Fixpoint depair {m n} (o : t m) (p : t n) : t (m * n) :=
match o with
|@F1 m' => L (m' * n) p
|FS o' => R n (depair o' p)
end.

(* Specifications: *)
Lemma depair_sanity {m n} (o : t m) (p : t n) :
proj1_sig (to_nat (depair o p)) = n * (proj1_sig (to_nat o)) + (proj1_sig (to_nat p)).