Theorems · Theorem · field theory

gal_isSolvable_tower

∀ {F : Type u_1} [inst : Field F] (p q : Polynomial F),
  (Polynomial.map (algebraMap F q.SplittingField) p).Splits →
    Group.IsSolvable p.Gal →
      Group.IsSolvable (Polynomial.map (algebraMap F p.SplittingField) q).Gal → Group.IsSolvable q.Gal

Defined in: Mathlib.FieldTheory.AbelRuffini
Cited by: 1 results in Mathlib
Foundations: Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field

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Cites18

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Fieldstatement and proof · cited by 7,404
Polynomialstatement and proof · cited by 5,681
Algebra.algebraMapstatement and proof · cited by 4,706
Factproof · cited by 2,726
AlgEquivproof · cited by 1,681
MulEquivproof · cited by 1,142
Polynomial.mapstatement and proof · cited by 806
Polynomial.Splitsstatement and proof · cited by 290
MulEquiv.toMonoidHomproof · cited by 126
Group.IsSolvablestatement and proof · cited by 46
Polynomial.SplittingFieldstatement and proof · cited by 42

Cited by1

Results whose statement or proof uses this declaration.

gal_X_pow_sub_C_isSolvableproof · cited by 0