Theorems · Theorem · real analysis
Real.rpow_lt_rpow_of_neg
∀ {x y z : ℝ}, 0 < x → x < y → z < 0 → y ^ z < x ^ z- Cited by
- 3 results in Mathlib
- Foundations
- Depth 197 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_of_ltproof · cited by 1,175
- LT.lt.transproof · cited by 370
- Real.rpow_pos_of_posproof · cited by 155
- neg_posproof · cited by 74
- Real.rpow_negproof · cited by 36
- inv_lt_inv₀proof · cited by 17
- Real.rpow_lt_rpowproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- Real.rpow_lt_rpow_iff_of_negproof · cited by 5
- NNReal.rpow_lt_rpow_of_negproof · cited by 0
- Real.strictAntiOn_rpow_Ioi_of_exponent_negproof · cited by 0