red in |- *.
intros x y dans_x dans_y egal_inv.
replace x with (f (inv E F f x)).
replace y with (f (inv E F f y)).
apply (f_equal (A:=Elt) (B:=Elt)); assumption.
auto.
auto.
Qed.

Lemma inv_is_epi : is_iso E F f -> is_epi F E invf.
unfold invf in |- *.