Theorems · Theorem · real analysis
Real.posLog_eq_zero_iff
∀ (x : ℝ), x.posLog = 0 ↔ |x| ≤ 1
The function log⁺ is zero in the interval [-1,1].
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- absstatement and proof · cited by 1,814
- Real.logproof · cited by 939
- abs_nonnegproof · cited by 168
- Real.posLogstatement and proof · cited by 61
- Real.log_absproof · cited by 17
- Real.log_nonpos_iffproof · cited by 4
- Real.posLog_absproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- circleAverage_log_norm_sub_const_eq_posLogproof · cited by 4
- circleAverage_log_norm_sub_const_of_mem_closedBallproof · cited by 1
- Real.posLog_powproof · cited by 1
- Real.continuous_posLogproof · cited by 1