Definition somes {A} (s : set (option A)) : set A :=
[set x | Some x \in s].

(* Specifications: *)
Lemma somes_subset {A} (s1 s2 : set (option A)) :
s1 \subset s2 ->
somes s1 \subset somes s2.
Lemma bigcup_somes {A B} (sA : set A) (s : A -> set (option B)) :
somes (\bigcup_(a in sA) s a) <--> \bigcup_(a in sA) somes (s a).