Theorems · Theorem · real analysis
Real.log_div
∀ {x y : ℝ}, x ≠ 0 → y ≠ 0 → Real.log (x / y) = Real.log x - Real.log y- Cited by
- 21 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
- abs_divproof · cited by 38
- div_ne_zeroproof · cited by 29
- Real.exp_subproof · cited by 13
- Real.exp_injectiveproof · cited by 12
- Real.exp_log_eq_absproof · cited by 7
Cited by21
Results whose statement or proof uses this declaration.
- strictConcaveOn_log_Ioiproof · cited by 5
- integral_invproof · cited by 5
- Stirling.log_stirlingSeq_sdiff_hasSumproof · cited by 4
- Real.strictMono_eulerMascheroniSeqproof · cited by 3
- Real.hasSum_log_one_add_invproof · cited by 2
- Real.strictAnti_eulerMascheroniSeq'proof · cited by 2
- UpperHalfPlane.dist_of_re_eqproof · cited by 2
- Stirling.log_stirlingSeq_bounded_by_constantproof · cited by 1
- Stirling.log_stirlingSeq_formulaproof · cited by 1
- Behrend.dValue_posproof · cited by 1
- Real.abs_log_mul_self_ltproof · cited by 1
- ZetaAsymptotics.term_oneproof · cited by 1