Theorems · Theorem · real analysis
Real.one_lt_rpow_of_pos_of_lt_one_of_neg
∀ {x z : ℝ}, 0 < x → x < 1 → z < 0 → 1 < x ^ z- Cited by
- 1 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
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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_gtproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- NNReal.one_lt_rpow_of_pos_of_lt_one_of_negproof · cited by 1