Theorems · Theorem · real analysis
Real.sq_le
∀ {x y : ℝ}, 0 ≤ y → (x ^ 2 ≤ y ↔ -√y ≤ x ∧ x ≤ √y)- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- absproof · cited by 1,814
- Real.sqrtstatement and proof · cited by 545
- abs_nonnegproof · cited by 168
- abs_leproof · cited by 64
- sq_absproof · cited by 49
- Real.le_sqrtproof · cited by 5
- Real.abs_le_sqrtproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Real.le_sqrt_of_sq_leproof · cited by 10
- Real.neg_sqrt_le_of_sq_leproof · cited by 0