Theorems · Theorem · real analysis
Real.rpow_le_rpow
∀ {x y z : ℝ}, 0 ≤ x → x ≤ y → 0 ≤ z → x ^ z ≤ y ^ z- Cited by
- 38 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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_reflproof · cited by 2,061
- le_of_ltproof · cited by 1,175
- eq_or_lt_of_leproof · cited by 92
- Real.rpow_zeroproof · cited by 69
- Real.rpow_lt_rpowproof · cited by 12
Cited by38
Results whose statement or proof uses this declaration.
- Real.rpow_le_rpow_of_nonposproof · cited by 12
- Real.rpow_lt_rpow_iffproof · cited by 9
- Function.hasTemperateGrowth_one_add_norm_sq_rpowproof · cited by 9
- NNReal.rpow_le_rpowproof · cited by 8
- Real.rpow_le_oneproof · cited by 5
- Integrable.norm_condExp_rpow_leproof · cited by 3
- AkraBazziRecurrence.GrowsPolynomially.rpowproof · cited by 3
- Asymptotics.IsBigOWith.rpowproof · cited by 2
- lp.sum_rpow_le_of_tendstoproof · cited by 2
- Memℓp.addproof · cited by 2
- Memℓp.monoproof · cited by 2
- Real.one_le_rpowproof · cited by 2