(*D11*)
Definition sub (x y : canonTree) : option canonTree :=
match eq_dec (glb x y) y with
| left _ => Some (glb x (comp y))
| right _ => None
end.

(*L10*)
Lemma decompose_share_height_no_increase: forall sh sh' sh'' ,
decompose sh = (sh',sh'')->
height sh' <= height sh /\ height sh'' <= height sh.