Fact regular_splittingAxiom F : SplittingField.axiom (regular_fieldExtType F).
Canonical regular_splittingFieldType (F : fieldType) :=
SplittingFieldType F F^o (regular_splittingAxiom F).
Section SplittingFieldTheory.
Variables (F : fieldType) (L : splittingFieldType F).
Implicit Types (U V W : {vspace L}).
Implicit Types (K M E : {subfield L}).

Lemma splittingFieldP : SplittingField.axiom L.
Fact fieldOver_splitting E : SplittingField.axiom (fieldOver_fieldExtType E).