Theorems · Theorem · real analysis
Real.log_lt_sub_one_of_pos
∀ {x : ℝ}, 0 < x → x ≠ 1 → Real.log x < x - 1- Cited by
- 4 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.
Cites14
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
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- Real.logstatement and proof · cited by 939
- Real.expproof · cited by 871
- zero_lt_oneproof · cited by 598
- lt_of_not_geproof · cited by 374
- sub_eq_zero_of_eqproof · cited by 154
- Real.log_oneproof · cited by 91
- Set.mem_Ioiproof · cited by 80
- Real.exp_logproof · cited by 58
- Real.log_injOn_posproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- strictConcaveOn_log_Ioiproof · cited by 5
- Real.strictMono_eulerMascheroniSeqproof · cited by 3
- Real.self_sub_one_lt_mul_logproof · cited by 2
- Real.strictAnti_eulerMascheroniSeq'proof · cited by 2