Theorems · Theorem · field theory
IsAlgClosed.card_roots_eq_natDegree
∀ {k : Type u} [inst : Field k] [IsAlgClosed k] {p : Polynomial k}, p.roots.card = p.natDegree- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 138 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.
Cites14
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
- add_zeroproof · cited by 2,707
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.natDegreestatement and proof · cited by 1,105
- Multiset.mapproof · cited by 876
- Multiset.prodproof · cited by 528
- Multiset.cardstatement and proof · cited by 375
- Polynomial.rootsstatement and proof · cited by 264
- IsAlgClosedstatement and proof · cited by 150
Cited by4
Results whose statement or proof uses this declaration.
- IsAlgClosed.card_roots_map_eq_natDegree_of_injectiveproof · cited by 1
- IsAlgClosed.card_roots_map_eq_natDegree_of_isUnit_leadingCoeffproof · cited by 1
- IsAlgClosed.card_roots_map_eq_natDegree_of_leadingCoeff_ne_zeroproof · cited by 1
- IsAlgClosed.card_roots_map_eq_natDegree_from_simpleRingproof · cited by 0