Theorems · Theorem · real analysis
Real.rpow_neg
∀ {x : ℝ}, 0 ≤ x → ∀ (y : ℝ), x ^ (-y) = (x ^ y)⁻¹See also rpow_neg_eq_inv_rpow for a version with x⁻¹ ^ y in the RHS.
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 194 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
- mul_negproof · cited by 590
- neg_zeroproof · cited by 542
- inv_oneproof · cited by 301
- inv_zeroproof · cited by 184
- Real.exp_negproof · cited by 28
- Real.rpow_def_of_nonnegproof · cited by 6
Cited by36
Results whose statement or proof uses this declaration.
- Real.inv_rpowproof · cited by 14
- Real.rpow_le_rpow_of_nonposproof · cited by 12
- Real.rpow_subproof · cited by 8
- NNReal.rpow_negproof · cited by 7
- Real.Gamma_one_half_eqproof · cited by 6
- Real.rpow_sub'proof · cited by 5
- EisensteinSeries.summable_inv_of_isBigO_rpow_invproof · cited by 5
- isLittleO_exp_neg_mul_rpow_atTopproof · cited by 4
- PeriodPair.hasSumLocallyUniformly_derivWeierstrassPExceptproof · cited by 4
- Real.summable_nat_rpowproof · cited by 4
- summable_riemannZetaSummandproof · cited by 4
- tendsto_rpow_neg_atTopproof · cited by 3