Theorems · Theorem · real analysis
NNReal.sqrt_mul_le_half_add
∀ (x y : NNReal), NNReal.sqrt (x * y) ≤ (x + y) / 2
The AM–GM inequality for two NNReals, with means in canonical form.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- NNRealstatement and proof · cited by 4,310
- mul_assocproof · cited by 1,667
- OrderIsostatement · cited by 874
- pow_posproof · cited by 292
- NNReal.sqrtstatement · cited by 91
- div_powproof · cited by 66
- le_div_iff₀'proof · cited by 32
- NNReal.sqrt_le_iff_le_sqproof · cited by 3
- four_mul_le_sq_addproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- NNReal.agmSequences_monotone_and_antitoneproof · cited by 2
- NNReal.agmSequences_fst_le_sndproof · cited by 1
- NNReal.dist_gm_am_leproof · cited by 1