Theorems · Theorem · real analysis
Real.sqrt_lt
∀ {x y : ℝ}, 0 ≤ x → 0 ≤ y → (√x < y ↔ x < y ^ 2)- 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.
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 and proof · cited by 545
- 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.le_sqrtproof · cited by 5
- Real.real_sqrt_lt_nat_sqrt_succproof · cited by 3
- RingOfIntegers.isPrincipalIdealRing_of_abs_discr_ltproof · cited by 2
- EuclideanSpace.ball_zero_eqproof · cited by 1