Theorems · Theorem · real analysis
Real.log_neg
∀ {x : ℝ}, 0 < x → x < 1 → Real.log x < 0- Cited by
- 15 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.
Cites3
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.log_neg_iffproof · cited by 7
Cited by15
Results whose statement or proof uses this declaration.
- Real.rpow_lt_rpow_of_exponent_gtproof · cited by 5
- Real.rpow_le_rpow_left_iff_of_base_lt_oneproof · cited by 4
- Real.strictAnti_rpow_of_base_lt_oneproof · cited by 3
- Real.logb_lt_logb_iff_of_base_lt_oneproof · cited by 2
- Real.logb_lt_logb_of_base_lt_oneproof · cited by 2
- Real.log_neg_of_lt_zeroproof · cited by 2
- Rat.AbsoluteValue.eq_one_of_not_dvdproof · cited by 1
- Real.tendsto_logb_nhdsNE_zero_of_base_lt_oneproof · cited by 1
- Real.not_differentiableAt_inv_log_zeroproof · cited by 1
- NumberField.Units.dirichletUnitTheorem.exists_unitproof · cited by 1
- AbsoluteValue.IsEquiv.log_div_log_posproof · cited by 1
- Real.logb_le_logb_of_base_lt_oneproof · cited by 0