Theorems · Theorem · real analysis
NNReal.rpow_add_le_mul_rpow_add_rpow
∀ (z₁ z₂ : NNReal) {p : ℝ}, 1 ≤ p → (z₁ + z₂) ^ p ≤ 2 ^ (p - 1) * (z₁ ^ p + z₂ ^ p)Unweighted mean inequality, version for two elements of ℝ≥0 and real exponents.
- Defined in
- Mathlib.Analysis.MeanInequalitiesPow
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound
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- Realstatement and proof · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- le_reflproof · cited by 2,061
- sub_selfproof · cited by 996
- ne_of_gtproof · cited by 637
- one_divproof · cited by 624
- sub_posproof · cited by 147
- eq_or_lt_of_leproof · cited by 92
- add_halvesproof · cited by 78
- inv_mul_cancel_left₀proof · cited by 47
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