Theorems · Theorem · real analysis
Real.zero_rpow
∀ {x : ℝ}, x ≠ 0 → 0 ^ x = 0- Cited by
- 57 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.
Cites3
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.reproof · cited by 882
- Complex.zero_cpowproof · cited by 29
Cited by57
Results whose statement or proof uses this declaration.
- NNReal.zero_rpowproof · cited by 16
- ENNReal.ofReal_rpow_of_nonnegproof · cited by 13
- Real.rpow_lt_rpowproof · cited by 12
- Real.rpow_add'proof · cited by 12
- Real.rpowIntegrand₀₁_eq_pow_divproof · cited by 6
- hasFDerivAt_norm_rpowproof · cited by 5
- Real.geom_mean_le_arith_mean_weightedproof · cited by 5
- Complex.norm_cpow_of_impproof · cited by 4
- Real.rpow_le_rpow_of_exponent_ge_of_impproof · cited by 4
- AbsoluteValue.isEquiv_iff_exists_rpow_eqproof · cited by 4
- Real.geom_mean_eq_arith_mean_weighted_iff_of_pos'proof · cited by 4
- Real.rpowIntegrand₀₁_nonnegproof · cited by 4