Theorems · Theorem · field theory

IntermediateField.restrictScalars_top

∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] {K : Type u_3}
  [inst_3 : Field K] [inst_4 : Algebra K E] [inst_5 : Algebra K F] [inst_6 : IsScalarTower K F E],
  IntermediateField.restrictScalars K ⊤ = ⊤

Defined in: Mathlib.FieldTheory.IntermediateField.Adjoin.Defs
Cited by: 3 results in Mathlib
Foundations: Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra Field Algebra Algebra IsScalarTower

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Cites6

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

Algebrastatement and proof · cited by 11,388
Top.topstatement · cited by 9,680
Fieldstatement and proof · cited by 7,404
IsScalarTowerstatement and proof · cited by 3,896
IntermediateFieldstatement · cited by 988
IntermediateField.restrictScalarsstatement · cited by 66

Cited by3

Results whose statement or proof uses this declaration.

IntermediateField.adjoin_eq_top_of_adjoin_eq_topproof · cited by 1
Polynomial.irreducible_compproof · cited by 1
exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow_of_adjoin_eq_topproof · cited by 0