Theorems · Theorem · real analysis
Real.rpow_lt_one_of_one_lt_of_neg
∀ {x z : ℝ}, 1 < x → z < 0 → x ^ z < 1- Cited by
- 3 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Real.rpow_zeroproof · cited by 69
- Real.rpow_lt_rpow_of_exponent_ltproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- NNReal.rpow_lt_one_of_one_lt_of_negproof · cited by 1
- DirichletCharacter.eulerProduct_log_eq_LSeriesproof · cited by 1
- closedBall_rpow_sub_one_eq_empty_auxproof · cited by 1