Theorems · Theorem · real analysis
Real.rpow_le_rpow_of_nonpos
∀ {x y z : ℝ}, 0 < x → x ≤ y → z ≤ 0 → y ^ z ≤ x ^ z- Cited by
- 12 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- LT.lt.trans_leproof · cited by 678
- Real.rpow_pos_of_posproof · cited by 155
- neg_nonnegproof · cited by 60
- Real.rpow_le_rpowproof · cited by 38
- Real.rpow_negproof · cited by 36
- inv_le_inv₀proof · cited by 23
Cited by12
Results whose statement or proof uses this declaration.
- Real.rpow_lt_rpow_iff_of_negproof · cited by 5
- AkraBazziRecurrence.GrowsPolynomially.rpowproof · cited by 3
- isBigO_norm_Icc_restrict_atTopproof · cited by 2
- pow_mul_le_of_le_of_pow_mul_leproof · cited by 2
- EisensteinSeries.summand_boundproof · cited by 2
- EisensteinSeries.summand_bound_of_mem_verticalStripproof · cited by 2
- Complex.norm_prime_cpow_le_one_halfproof · cited by 2
- AkraBazziRecurrence.eventually_atTop_sumTransform_geproof · cited by 1
- AkraBazziRecurrence.eventually_atTop_sumTransform_leproof · cited by 1
- ZLattice.sum_piFinset_Icc_rpow_leproof · cited by 1
- NNReal.rpow_le_rpow_of_nonposproof · cited by 0
- Real.antitoneOn_rpow_Ioi_of_exponent_nonposproof · cited by 0