Theorems · Theorem · field theory
Polynomial.Splits.mem_range_of_isRoot
∀ {R : Type u_1} {S : Type u_2} [inst : Field R] [inst_1 : CommRing S] [IsDomain S] {f : Polynomial R},
f.Splits → f ≠ 0 → ∀ {i : R →+* S} {x : S}, (Polynomial.map i f).IsRoot x → x ∈ i.range- Defined in
- Mathlib.Algebra.Polynomial.Splits
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Multisetproof · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Polynomial.mapstatement and proof · cited by 806
- Subringstatement · cited by 602
- Polynomial.Splitsstatement and proof · cited by 290
- Polynomial.rootsproof · cited by 264
- Polynomial.IsRootstatement and proof · cited by 152
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Splits.mem_subfield_of_isRootproof · cited by 0