Theorems · Theorem · real analysis
Real.log_nonneg
∀ {x : ℝ}, 1 ≤ x → 0 ≤ Real.log x- Cited by
- 28 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.
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 · cited by 939
- LT.lt.trans_leproof · cited by 678
- zero_lt_oneproof · cited by 598
- Real.log_nonneg_iffproof · cited by 3
Cited by28
Results whose statement or proof uses this declaration.
- Real.rpow_le_rpow_of_exponent_leproof · cited by 32
- ArithmeticFunction.vonMangoldt_nonnegproof · cited by 6
- Real.log_intCast_nonnegproof · cited by 4
- NumberField.hermiteTheorem.rank_le_rankOfDiscrBddproof · cited by 4
- Real.log_natCast_nonnegproof · cited by 4
- Stirling.log_stirlingSeq_sdiff_leproof · cited by 3
- Function.locallyFinsuppWithin.logCounting_nonnegproof · cited by 3
- Real.posLog_eq_logproof · cited by 3
- Chebyshev.theta_nonnegproof · cited by 3
- Function.locallyFinsuppWithin.logCounting_monoproof · cited by 2
- Chebyshev.abs_psi_sub_theta_le_sqrt_mul_logproof · cited by 2
- Height.logHeight_nonnegproof · cited by 1