Section kHomExtend.
Variables (K E : {subfield L}) (f : 'End(L)) (x y : L).
Fact kHomExtend_subproof :
linear (fun z => (map_poly f (Fadjoin_poly E x z)).[y]).
Definition kHomExtend := linfun (Linear kHomExtend_subproof).

Lemma kHomExtend_poly p :
p \in polyOver E -> kHomExtend p.[x] = (map_poly f p).[y].