Theorems · Theorem · field theory
Polynomial.rootSet_prod
∀ {R : Type u} {S : Type v} [inst : Field R] [inst_1 : CommRing S] [inst_2 : IsDomain S] [inst_3 : Algebra R S]
{ι : Type u_1} (f : ι → Polynomial R) (s : Finset ι), s.prod f ≠ 0 → (s.prod f).rootSet S = ⋃ i ∈ s, (f i).rootSet S- Defined in
- Mathlib.Algebra.Polynomial.FieldDivision
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Finsetstatement and proof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- SetLike.coeproof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Multisetproof · cited by 2,627
- Set.iUnionstatement and proof · cited by 2,483
- Finset.prodstatement and proof · cited by 2,356
- IsDomainstatement and proof · cited by 2,196
Cited by1
Results whose statement or proof uses this declaration.
- IntermediateField.isSplittingField_iSupproof · cited by 0