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

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