Theorems · Theorem · real analysis
Real.rpow_lt_rpow_of_exponent_gt
∀ {x y z : ℝ}, 0 < x → x < 1 → z < y → x ^ y < x ^ z- Cited by
- 5 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.
Cites7
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.logproof · cited by 939
- Real.expproof · cited by 871
- Real.rpow_def_of_posproof · cited by 35
- Real.log_negproof · cited by 15
- Real.exp_lt_expproof · cited by 11
- mul_lt_mul_of_neg_leftproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- Rat.AbsoluteValue.eq_one_of_not_dvdproof · cited by 1
- NNReal.rpow_lt_rpow_of_exponent_gtproof · cited by 1
- Real.one_lt_rpow_of_pos_of_lt_one_of_negproof · cited by 1
- Real.self_lt_rpow_of_lt_oneproof · cited by 0
- Real.rpow_lt_self_of_lt_oneproof · cited by 0