Theorems · Theorem · field theory

Field.Emb.Cardinal.isLeast_leastExt

∀ {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 : (Module.rank F E).ord.ToType),
  IsLeast
    {k |
      (Field.Emb.Cardinal.wellOrderedBasis F E) k ∉
        IntermediateField.adjoin F
          (⇑(Field.Emb.Cardinal.wellOrderedBasis F E) ∘ Field.Emb.Cardinal.leastExt F E '' Set.Iio i)}
    (Field.Emb.Cardinal.leastExt F E i)

Defined in: Mathlib.FieldTheory.CardinalEmb
Cited by: 4 results in Mathlib
Foundations: Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra Fact Algebra.IsAlgebraic

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Cites27

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
Setproof · cited by 53,352
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
Set.Elemproof · cited by 7,166
Set.ofPredstatement and proof · cited by 6,101
Set.imagestatement · cited by 5,609
Set.rangeproof · cited by 4,705
Factstatement and proof · cited by 2,726
Cardinalstatement · cited by 2,598
Module.Basisstatement · cited by 1,477
Set.Iiostatement and proof · cited by 1,166

Cited by4

Results whose statement or proof uses this declaration.

Field.Emb.Cardinal.strictMono_leastExtproof · cited by 2
Field.Emb.Cardinal.strictMono_filtrationproof · cited by 1
Field.Emb.Cardinal.adjoin_image_leastExtproof · cited by 1
Field.Emb.Cardinal.two_le_degproof · cited by 1