Theorems · Theorem · real analysis
Real.rpow_le_rpow_of_exponent_ge
∀ {x y z : ℝ}, 0 < x → x ≤ 1 → z ≤ y → x ^ y ≤ x ^ z- Cited by
- 8 results in Mathlib
- Foundations
- Depth 195 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
- Real.logproof · cited by 939
- Real.expproof · cited by 871
- Real.rpow_def_of_posproof · cited by 35
- Real.exp_le_expproof · cited by 16
- mul_le_mul_of_nonpos_leftproof · cited by 11
- Real.log_nonposproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- Real.rpow_le_rpow_of_exponent_ge_of_impproof · cited by 4
- Real.one_le_rpow_of_pos_of_le_one_of_nonposproof · cited by 4
- NNReal.rpow_le_rpow_of_exponent_geproof · cited by 3
- mellin_hasDerivAt_of_isBigO_rpowproof · cited by 2
- Rat.AbsoluteValue.eq_one_of_not_dvdproof · cited by 1
- Complex.HadamardThreeLines.F_BddAboveproof · cited by 1
- sum_div_pow_sq_le_div_sqproof · cited by 1
- Real.rpow_le_rpow_of_exponent_le_or_geproof · cited by 0