Theorems · Theorem · real analysis
Real.eq_one_of_pos_of_log_eq_zero
∀ {x : ℝ}, 0 < x → Real.log x = 0 → x = 1- Cited by
- 2 results in Mathlib
- Foundations
- Depth 175 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
- zero_lt_oneproof · cited by 598
- Real.log_oneproof · cited by 91
- Set.mem_Ioiproof · cited by 80
- Real.log_injOn_posproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Real.log_ne_zero_of_pos_of_ne_oneproof · cited by 5
- Real.log_eq_zeroproof · cited by 2