Section filter_map.
Variables A B C : Type.
Proof using.
induction l; intros; simpl in *.
- auto.
- repeat break_match; simpl; auto using f_equal.
Qed.
Proof using.
induction l; intros; simpl in *.
- auto.
- repeat find_higher_order_rewrite; auto.
Qed.
Proof using.
simpl. auto.
Qed.

Lemma In_filterMap :
forall (f : A -> option B) b xs,
In b (filterMap f xs) ->
exists a,
In a xs /\ f a = Some b.