Theorems · Theorem · real analysis
Real.log_pos
∀ {x : ℝ}, 1 < x → 0 < Real.log x- Cited by
- 51 results in Mathlib
- Foundations
- Depth 174 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.
- Realstatement and proof · cited by 25,697
- LT.lt.leproof · cited by 2,189
- Real.logstatement · cited by 939
- zero_lt_oneproof · cited by 598
- lt_transproof · cited by 165
- Real.log_pos_iffproof · cited by 6
Cited by51
Results whose statement or proof uses this declaration.
- Mathlib.Meta.Positivity.log_pos_of_isNatproof · cited by 12
- Real.isLittleO_const_log_atTopproof · cited by 5
- Real.rpow_lt_rpow_of_exponent_ltproof · cited by 5
- AkraBazziRecurrence.strictAntiOn_smoothingFnproof · cited by 4
- Real.rpow_le_rpow_left_iffproof · cited by 4
- ProbabilityTheory.Fernique.logRatio_posproof · cited by 4
- Real.binEntropy_neg_of_negproof · cited by 4
- Behrend.nValue_posproof · cited by 3
- AkraBazziRecurrence.eventually_one_add_smoothingFn_posproof · cited by 3
- ArithmeticFunction.vonMangoldt_ne_zero_iffproof · cited by 3
- Real.binEntropy_posproof · cited by 3
- Real.strictMono_rpow_of_base_gt_oneproof · cited by 2