Theorems · Theorem · number theory
irrational_sqrt_ratCast_iff_of_nonneg
∀ {q : ℚ}, 0 ≤ q → (Irrational √↑q ↔ ¬IsSquare q)- Defined in
- Mathlib.NumberTheory.Real.Irrational
- Cited by
- 3 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.
Cites11
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
- Iff.notproof · cited by 489
- Irrationalstatement · cited by 139
- IsSquarestatement · cited by 132
- Real.mul_self_sqrtproof · cited by 23
- Rat.cast_mulproof · cited by 19
- Rat.cast_nonnegproof · cited by 5
- Rat.cast_injectiveproof · cited by 5
- Real.sqrt_mul_self_eq_absproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- irrational_sqrt_natCast_iffproof · cited by 2
- irrational_sqrt_ratCast_iffproof · cited by 1
- irrational_sqrt_intCast_iff_of_nonnegproof · cited by 0