Theorems · Theorem · real analysis
Real.log_mul
∀ {x y : ℝ}, x ≠ 0 → y ≠ 0 → Real.log (x * y) = Real.log x + Real.log y- Cited by
- 52 results in Mathlib
- Foundations
- Depth 171 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
- absproof · cited by 1,814
- Real.logstatement and proof · cited by 939
- Real.expproof · cited by 871
- mul_ne_zeroproof · cited by 178
- abs_mulproof · cited by 98
- Real.exp_addproof · cited by 39
- Real.exp_injectiveproof · cited by 12
- Real.exp_log_eq_absproof · cited by 7
Cited by52
Results whose statement or proof uses this declaration.
- Real.mul_rpowproof · cited by 37
- Real.log_powproof · cited by 29
- Polynomial.mahlerMeasure_mulproof · cited by 5
- Real.convexOn_log_Gammaproof · cited by 5
- ENNReal.log_mul_addproof · cited by 4
- Function.locallyFinsuppWithin.logCounting_single_eq_log_sub_constproof · cited by 4
- Stirling.log_stirlingSeq_sdiff_hasSumproof · cited by 4
- Real.posLog_mulproof · cited by 3
- MeromorphicOn.extract_zeros_poles_logproof · cited by 3
- Chebyshev.psi_geproof · cited by 3
- MeasureTheory.llr_smul_rightproof · cited by 3
- Real.log_list_prodproof · cited by 2