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

(* Specifications: *)
Lemma lpreim_cap_limg f W : (f @^-1: (W :&: limg f))%VS = (f @^-1: W)%VS.
Lemma memv_preim f u W : (f u \in W) = (u \in f @^-1: W)%VS.
End LinearPreimage.