Theorems · Theorem · real analysis
Real.rpow_lt_rpow_left_iff_of_base_lt_one
∀ {x y z : ℝ}, 0 < x → x < 1 → (x ^ y < x ^ z ↔ z < y)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- lt_iff_not_geproof · cited by 22
- Real.rpow_le_rpow_left_iff_of_base_lt_oneproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Real.lt_logb_iff_rpow_lt_of_base_lt_oneproof · cited by 0
- Real.logb_lt_iff_lt_rpow_of_base_lt_oneproof · cited by 0