Theorems · Theorem · real analysis
Real.one_lt_rpow_iff_of_pos
∀ {x y : ℝ}, 0 < x → (1 < x ^ y ↔ 1 < x ∧ 0 < y ∨ x < 1 ∧ y < 0)- Cited by
- 2 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
- mul_pos_iffproof · cited by 8
- Real.log_neg_iffproof · cited by 7
- Real.log_pos_iffproof · cited by 6
- Real.one_lt_exp_iffproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Real.summable_nat_rpow_invproof · cited by 1
- Real.one_lt_rpow_iffproof · cited by 0