Theorems · Theorem · real analysis
NNReal.rpow_pos
∀ {p : ℝ} {x : NNReal}, 0 < x → 0 < x ^ p- Cited by
- 3 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.
Cites11
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
- LT.lt.ne'proof · cited by 1,417
- neg_negproof · cited by 960
- lt_trichotomyproof · cited by 178
- inv_posproof · cited by 124
- neg_posproof · cited by 74
- NNReal.rpow_zeroproof · cited by 20
- NNReal.zero_rpowproof · cited by 16
- NNReal.rpow_negproof · cited by 7
- NNReal.rpow_lt_rpowproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- NNReal.inner_le_Lp_mul_Lqproof · cited by 5
- MeasureTheory.lintegral_pow_le_pow_lintegral_fderivproof · cited by 1
- MeasureTheory.UniformIntegrable.spec'proof · cited by 1