Theorems · Theorem · real analysis
Real.rpow_natCast
∀ (x : ℝ) (n : ℕ), x ^ ↑n = x ^ n
- Cited by
- 93 results in Mathlib
- Foundations
- Depth 197 from the axioms, rests on 4,769 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Int.cast_natCastproof · cited by 393
- zpow_natCastproof · cited by 271
- Real.rpow_intCastproof · cited by 35
Cited by93
Results whose statement or proof uses this declaration.
- Real.sqrt_eq_rpowproof · cited by 25
- NNReal.rpow_natCastproof · cited by 14
- Real.rpow_ofNatproof · cited by 12
- Function.hasTemperateGrowth_one_add_norm_sq_rpowproof · cited by 9
- PeriodPair.hasSumLocallyUniformly_derivWeierstrassPExceptproof · cited by 4
- NumberField.hermiteTheorem.rank_le_rankOfDiscrBddproof · cited by 4
- Real.rpow_natCast_mulproof · cited by 3
- norm_root_le_spectralValueproof · cited by 3
- Real.pow_rpow_inv_natCastproof · cited by 3
- MeasureTheory.MemLp.integrable_norm_pow'proof · cited by 3
- pow_mul_le_of_le_of_pow_mul_leproof · cited by 2