Theorems · Theorem · field theory
Polynomial.Gal.ext_iff
∀ {F : Type u_1} [inst : Field F] {p : Polynomial F} {σ τ : p.Gal}, σ = τ ↔ ∀ x ∈ p.rootSet p.SplittingField, σ x = τ x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 157 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.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Polynomial.rootSetstatement and proof · cited by 101
- Polynomial.SplittingFieldstatement and proof · cited by 42
- Polynomial.Galstatement and proof · cited by 37
- Polynomial.Gal.extproof · cited by 5
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