Theorems · Theorem · real analysis
Real.log_le_log_iff
∀ {x y : ℝ}, 0 < x → 0 < y → (Real.log x ≤ Real.log y ↔ x ≤ y)- Cited by
- 12 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 and proof · cited by 939
- Real.expproof · cited by 871
- Real.exp_logproof · cited by 58
- Real.exp_le_expproof · cited by 16
Cited by12
Results whose statement or proof uses this declaration.
- Real.log_le_logproof · cited by 39
- Real.rpow_le_rpow_left_iffproof · cited by 4
- Real.rpow_le_rpow_left_iff_of_base_lt_oneproof · cited by 4
- Real.le_rpow_iff_log_leproof · cited by 4
- Real.logb_le_logbproof · cited by 2
- Stirling.stirlingSeq'_antitoneproof · cited by 2
- Real.rpow_le_iff_le_logproof · cited by 2
- Behrend.dValue_posproof · cited by 1
- Complex.IsExpCmpFilter.isLittleO_log_norm_reproof · cited by 1
- Behrend.lower_bound_le_one'proof · cited by 1
- Behrend.boundproof · cited by 1
- Real.logb_le_logb_of_base_lt_oneproof · cited by 0