Theorems · Theorem · real analysis
Real.le_rpow_inv_iff_of_neg
∀ {x y z : ℝ}, 0 < x → 0 < y → z < 0 → (x ≤ y ^ z⁻¹ ↔ y ≤ x ^ z)- Cited by
- 2 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
- le_of_ltproof · cited by 1,175
- LT.lt.neproof · cited by 872
- Real.rpow_pos_of_posproof · cited by 155
- Real.rpow_inv_rpowproof · cited by 12
- Real.rpow_le_rpow_iff_of_negproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- le_rpow_one_add_norm_iff_norm_leproof · cited by 1
- NNReal.le_rpow_inv_iff_of_negproof · cited by 0