Theorems · Theorem · real analysis
Real.rpow_lt_one_iff_of_pos
∀ {x y : ℝ}, 0 < x → (x ^ y < 1 ↔ 1 < x ∧ y < 0 ∨ x < 1 ∧ 0 < y)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 195 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
- LT.lt.leproof · cited by 2,189
- Real.logproof · cited by 939
- Real.rpow_def_of_posproof · cited by 35
- Real.log_neg_iffproof · cited by 7
- Real.exp_lt_one_iffproof · cited by 7
- Real.log_pos_iffproof · cited by 6
- mul_neg_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Real.rpow_lt_one_iffproof · cited by 1