Theorems · Theorem · real analysis
Real.log_exp
∀ (x : ℝ), Real.log (Real.exp x) = x
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 and proof · cited by 939
- Real.expstatement and proof · cited by 871
- Real.exp_posproof · cited by 169
- Real.exp_logproof · cited by 58
- Real.exp_injectiveproof · cited by 12
Cited by33
Results whose statement or proof uses this declaration.
- Real.tendsto_log_atTopproof · cited by 26
- Real.exp_mulproof · cited by 13
- Real.aemeasurable_of_aemeasurable_expproof · cited by 11
- EReal.log_expproof · cited by 6
- Real.tendsto_log_nhdsGT_zeroproof · cited by 5
- Stirling.log_stirlingSeq_sdiff_hasSumproof · cited by 4
- Complex.log_expproof · cited by 4
- Polynomial.logMahlerMeasure_eq_log_MahlerMeasureproof · cited by 4
- ProbabilityTheory.Kernel.HasSubgaussianMGF.cgf_leproof · cited by 2
- MeasureTheory.llr_tilted_leftproof · cited by 2
- MeasureTheory.llr_tilted_rightproof · cited by 2
- Real.log_comp_expproof · cited by 2