Theorems · Theorem · real analysis
Real.rpow_def_of_pos
∀ {x : ℝ}, 0 < x → ∀ (y : ℝ), x ^ y = Real.exp (Real.log x * y)- Cited by
- 35 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by35
Results whose statement or proof uses this declaration.
- Real.rpow_pos_of_posproof · cited by 155
- Real.rpow_addproof · cited by 41
- Real.mul_rpowproof · cited by 37
- Real.rpow_le_rpow_of_exponent_leproof · cited by 32
- Real.log_rpowproof · cited by 31
- Real.exp_mulproof · cited by 13
- Real.rpow_lt_rpowproof · cited by 12
- Function.hasTemperateGrowth_one_add_norm_sq_rpowproof · cited by 9
- Real.rpow_le_rpow_of_exponent_geproof · cited by 8
- Real.abs_rpow_le_abs_rpowproof · cited by 7
- intervalIntegral.intervalIntegrable_rpow'proof · cited by 6
- Real.rpow_lt_rpow_of_exponent_gtproof · cited by 5