Theorems · Theorem · field theory
Polynomial.Splits.mem_subfield_of_isRoot
∀ {R : Type u_1} [inst : Field R] (F : Subfield R) {f : Polynomial ↥F},
f.Splits → f ≠ 0 → ∀ {x : R}, (Polynomial.map F.subtype f).IsRoot x → x ∈ F- Defined in
- Mathlib.Algebra.Polynomial.Splits
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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Cites8
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
- Polynomial.mapstatement and proof · cited by 806
- Subfieldstatement and proof · cited by 303
- Polynomial.Splitsstatement and proof · cited by 290
- Polynomial.IsRootstatement and proof · cited by 152
- Subfield.subtypestatement and proof · cited by 16
- Polynomial.Splits.mem_range_of_isRootproof · cited by 1
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