Module Exports.
Coercion sort : type >-> Sortclass.
Bind Scope ring_scope with sort.
Coercion base : class_of >-> FieldExt.class_of.
Coercion eqType : type >-> Equality.type.
Canonical eqType.
Coercion choiceType : type >-> Choice.type.
Canonical choiceType.
Coercion zmodType : type >-> Zmodule.type.
Canonical zmodType.
Coercion ringType : type >-> Ring.type.
Canonical ringType.
Coercion unitRingType : type >-> UnitRing.type.
Canonical unitRingType.
Coercion comRingType : type >-> ComRing.type.
Canonical comRingType.
Coercion comUnitRingType : type >-> ComUnitRing.type.
Canonical comUnitRingType.
Coercion idomainType : type >-> IntegralDomain.type.
Canonical idomainType.
Coercion fieldType : type >-> Field.type.
Canonical fieldType.
Coercion lmodType : type >-> Lmodule.type.
Canonical lmodType.
Coercion lalgType : type >-> Lalgebra.type.
Canonical lalgType.
Coercion algType : type >-> Algebra.type.
Canonical algType.
Coercion comAlgType : type >-> ComAlgebra.type.
Canonical comAlgType.
Coercion unitAlgType : type >-> UnitAlgebra.type.
Canonical unitAlgType.
Coercion comUnitAlgType : type >-> ComUnitAlgebra.type.
Canonical comUnitAlgType.
Coercion vectType : type >-> Vector.type.
Canonical vectType.
Coercion FalgType : type >-> Falgebra.type.
Canonical FalgType.
Coercion fieldExtType : type >-> FieldExt.type.
Canonical fieldExtType.
Notation splittingFieldType F := (type (Phant F)).
Notation SplittingFieldType F L ax := (@pack _ (Phant F) L _ ax _ _ id _ id).
Notation "[ 'splittingFieldType' F 'of' L 'for' K ]" :=
(@clone _ (Phant F) L K _ idfun)
(at level 0, format "[ 'splittingFieldType'  F  'of'  L  'for'  K ]")
: form_scope.
Notation "[ 'splittingFieldType' F 'of' L ]" :=
(@clone _ (Phant F) L _ _ id)
(at level 0, format "[ 'splittingFieldType'  F  'of'  L ]") : form_scope.
End Exports.
End SplittingField.
Export SplittingField.Exports.

Lemma normal_field_splitting (F : fieldType) (L : fieldExtType F) :
(forall (K : {subfield L}) x,
exists r, minPoly K x == \prod_(y <- r) ('X - y%:P)) ->
SplittingField.axiom L.