Section CardFunImage.
Variables (T T' : finType) (f : T -> T').
Implicit Type A : {pred T}.
Hypothesis card_range : #|T| >= #|T'|.
Let eq_card : #|T| = #|T'|. Proof. by apply/eqP; rewrite eqn_leq leq_card. Qed.
End CardFunImage.
Arguments image_injP {T T' f A}.
Arguments leq_card_in [T T'] f.
Arguments leq_card [T T'] f.

Lemma bij_eq_card (T T' : finType) (f : T -> T') : bijective f -> #|T| = #|T'|.