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.

(* Specifications: *)
Lemma lfun_mulVr f : lker f == 0%VS -> f^-1%VF * f = 1.
Lemma lfun_invr_out f : lker f != 0%VS -> lfun_invr f = f.
Canonical amull_additive := Eval hnf in Additive amull_is_linear.