Theorems · Theorem · real analysis
Real.rpow_le_rpow_iff
∀ {x y z : ℝ}, 0 ≤ x → 0 ≤ y → 0 < z → (x ^ z ≤ y ^ z ↔ x ≤ y)- Cited by
- 14 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.
Cites3
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_iff_le_iff_lt_iff_ltproof · cited by 25
- Real.rpow_lt_rpow_iffproof · cited by 9
Cited by14
Results whose statement or proof uses this declaration.
- NNReal.rpow_le_rpow_iffproof · cited by 7
- lp.norm_apply_le_normproof · cited by 6
- Real.le_rpow_inv_iff_of_posproof · cited by 2
- NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_leproof · cited by 2
- Real.rpow_inv_le_iff_of_posproof · cited by 2
- MeasureTheory.MemLp.eLpNorm_indicator_norm_ge_leproof · cited by 1
- smoothingFun_one_leproof · cited by 1
- lp.norm_le_of_tsum_leproof · cited by 1
- MeasureTheory.MemLp.exists_hasCompactSupport_integral_rpow_sub_leproof · cited by 1
- max_norm_root_eq_spectralValueproof · cited by 1
- MeasureTheory.MemLp.exists_boundedContinuous_integral_rpow_sub_leproof · cited by 1
- Real.arith_mean_le_rpow_meanproof · cited by 1