Definition iinv A y fAy := s2val (@iinv_proof A y fAy).

(* Specifications: *)
Lemma f_iinv A y fAy : f (@iinv A y fAy) = y.
Lemma preim_iinv A B y fAy : preim f B (@iinv A y fAy) = B y.
Lemma image_codom A : {subset image f A <= codom f}.
Lemma image_pred0 : image f pred0 =i pred0.
Lemma iinv_f x fTfx : @iinv T (f x) fTfx = x.
Lemma map_preim (s : seq T') : {subset s <= codom f} -> map f (preim_seq s) = s.
Lemma inj_card_bij : bijective f.