Theorems · Theorem · real analysis
Real.div_rpow
∀ {x y : ℝ}, 0 ≤ x → 0 ≤ y → ∀ (z : ℝ), (x / y) ^ z = x ^ z / y ^ z- Cited by
- 10 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- div_eq_mul_invproof · cited by 715
- inv_nonnegproof · cited by 56
- Real.mul_rpowproof · cited by 37
- Real.inv_rpowproof · cited by 14
Cited by10
Results whose statement or proof uses this declaration.
- NNReal.div_rpowproof · cited by 4
- tendsto_exp_mul_div_rpow_atTopproof · cited by 3
- pow_mul_le_of_le_of_pow_mul_leproof · cited by 2
- strictConvexOn_rpowproof · cited by 2
- ProbabilityTheory.lintegral_gammaPDF_eq_oneproof · cited by 2
- Behrend.roth_lower_bound_explicitproof · cited by 1
- Rat.AbsoluteValue.exists_nat_rpow_iff_isEquivproof · cited by 1
- Mathlib.Meta.NormNum.IsNNRat.rpow_isNNRatproof · cited by 0
- NumberField.abs_discr_rpow_ge_of_isTotallyComplexproof · cited by 0
- Real.compact_inner_le_weight_mul_Lp_of_nonnegproof · cited by 0