Theorems · Theorem · field theory

isSolvable_of_isScalarTower

∀ (F : Type u_1) [inst : Field F] (K₁ : Type u_3) [inst_1 : Field K₁] [inst_2 : Algebra F K₁] (E : Type u_6)
  [inst_3 : Field E] [inst_4 : Algebra F E] [inst_5 : Algebra K₁ E] [IsScalarTower F K₁ E] [Normal F K₁]
  [h1 : Group.IsSolvable Gal(K₁/F)] [h2 : Group.IsSolvable Gal(E/K₁)], Group.IsSolvable Gal(E/F)

Defined in: Mathlib.FieldTheory.Normal.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra Field Algebra Algebra IsScalarTower Normal Group.IsSolvable Group.IsSolvable

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Cites25

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

DFunLike.coeproof · cited by 62,936
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
Algebra.algebraMapproof · cited by 4,706
IsScalarTowerstatement and proof · cited by 3,896
MonoidHomproof · cited by 3,629
AlgEquivstatement and proof · cited by 1,681
AlgEquiv.symmproof · cited by 615
AlgEquiv.toAlgHomproof · cited by 273
MonoidHom.kerproof · cited by 212
AlgHom.extproof · cited by 170
Normalstatement and proof · cited by 92

Cited by1

Results whose statement or proof uses this declaration.

gal_isSolvable_towerproof · cited by 1