End SplittingFieldFor.
Section kHom.
Variables (F : fieldType) (L : fieldExtType F).
Implicit Types (U V : {vspace L}) (K E : {subfield L}) (f g : 'End(L)).
Definition kHom U V f := ahom_in V f && (U <= fixedSpace f)%VS.

Lemma kAHomP {U V} {f : 'AEnd(L)} :
reflect {in U, forall x, f x = x} (kHom U V f).