Theorems · Theorem · real analysis
Real.log_le_iff_le_exp
∀ {x y : ℝ}, 0 < x → (Real.log x ≤ y ↔ x ≤ Real.exp 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.
- Real.Gamma_three_div_two_lt_oneproof · cited by 2
- Behrend.lower_bound_le_one'proof · cited by 1
- Complex.IsExpCmpFilter.isLittleO_log_norm_reproof · cited by 1
- Real.le_exp_of_log_leproof · cited by 0
- NumberField.Units.dirichletUnitTheorem.unitLattice_inter_ball_finiteproof · cited by 0