Theorems · Theorem · real analysis
Real.rpow_mul
∀ {x : ℝ}, 0 ≤ x → ∀ (y z : ℝ), x ^ (y * z) = (x ^ y) ^ z- Cited by
- 67 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.
Cites14
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
- Complexproof · cited by 5,565
- Real.piproof · cited by 1,774
- Complex.ofRealproof · cited by 1,654
- le_of_ltproof · cited by 1,175
- Real.logproof · cited by 939
- Complex.improof · cited by 591
- Complex.ofReal_mulproof · cited by 180
- Real.pi_posproof · cited by 173
- Real.rpow_nonnegproof · cited by 111
- Complex.ofReal_injproof · cited by 38
- Complex.ofReal_cpowproof · cited by 36
Cited by67
Results whose statement or proof uses this declaration.
- Real.sqrt_eq_rpowproof · cited by 25
- NNReal.rpow_mulproof · cited by 18
- Real.rpow_inv_rpowproof · cited by 12
- Real.Gamma_one_half_eqproof · cited by 6
- CFC.nnrpow_nnrpowproof · cited by 5
- Real.rpow_left_injOnproof · cited by 4
- Real.rpow_rpow_invproof · cited by 4
- MeasureTheory.memLp_norm_rpow_iffproof · cited by 4
- AbsoluteValue.isEquiv_iff_exists_rpow_eqproof · cited by 4
- integral_rpow_mul_exp_neg_rpowproof · cited by 4
- Real.rpow_natCast_mulproof · cited by 3
- norm_root_le_spectralValueproof · cited by 3