Section Interfaces.
Variable F : finFieldType.
Implicit Types (vT : vectType F) (aT : FalgType F) (fT : fieldExtType F).
Canonical vect_finType vT := FinType vT (VectFinMixin vT).
Canonical Falg_finType aT := FinType aT (VectFinMixin aT).
Canonical fieldExt_finType fT := FinType fT (VectFinMixin fT).
Canonical Falg_finRingType aT := [finRingType of aT].
Canonical fieldExt_finRingType fT := [finRingType of fT].
Canonical fieldExt_finFieldType fT := [finFieldType of fT].

Lemma finField_splittingField_axiom fT : SplittingField.axiom fT.