Definition add_lfun f g := linfun (f \+ g).
Definition opp_lfun f := linfun (-%R \o f).
Fact lfun_addA : associative add_lfun.
Definition lfun_vectMixin := VectMixin lfun_vect_iso.
Canonical lfun_vectType := VectType R 'Hom(aT, rT) lfun_vectMixin.
End LfunVectType.
Section CompLfun.
Variables (R : ringType) (wT aT vT rT : vectType R).
Implicit Types (f : 'Hom(vT, rT)) (g : 'Hom(aT, vT)) (h : 'Hom(wT, aT)).

Lemma limg_ker0 f U V : lker f == 0%VS -> (f @: U <= f @: V)%VS = (U <= V)%VS.