Theorems · Theorem · real analysis
Real.one_le_rpow_of_pos_of_le_one_of_nonpos
∀ {x z : ℝ}, 0 < x → x ≤ 1 → z ≤ 0 → 1 ≤ x ^ z- Cited by
- 4 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_le_rpow_of_exponent_geproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- pow_mul_le_of_le_of_pow_mul_leproof · cited by 2
- finite_integral_one_add_normproof · cited by 1
- finite_integral_rpow_sub_one_pow_auxproof · cited by 1
- NNReal.one_le_rpow_of_pos_of_le_one_of_nonposproof · cited by 1