Theorems · Theorem · real analysis
Real.log_neg_of_lt_zero
∀ {x : ℝ}, x < 0 → -1 < x → Real.log x < 0- 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.
Cites8
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
- neg_negproof · cited by 960
- Real.logstatement and proof · cited by 939
- lt_of_not_geproof · cited by 374
- Real.log_neg_eq_logproof · cited by 27
- Real.log_negproof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- Real.binEntropy_neg_of_negproof · cited by 4
- Mathlib.Meta.Positivity.log_nz_of_isRat_negproof · cited by 0