Canonical Structure fmap_eqMixin := EqMixin feqP.Canonical Structure fmap_eqType := EqType (finMap K V) fmap_eqMixin.Definition mapf' (m : seq (K * U)) : seq (K * V) := 
  map (fun kv => (key kv, f (value kv))) m.

(* Specifications: *)
Lemma map_key_mapf (m : seq (K * U)) : map key (mapf' m) = map key m.
Lemma sorted_map (m : seq (K * U)) : sorted ord (map key m) -> sorted ord (map key (mapf' m)).