Theorems · Theorem · real analysis
Real.sqrt_le_sqrt_iff
∀ {x y : ℝ}, 0 ≤ y → (√x ≤ √y ↔ x ≤ y)- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 6 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_toNNReal_iffproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- Real.sqrt_lt_sqrt_iffproof · cited by 5
- ContinuousLinearMap.norm_adjoint_comp_selfproof · cited by 3
- EisensteinSeries.auxbound2proof · cited by 1
- Real.sqrt_le_sqrt_iff'proof · cited by 1
- Unitization.norm_splitMul_snd_sqproof · cited by 0
- Real.sqrt_le_oneproof · cited by 0