End Map_option.
Section Map2_opt.
Variable elt elt' elt'' : Type.
Variable f0 : key -> option elt -> option elt' -> option elt''.
Variable f : key -> elt -> option elt' -> option elt''.
Variable mapl : t elt -> t elt''.
Variable mapr : t elt' -> t elt''.
Hypothesis f0_f : forall x d o, f x d o = f0 x (Some d) o.
Hypothesis mapl_bst : forall m, bst m -> bst (mapl m).
Hypothesis mapr_bst : forall m', bst m' -> bst (mapr m').
Hypothesis mapl_f0 : forall x m, bst m ->
find x (mapl m) =
match find x m with Some d => f0 x (Some d) None | None => None end.
Hypothesis mapr_f0 : forall x m', bst m' ->
find x (mapr m') =
match find x m' with Some d' => f0 x None (Some d') | None => None end.
Hypothesis f0_compat : forall x x' o o', X.eq x x' -> f0 x o o' = f0 x' o o'.
Notation map2_opt := (map2_opt f mapl mapr).

Lemma map2_opt_2 : forall m m' y, bst m -> bst m' ->
In y (map2_opt m m') -> In y m \/ In y m'.