Theorems · Theorem · real analysis
Real.rpow_le_rpow_of_exponent_le
∀ {x y z : ℝ}, 1 ≤ x → y ≤ z → x ^ y ≤ x ^ z- Cited by
- 32 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Real.logproof · cited by 939
- Real.expproof · cited by 871
- zero_lt_oneproof · cited by 598
- lt_of_lt_of_leproof · cited by 438
- mul_le_mul_of_nonneg_leftproof · cited by 361
- Real.rpow_def_of_posproof · cited by 35
- Real.log_nonnegproof · cited by 28
- Real.exp_le_expproof · cited by 16
Cited by32
Results whose statement or proof uses this declaration.
- Function.hasTemperateGrowth_one_add_norm_sq_rpowproof · cited by 9
- PhragmenLindelof.isBigO_sub_exp_rpowproof · cited by 5
- Real.rpow_le_one_of_one_le_of_nonposproof · cited by 4
- SchwartzMap.isBigO_cocompact_rpowproof · cited by 3
- integrableOn_Ioi_rpow_iffproof · cited by 3
- ZetaAsymptotics.continuousOn_termTSumproof · cited by 2
- Chebyshev.abs_psi_sub_theta_le_sqrt_mul_logproof · cited by 2
- Real.rpow_le_self_of_one_leproof · cited by 2
- Real.floor_logb_natCastproof · cited by 2
- mellin_hasDerivAt_of_isBigO_rpowproof · cited by 2
- Complex.norm_prime_cpow_le_one_halfproof · cited by 2
- LSeries.tendsto_cpow_mul_atTopproof · cited by 2