Theorems · Theorem · real analysis
Real.sqrt_le_sqrt
∀ {x y : ℝ}, x ≤ y → √x ≤ √y- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NNReal.toRealproof · cited by 1,260
- Real.sqrtstatement and proof · cited by 545
- Real.toNNRealproof · cited by 267
- NNReal.sqrtproof · cited by 91
- NNReal.coe_le_coeproof · cited by 73
- NNReal.sqrt_le_sqrtproof · cited by 5
- Real.toNNReal_le_toNNRealproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Real.sqrt_monotoneproof · cited by 9
- ContinuousLinearMap.norm_adjoint_comp_selfproof · cited by 3
- Real.abs_le_sqrtproof · cited by 2
- Behrend.dValue_posproof · cited by 1
- EuclideanGeometry.dist_le_of_wbtw_of_inner_eq_zeroproof · cited by 1