Section SplittingFieldTheory.
Variables (F : fieldType) (L : splittingFieldType F).
Implicit Types (U V W : {vspace L}).
Implicit Types (K M E : {subfield L}).
Fact fieldOver_splitting E : SplittingField.axiom (fieldOver_fieldExtType E).
Canonical fieldOver_splittingFieldType E :=
SplittingFieldType (subvs_of E) (fieldOver E) (fieldOver_splitting E).

Lemma splitting_field_normal K x :
exists r, minPoly K x == \prod_(y <- r) ('X - y%:P).