Theorems · Theorem · real analysis
Real.rpow_pos_of_pos
∀ {x : ℝ}, 0 < x → ∀ (y : ℝ), 0 < x ^ y- Cited by
- 155 results in Mathlib
- Foundations
- Depth 195 from the axioms, rests on 4,760 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
- Real.logproof · cited by 939
- Real.exp_posproof · cited by 169
- Real.rpow_def_of_posproof · cited by 35
Cited by155
Results whose statement or proof uses this declaration.
- Real.log_rpowproof · cited by 31
- Real.Gamma_pos_of_posproof · cited by 17
- Real.rpow_le_rpow_of_nonposproof · cited by 12
- Real.rpow_lt_rpowproof · cited by 12
- Real.rpowIntegrand₀₁_eq_pow_divproof · cited by 6
- Real.lt_rpow_iff_log_ltproof · cited by 5
- PhragmenLindelof.isBigO_sub_exp_rpowproof · cited by 5
- Real.convexOn_log_Gammaproof · cited by 5
- Real.rpow_le_rpow_left_iffproof · cited by 4
- PeriodPair.hasSumLocallyUniformly_derivWeierstrassPExceptproof · cited by 4
- Real.rpow_le_rpow_left_iff_of_base_lt_oneproof · cited by 4
- LiouvilleWith.exists_posproof · cited by 4