Theorems · Theorem · real analysis
Real.log_sqrt
∀ {x : ℝ}, 0 ≤ x → Real.log √x = Real.log x / 2- Cited by
- 5 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.
Cites9
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
- mul_commproof · cited by 2,262
- Real.logstatement and proof · cited by 939
- Real.sqrtstatement and proof · cited by 545
- two_ne_zeroproof · cited by 251
- Real.sq_sqrtproof · cited by 53
- eq_div_iffproof · cited by 38
- Nat.cast_twoproof · cited by 32
- Real.log_powproof · cited by 29
Cited by5
Results whose statement or proof uses this declaration.
- AnalyticAt.harmonicAt_log_normproof · cited by 4
- Stirling.log_stirlingSeq_bounded_by_constantproof · cited by 1
- circleAverage_log_norm_sub_const₁proof · cited by 1
- Stirling.le_log_factorial_stirlingproof · cited by 0
- Real.artanh_eq_half_logproof · cited by 0