Section InvLfun.
Variable (K : fieldType) (aT : FalgType K).
Implicit Types f g : 'End(aT).
Definition lfun_invr f := if lker f == 0%VS then f^-1%VF else f.
Canonical amull_additive := Eval hnf in Additive amull_is_linear.
Canonical amull_linear := Eval hnf in AddLinear amull_is_linear.
Canonical amulr_additive := Eval hnf in Additive amulr_is_lrmorphism.
Canonical amulr_linear := Eval hnf in AddLinear amulr_is_lrmorphism.
Canonical amulr_rmorphism := Eval hnf in AddRMorphism amulr_is_lrmorphism.
Canonical amulr_lrmorphism := Eval hnf in LRMorphism amulr_is_lrmorphism.

Lemma prodvP {U V W} :
reflect {in U & V, forall u v, u * v \in W} (U * V <= W)%VS.