Theorems · Theorem · field theory
IsRealClosed.exists_eq_pow_of_isSquare
∀ {R : Type u} [inst : Field R] [IsRealClosed R] {x : R}, IsSquare x → ∀ {n : ℕ}, n ≠ 0 → ∃ r, x = r ^ n- Defined in
- Mathlib.FieldTheory.IsRealClosed.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 116 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.
Cites13
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
- neg_negproof · cited by 960
- neg_mulproof · cited by 654
- mul_negproof · cited by 590
- Evenproof · cited by 444
- Oddproof · cited by 364
- pow_addproof · cited by 315
- IsSquarestatement and proof · cited by 132
- Nat.strong_induction_onproof · cited by 52
- Nat.even_or_oddproof · cited by 28
- IsRealClosedstatement and proof · cited by 13
- IsRealClosed.isSquare_or_isSquare_negproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- IsRealClosed.exists_eq_zpow_of_isSquareproof · cited by 1
- IsRealClosed.exists_eq_pow_of_nonnegproof · cited by 0