Theorems · Theorem · real analysis
Real.rpow_zero
∀ (x : ℝ), x ^ 0 = 1
- Cited by
- 69 results in Mathlib
- Foundations
- Depth 193 from the axioms · 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_zeroproof · cited by 18
Cited by69
Results whose statement or proof uses this declaration.
- Real.rpow_le_rpowproof · cited by 38
- Real.mul_rpowproof · cited by 37
- NNReal.rpow_zeroproof · cited by 20
- ENNReal.ofReal_rpow_of_nonnegproof · cited by 13
- memℓp_genproof · cited by 8
- Real.continuousAt_rpow_constproof · cited by 8
- integrable_exp_neg_mul_sqproof · cited by 6
- Filter.Tendsto.rpow_constproof · cited by 6
- Real.deriv_rpow_constproof · cited by 5
- Real.geom_mean_le_arith_mean_weightedproof · cited by 5
- LSeriesSummable_of_bounded_of_one_lt_reproof · cited by 5
- Complex.norm_cpow_of_impproof · cited by 4