Theorems · Theorem · real analysis
Real.one_lt_rpow_iff
∀ {x y : ℝ}, 0 ≤ x → (1 < x ^ y ↔ 1 < x ∧ 0 < y ∨ 0 < x ∧ x < 1 ∧ y < 0)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 196 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
- LE.le.eq_or_ltproof · cited by 220
- emproof · cited by 115
- Real.rpow_zeroproof · cited by 69
- Real.zero_rpowproof · cited by 57
- LT.lt.not_gtproof · cited by 54
- zero_lt_one'proof · cited by 16
- Real.one_lt_rpow_iff_of_posproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.