Theorems · Theorem · real analysis
Real.exp_log_eq_abs
∀ {x : ℝ}, x ≠ 0 → Real.exp (Real.log x) = |x|- Cited by
- 7 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Set.Elemproof · cited by 7,166
- absstatement and proof · cited by 1,814
- Set.Ioiproof · cited by 1,463
- Real.logstatement · cited by 939
- Real.expstatement and proof · cited by 871
- OrderIso.symmproof · cited by 475
- Subtype.coe_mkproof · cited by 81
- abs_posproof · cited by 45
- OrderIso.apply_symm_applyproof · cited by 45
- Real.expOrderIsoproof · cited by 12
Cited by7
Results whose statement or proof uses this declaration.
- Real.exp_logproof · cited by 58
- Real.log_mulproof · cited by 52
- Real.log_invproof · cited by 35
- Real.log_divproof · cited by 21
- Real.log_absproof · cited by 17
- Real.le_exp_logproof · cited by 2
- Real.exp_log_of_negproof · cited by 0