Theorems · Theorem · real analysis
Real.rpow_nonneg
∀ {x : ℝ}, 0 ≤ x → ∀ (y : ℝ), 0 ≤ x ^ y- Cited by
- 111 results in Mathlib
- Foundations
- Depth 194 from the axioms, rests on 4,760 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- le_of_ltproof · cited by 1,175
- Real.logproof · cited by 939
- Real.exp_posproof · cited by 169
- Real.rpow_def_of_nonnegproof · cited by 6
Cited by111
Results whose statement or proof uses this declaration.
- Real.rpow_mulproof · cited by 67
- Real.sqrt_eq_rpowproof · cited by 25
- Real.abs_rpow_of_nonnegproof · cited by 11
- lp.norm_apply_le_normproof · cited by 6
- lp.norm_nonneg'proof · cited by 6
- intervalIntegral.intervalIntegrable_rpow'proof · cited by 6
- ZLattice.summable_norm_rpowproof · cited by 4
- memℓp_gen'proof · cited by 4
- MeasureTheory.MemLp.eLpNorm_eq_integral_rpow_normproof · cited by 4
- EisensteinSeries.summable_one_div_norm_rpowproof · cited by 4
- Integrable.norm_condExp_rpow_leproof · cited by 3
- norm_root_le_spectralValueproof · cited by 3