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Theorems · Theorem · field theory

Field.Emb.Cardinal.succEquiv_coherence

∀ {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)
  (f :
    ↥(IntermediateField.adjoin F
          (⇑(Field.Emb.Cardinal.wellOrderedBasis F E) ∘ Field.Emb.Cardinal.leastExt F E ''
            Set.Iio (Order.succ i))) →ₐ[F]
      AlgebraicClosure E),
  ((Field.Emb.Cardinal.succEquiv i) f).1 = f.comp (Subalgebra.inclusion ⋯)
Defined in
Mathlib.FieldTheory.CardinalEmb
Cited by
1 results in Mathlib
Foundations
Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFieldAlgebraFactAlgebra.IsAlgebraic
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Field.Emb.Cardinal.equivSucc_coherence · cited by 0Cardinal.equivSucc_cohere…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetAlgebra · cited by 11388AlgebraEquiv · cited by 8337EquivField · cited by 7404FieldSet.image · cited by 5609Set.imageAlgHom · cited by 3236AlgHomFact · cited by 2726FactCardinal · cited by 2598CardinalModule.Basis · cited by 1477Module.BasisSubalgebra · cited by 1353SubalgebraSet.Iio · cited by 1166Set.IioIntermediateField · cited by 988IntermediateFieldOrder.succ · cited by 633Order.succCardinal.aleph0 · cited by 521Cardinal.aleph0Cardinal.succEquiv_coherenceCITED BYCITES

Cites32

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
  • Equivstatement · cited by 8,337
  • Fieldstatement and proof · cited by 7,404
  • Set.imagestatement and proof · cited by 5,609
  • AlgHomstatement and proof · cited by 3,236
  • Factstatement and proof · cited by 2,726
  • Cardinalstatement · cited by 2,598
  • Module.Basisstatement · cited by 1,477
  • Subalgebrastatement · cited by 1,353
  • Set.Iiostatement and proof · cited by 1,166

Cited by1

Results whose statement or proof uses this declaration.