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 kHomSl U1 U2 V f : (U1 <= U2)%VS -> kHom U2 V f -> kHom U1 V f.