Inductive Exists2 {A B} (R: A -> B -> Prop) : list A -> list B -> Prop :=
 | Exists2_cons_hd : forall x xs y ys, R x y -> Exists2 R (x::xs) (y::ys)
 | Exists2_cons_tl : forall x xs y ys, Exists2 R xs ys -> Exists2 R (x::xs) (y::ys).Inductive Exists2 {A B} (R: A -> B -> Prop) : list A -> list B -> Prop :=
 | Exists2_cons_hd : forall x xs y ys, R x y -> Exists2 R (x::xs) (y::ys)
 | Exists2_cons_tl : forall x xs y ys, Exists2 R xs ys -> Exists2 R (x::xs) (y::ys).Inductive Exists2 {A B} (R: A -> B -> Prop) : list A -> list B -> Prop :=
 | Exists2_cons_hd : forall x xs y ys, R x y -> Exists2 R (x::xs) (y::ys)
 | Exists2_cons_tl : forall x xs y ys, Exists2 R xs ys -> Exists2 R (x::xs) (y::ys).

Lemma suml_map_count_occ_remove A eq_dec (a: A) l1 l2 : ~In a l2 -> suml (map (count_occ eq_dec (remove eq_dec a l1)) l2) = suml (map (count_occ eq_dec l1) l2).