Theorems · Theorem · real analysis
Real.le_log_iff_exp_le
∀ {x y : ℝ}, 0 < y → (x ≤ Real.log y ↔ Real.exp x ≤ y)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 172 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 · cited by 939
- Real.expstatement and proof · cited by 871
- Real.exp_logproof · cited by 58
- Real.exp_le_expproof · cited by 16
Cited by5
Results whose statement or proof uses this declaration.
- Behrend.roth_lower_bound_explicitproof · cited by 1
- Real.log_div_self_antitoneOnproof · cited by 1
- Behrend.dValue_posproof · cited by 1
- Stirling.stirlingSeq'_bounded_by_pos_constantproof · cited by 1
- Real.le_log_one_add_of_nonnegproof · cited by 0