SeparableDegree.lean`

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1 declarations, 0 contain sorry, 0 declared as axioms

A field extension generated by a separable element is separable

Material for Mathlib.FieldTheory.SeparableDegree.

Imports (1)

Mathlib.FieldTheory.SeparableDegree

Imported by 2 files

theorem Algebra.IsSeparable.of_isSeparable_of_adjoin_eq_top A field extension generated by a single separable element is separable line 19 source
Source documentation
A field extension generated by a single separable element is separable.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Field, Algebra, IsSeparable, Eq, IntermediateField, IntermediateField.adjoin, Singleton.singleton, Set, Top.top, Algebra.IsSeparable
Proof uses: Subtype, Membership.mem, Eq.mpr, id, congrArg, Eq.symm, Iff.mpr, IntermediateField.isSeparable_adjoin_simple_iff_isSeparable, AlgEquiv.Algebra.isSeparable, IntermediateField.topEquiv
47 instances, coercions and auxiliary constants left out.

Tactic trace: 4 steps
Open to load the checked before-and-after goal states.
```
theorem Algebra.IsSeparable.of_isSeparable_of_adjoin_eq_top {F E : Type*} [Field F] [Field E]
    [Algebra F E] {x : E} (hx : IsSeparable F x)
    (hgen : IntermediateField.adjoin F {x} = ⊤) : Algebra.IsSeparable F E := by
…
```