Theorems · Theorem · field theory

Field.Emb.Cardinal.filtration_apply

∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E]
  [rank_inf : Fact (Cardinal.aleph0 ≤ Module.rank F E)] [inst_3 : Algebra.IsAlgebraic F E]
  (i : WithTop (Module.rank F E).ord.ToType),
  Field.Emb.Cardinal.filtration i =
    WithTop.recTopCoe ⊤
      (fun x =>
        IntermediateField.adjoin F
          ((fun a => (Field.Emb.Cardinal.wellOrderedBasis F E) (Field.Emb.Cardinal.leastExt F E a)) '' Set.Iio x))
      i

Defined in

Mathlib.FieldTheory.CardinalEmb

Cited by

0 results in Mathlib

Foundations

Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebraFactAlgebra.IsAlgebraic