Local Open Scope nat_scope.

Lemma fac_tok_classification : forall fac n,
isTokenFactory' fac n ->
forall tok m,
isToken' tok m ->
shareTreeOrd (intersect_tree fac tok) (Leaf false) ->
( n = m -> shareTreeEq (union_tree tok fac) (Leaf true)) /\
( n < m -> False ) /\
( n > m -> shareTreeEq (union_tree tok fac) (Leaf true) -> False).