Theorems · Theorem · real analysis
Real.lt_rpow_iff_log_lt
∀ {x y z : ℝ}, 0 < x → 0 < y → (x < y ^ z ↔ Real.log x < z * Real.log y)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.logstatement and proof · cited by 939
- Real.rpow_pos_of_posproof · cited by 155
- Real.log_rpowproof · cited by 31
- Real.log_lt_log_iffproof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- Real.rpow_lt_of_lt_logproof · cited by 2
- Real.lt_rpow_of_log_ltproof · cited by 2
- SzemerediRegularity.hundred_lt_pow_initialBound_mulproof · cited by 1
- Real.lt_zpow_iff_log_ltproof · cited by 0
- Real.lt_pow_iff_log_ltproof · cited by 0