Theorems · Theorem · real analysis
NNReal.le_sqrt_iff_sq_le
∀ {x y : NNReal}, x ≤ NNReal.sqrt y ↔ x ^ 2 ≤ y- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- OrderIsostatement · cited by 874
- OrderIso.symmproof · cited by 475
- NNReal.sqrtstatement and proof · cited by 91
- OrderIso.to_galoisConnectionproof · cited by 32
Cited by4
Results whose statement or proof uses this declaration.
- NNReal.le_gm_and_am_leproof · cited by 5
- NNReal.dist_gm_am_leproof · cited by 1
- NNReal.sum_mul_le_sqrt_mul_sqrtproof · cited by 1
- CStarAlgebra.nnnorm_sub_mul_self_leproof · cited by 1