Theorems · Theorem · real analysis
Real.rpow_one
∀ (x : ℝ), x ^ 1 = x
- Cited by
- 114 results in Mathlib
- Foundations
- Depth 195 from the axioms, rests on 4,766 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
- Complex.ofRealproof · cited by 1,654
- Complex.reproof · cited by 882
- Complex.cpow_oneproof · cited by 20
Cited by114
Results whose statement or proof uses this declaration.
- NNReal.rpow_oneproof · cited by 38
- Real.sqrt_eq_rpowproof · cited by 25
- Real.rpow_neg_oneproof · cited by 22
- Real.rpow_inv_rpowproof · cited by 12
- Real.continuous_mul_logproof · cited by 9
- Real.Gamma_one_half_eqproof · cited by 6
- 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
- EisensteinSeries.summable_one_div_norm_rpowproof · cited by 4