Section LinearPreimage.
Variables (K : fieldType) (aT rT : vectType K).
Implicit Types (f : 'Hom(aT, rT)) (U : {vspace aT}) (V W : {vspace rT}).

Lemma lpreim_cap_limg f W : (f @^-1: (W :&: limg f))%VS = (f @^-1: W)%VS.