Theorems · Theorem · field theory
IsSepClosed.exists_root
∀ {k : Type u} [inst : Field k] [IsSepClosed k] (p : Polynomial k), p.degree ≠ 0 → p.Separable → ∃ x, p.IsRoot x- Defined in
- Mathlib.FieldTheory.IsSepClosed
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldIsSepClosed
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Polynomialstatement and proof · cited by 5,681
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.IsRootstatement · cited by 152
- Polynomial.Separablestatement and proof · cited by 117
- IsSepClosedstatement and proof · cited by 41
- Polynomial.Splits.exists_eval_eq_zeroproof · cited by 14
- IsSepClosed.splits_of_separableproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- IsSepClosed.exists_eval₂_eq_zero_of_injectiveproof · cited by 2
- IsSepClosed.exists_root_C_mul_X_pow_add_C_mul_X_add_Cproof · cited by 1
- IsSepClosed.exists_pow_nat_eqproof · cited by 1
- IsSepClosed.roots_eq_zero_iffproof · cited by 0