Theorems · Theorem · real analysis
Real.abs_rpow_le_abs_rpow
∀ (x y : ℝ), |x ^ y| ≤ |x| ^ y
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
- absstatement and proof · cited by 1,814
- Real.piproof · cited by 1,774
- Real.logproof · cited by 939
- Real.expproof · cited by 871
- Real.cosproof · cited by 424
- le_or_gtproof · cited by 269
- Real.exp_posproof · cited by 169
- abs_of_posproof · cited by 114
- abs_mulproof · cited by 98
Cited by7
Results whose statement or proof uses this declaration.
- Function.hasTemperateGrowth_one_add_norm_sq_rpowproof · cited by 9
- ProbabilityTheory.integrable_rpow_mul_exp_of_integrable_exp_mulproof · cited by 3
- integrable_rpow_mul_exp_neg_mul_sqproof · cited by 2
- Asymptotics.IsBigOWith.rpowproof · cited by 2
- Real.abs_rpow_le_exp_log_mulproof · cited by 1
- Real.rpow_inv_log_le_exp_oneproof · cited by 0