Arguments image_injP {T T' f A}.
Section FinCancel.
Variables (T : finType) (f g : T -> T).
Section Inv.
Hypothesis injf : injective f.

(* Specifications: *)
Lemma injF_onto y : y \in codom f. Proof. exact: inj_card_onto. Qed.
Definition invF y := iinv (injF_onto y).
Lemma invF_f : cancel f invF. Proof. by move=> x; apply: iinv_f. Qed.
Lemma f_invF : cancel invF f. Proof. by move=> y; apply: f_iinv. Qed.
Lemma injF_bij : bijective f. Proof. exact: inj_card_bij. Qed.
End Inv.