Theorems · Theorem · field theory

Field.Emb.Cardinal.two_le_deg

∀ {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] [Algebra.IsSeparable F E]
  (i : (Module.rank F E).ord.ToType),
  2 ≤
    Cardinal.mk
      (Field.Emb
        ↥(IntermediateField.adjoin F
            (⇑(Field.Emb.Cardinal.wellOrderedBasis F E) ∘ Field.Emb.Cardinal.leastExt F E '' Set.Iio i))
        ↥(↥(IntermediateField.adjoin F
                (⇑(Field.Emb.Cardinal.wellOrderedBasis F E) ∘ Field.Emb.Cardinal.leastExt F E ''
                  Set.Iio i)))⟮(Field.Emb.Cardinal.wellOrderedBasis F E) (Field.Emb.Cardinal.leastExt F E i)⟯)

Defined in: Mathlib.FieldTheory.CardinalEmb
Cited by: 1 results in Mathlib
Foundations: Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra Fact Algebra.IsAlgebraic Algebra.IsSeparable

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Cites35

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
Setstatement · cited by 53,352
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
Set.imagestatement and proof · cited by 5,609
Factstatement and proof · cited by 2,726
Cardinalstatement and proof · cited by 2,598
Module.finrankproof · cited by 1,770
Module.Basisstatement · cited by 1,477
Set.Iiostatement and proof · cited by 1,166
IntermediateFieldstatement · cited by 988
Cardinal.mkstatement and proof · cited by 942

Cited by1

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Field.Emb.cardinal_eq_two_pow_rankproof · cited by 2