Theorems · Theorem · number theory
irrational_sqrt_natCast_iff
∀ {n : ℕ}, Irrational √↑n ↔ ¬IsSquare n- Defined in
- Mathlib.NumberTheory.Real.Irrational
- Cited by
- 2 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.
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
- Real.sqrtstatement and proof · cited by 545
- Irrationalstatement and proof · cited by 139
- IsSquarestatement · cited by 132
- Nat.cast_nonnegproof · cited by 109
- Rat.cast_natCastproof · cited by 67
- irrational_sqrt_ratCast_iff_of_nonnegproof · cited by 3
- Rat.isSquare_natCast_iffproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Nat.Prime.irrational_sqrtproof · cited by 3
- irrational_sqrt_ofNat_iffproof · cited by 0