Theorems · Theorem · real analysis
Real.lt_sqrt
∀ {x y : ℝ}, 0 ≤ x → (x < √y ↔ x ^ 2 < y)- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 and proof · cited by 545
- sq_nonnegproof · cited by 106
- Real.sqrt_sqproof · cited by 36
- Real.sqrt_lt_sqrt_iffproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Real.sq_ltproof · cited by 2
- InnerProductGeometry.angle_add_pos_of_inner_eq_zeroproof · cited by 2
- Complex.abs_re_lt_normproof · cited by 2
- NumberField.mixedEmbedding.exists_primitive_element_lt_of_isComplexproof · cited by 1