Theorems · Theorem · field theory
IsRealClosed.exists_eq_zpow_of_isSquare
∀ {R : Type u} [inst : Field R] [IsRealClosed R] {x : R}, IsSquare x → ∀ {k : ℤ}, k ≠ 0 → ∃ r, x = r ^ k- Defined in
- Mathlib.FieldTheory.IsRealClosed.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldIsRealClosed
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.
- Fieldstatement and proof · cited by 7,404
- inv_invproof · cited by 494
- zpow_natCastproof · cited by 271
- zpow_negproof · cited by 198
- inv_powproof · cited by 140
- IsSquarestatement and proof · cited by 132
- IsRealClosedstatement and proof · cited by 13
- IsRealClosed.exists_eq_pow_of_isSquareproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsRealClosed.exists_eq_zpow_of_nonnegproof · cited by 0