Theorems · Theorem · real analysis
Real.abs_rpow_of_nonneg
∀ {x y : ℝ}, 0 ≤ x → |x ^ y| = |x| ^ y- Cited by
- 11 results in Mathlib
- Foundations
- Depth 195 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
- absstatement and proof · cited by 1,814
- Real.rpow_nonnegproof · cited by 111
- abs_eq_selfproof · cited by 59
Cited by11
Results whose statement or proof uses this declaration.
- Real.abs_rpow_le_abs_rpowproof · cited by 7
- Real.norm_rpow_of_nonnegproof · cited by 5
- MeasureTheory.memLp_norm_rpow_iffproof · cited by 4
- Asymptotics.IsBigOWith.rpowproof · cited by 2
- lp.hasSum_singleproof · cited by 2
- Asymptotics.IsBigO.rpow_rpow_nhdsGE_zero_of_le_of_impproof · cited by 2
- ProbabilityTheory.integrable_rpow_abs_mul_exp_add_of_integrable_exp_mulproof · cited by 2
- LSeriesSummable_of_isBigO_rpowproof · cited by 1
- ContDiffPointwiseHolderAt.of_contDiffOn_holderOnWithproof · cited by 0
- LSeriesSummable.isBigO_rpowproof · cited by 0