Theorems · Theorem · real analysis
Real.le_sqrt
∀ {x y : ℝ}, 0 ≤ x → 0 ≤ y → (x ≤ √y ↔ x ^ 2 ≤ y)Note: if you want to conclude x ≤ √y, then use Real.le_sqrt_of_sq_le.
If you have x > 0, consider using Real.le_sqrt'
- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Real.sqrtstatement · cited by 545
- le_iff_le_iff_lt_iff_ltproof · cited by 25
- Real.sqrt_ltproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- Real.nat_sqrt_le_real_sqrtproof · cited by 3
- Real.sq_leproof · cited by 2
- NumberField.abs_discr_ge'proof · cited by 2
- Unitization.norm_splitMul_snd_sqproof · cited by 0
- Unitary.continuousOn_argSelfAdjointproof · cited by 0