum_le_const_mul_sum_rpowproof · cited by 1
- NNReal.rpow_add_le_mul_rpow_add_rpowproof · cited by 0