Definition combine (m1 m2: PTree.t L.t) : PTree.t L.t :=
match xcombine m1 m2 with
| Same|Same1 => m1
| Same2 => m2
| CC m => m
end.

(* Specifications: *)
Lemma gcombine:
forall m1 m2 i, opt_eq (PTree.get i (combine m1 m2)) (f (PTree.get i m1) (PTree.get i m2)).