Theorems · Theorem · field theory
Field.isAlgebraic_of_finite_intermediateField
∀ (F : Type u_1) (E : Type u_2) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] [Finite (IntermediateField F E)], Algebra.IsAlgebraic F E
- Defined in
- Mathlib.FieldTheory.PrimitiveElement
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Finitestatement and proof · cited by 3,029
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.adjoinproof · cited by 382
- Algebra.IsAlgebraicstatement · cited by 322
- IsAlgebraicproof · cited by 163
- Finite.exists_ne_map_eq_of_infiniteproof · cited by 5
- Field.isAlgebraic_of_adjoin_eq_adjoinproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Field.FiniteDimensional.of_finite_intermediateFieldproof · cited by 1
- Field.exists_primitive_element_iff_finite_intermediateFieldproof · cited by 0