Variables (T' : Type) (f : T -> T') (A : pred T).
Canonical image_tuple : #|A|.-tuple T' := [tuple of image f A].
Canonical codom_tuple : #|T|.-tuple T' := [tuple of codom f].
End ImageTuple.
Section MkTuple.
Variables (T' : Type) (f : 'I_n -> T').
Definition mktuple := map_tuple f ord_tuple.

(* Specifications: *)
Lemma tnth_mktuple i : tnth mktuple i = f i.