Theorems · Theorem · field theory
IsSepClosed.of_exists_root
∀ (k : Type u) [inst : Field k], (∀ (p : Polynomial k), p.Monic → Irreducible p → p.Separable → ∃ x, Polynomial.eval x p = 0) → IsSepClosed k
- Defined in
- Mathlib.FieldTheory.IsSepClosed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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
- Polynomialstatement and proof · cited by 5,681
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- Polynomial.Cproof · cited by 1,598
- Polynomial.evalstatement and proof · cited by 796
- Multiset.prodproof · cited by 528
- Polynomial.leadingCoeffproof · cited by 498
- Irreduciblestatement and proof · cited by 496
- Polynomial.Monicstatement and proof · cited by 461
- Polynomial.Splitsproof · cited by 290
Cited by1
Results whose statement or proof uses this declaration.
- IsSepClosed.separableClosure_eq_bot_iffproof · cited by 1