Theorems · Theorem · real analysis
NNReal.le_rpow_inv_iff
∀ {x y : NNReal} {z : ℝ}, 0 < z → (x ≤ y ^ z⁻¹ ↔ x ^ z ≤ y)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 201 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
- NNRealstatement and proof · cited by 4,310
- LT.lt.ne'proof · cited by 1,417
- one_divproof · cited by 624
- NNReal.rpow_le_rpow_iffproof · cited by 7
- NNReal.rpow_self_rpow_invproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- NNReal.rpow_add_rpow_le_addproof · cited by 2
- NNReal.rpow_add_rpow_leproof · cited by 2
- NNReal.rpow_add_le_add_rpowproof · cited by 2
- NNReal.rpow_inv_lt_iffproof · cited by 0