Theorems · Theorem · field theory
IsAlgClosed.exists_pow_nat_eq
∀ {k : Type u} [inst : Field k] [IsAlgClosed k] (x : k) {n : ℕ}, 0 < n → ∃ z, z ^ n = x- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldIsAlgClosed
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- WithBotproof · cited by 1,498
- Polynomial.degreeproof · cited by 643
- ne_of_gtproof · cited by 637
- sub_eq_zeroproof · cited by 407
- Polynomial.eval_Xproof · cited by 172
- Polynomial.IsRootproof · cited by 152
- IsAlgClosedstatement and proof · cited by 150
- Polynomial.eval_Cproof · cited by 145
Cited by2
Results whose statement or proof uses this declaration.
- WittVector.RecursionBase.solution_powproof · cited by 1
- IsAlgClosed.exists_eq_mul_selfproof · cited by 0