Theorems · Theorem · real analysis
ENNReal.rpow_mul
∀ (x : ENNReal) (y z : ℝ), x ^ (y * z) = (x ^ y) ^ z
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- ENNRealstatement and proof · cited by 9,879
- Top.topproof · cited by 9,680
- NNRealproof · cited by 4,310
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- ENNReal.ofNNRealproof · cited by 1,279
- lt_trichotomyproof · cited by 178
- ENNReal.recTopCoeproof · cited by 48
- ENNReal.rpow_zeroproof · cited by 47
- ENNReal.zero_rpow_of_posproof · cited by 36
- ENNReal.top_rpow_of_posproof · cited by 22
Cited by33
Results whose statement or proof uses this declaration.
- IsSelfAdjoint.spectralRadius_eq_nnnormproof · cited by 7
- ENNReal.le_rpow_inv_iffproof · cited by 6
- ENNReal.rpow_inv_le_iffproof · cited by 5
- ENNReal.rpow_inv_rpowproof · cited by 5
- ProbabilityTheory.evariance_lt_topproof · cited by 3
- HolderOnWith.interpolateproof · cited by 3
- MeasureTheory.mul_meas_ge_le_pow_eLpNormproof · cited by 3
- MeasureTheory.eLpNorm'_constproof · cited by 3
- MeasureTheory.eLpNorm'_le_eLpNormEssSup_mul_rpow_measure_univproof · cited by 3
- MeasureTheory.Measure.hausdorffMeasure_zero_or_topproof · cited by 3
- ENNReal.rpow_rpow_invproof · cited by 3
- HolderOnWith.compproof · cited by 2