Theorems · Theorem · field theory
Polynomial.Gal.ext
∀ {F : Type u_1} [inst : Field F] (p : Polynomial F) {σ τ : p.Gal},
(∀ x ∈ p.rootSet p.SplittingField, σ x = τ x) → σ = τ- Cited by
- 5 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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.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
- Subalgebraproof · cited by 1,353
- AlgEquiv.toAlgHomproof · cited by 273
- eq_top_iffproof · cited by 236
- Polynomial.rootSetstatement and proof · cited by 101
- SetLike.ext_iffproof · cited by 64
- AlgEquiv.extproof · cited by 60
- Polynomial.SplittingFieldstatement and proof · cited by 42
- Polynomial.Galstatement and proof · cited by 37
Cited by5
Results whose statement or proof uses this declaration.
- gal_X_pow_sub_C_isSolvable_auxproof · cited by 1
- gal_X_pow_sub_one_isSolvableproof · cited by 1
- Polynomial.Gal.galActionHom_injectiveproof · cited by 1
- Polynomial.Gal.restrictProd_injectiveproof · cited by 1
- Polynomial.Gal.ext_iffproof · cited by 0