Theorems · Theorem · real analysis
NNReal.sqrt_mul_lt_half_add_of_ne
∀ {x y : NNReal}, x ≠ y → NNReal.sqrt (x * y) < (x + y) / 2The strict AM–GM inequality for two NNReals, with means in canonical form.
- Cited by
- 1 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.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- NNRealstatement and proof · cited by 4,310
- mul_commproof · cited by 2,262
- le_reflproof · cited by 2,061
- add_commproof · cited by 1,535
- le_of_ltproof · cited by 1,175
- OrderIsostatement · cited by 874
- pow_posproof · cited by 292
- sqproof · cited by 280
- mul_le_mul'proof · cited by 274
- NNReal.sqrtstatement and proof · cited by 91
- add_right_commproof · cited by 85
Cited by1
Results whose statement or proof uses this declaration.
- NNReal.agmSequences_fst_lt_snd_of_neproof · cited by 2