Theorems · Theorem · real analysis
Real.log_pos_iff
∀ {x : ℝ}, 0 ≤ x → (0 < Real.log x ↔ 1 < x)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- zero_lt_oneproof · cited by 598
- LE.le.eq_or_ltproof · cited by 220
- Real.log_oneproof · cited by 91
- Real.log_zeroproof · cited by 84
- Real.log_lt_log_iffproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- Real.log_posproof · cited by 51
- Real.log_nonpos_iffproof · cited by 4
- Real.monotoneOn_posLogproof · cited by 2
- Real.one_lt_rpow_iff_of_posproof · cited by 2
- Real.rpow_lt_one_iff_of_posproof · cited by 1
- tendsto_rpow_atBot_of_base_gt_oneproof · cited by 0