Local Hint Immediate In_1 : core.
#[global]
Instance In_compat : Proper (X.eq==>eq==>iff) InT.

Lemma lt_tree_node :
forall (x y : elt) (l r : tree) (i : Info.t),
lt_tree x l -> lt_tree x r -> X.lt y x -> lt_tree x (Node i l y r).