Theorems · Theorem · field theory
Field.finite_intermediateField_of_exists_primitive_element
∀ (F : Type u_1) (E : Type u_2) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] [Algebra.IsAlgebraic F E], (∃ α, F⟮α⟯ = ⊤) → Finite (IntermediateField F E)
- Defined in
- Mathlib.FieldTheory.PrimitiveElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- FiniteDimensionalproof · cited by 1,854
- SetLikeproof · cited by 1,084
Cited by1
Results whose statement or proof uses this declaration.
- Field.exists_primitive_element_iff_finite_intermediateFieldproof · cited by 0