Theorems · Theorem · real analysis
Real.logb_lt_logb_iff_of_base_lt_one
∀ {b x y : ℝ}, 0 < b → b < 1 → 0 < x → 0 < y → (Real.logb b x < Real.logb b y ↔ y < x)- 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.logproof · cited by 939
- Real.logbstatement and proof · cited by 119
- Real.log_negproof · cited by 15
- Real.log_lt_log_iffproof · cited by 8
- div_lt_div_right_of_negproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Real.logb_pos_iff_of_base_lt_oneproof · cited by 2
- Real.logb_neg_iff_of_base_lt_oneproof · cited by 2