Goal:
  
  elt : Type
  gt_tree_dec : forall (x : T.t) (t : M.Raw.tree elt),
                {M.Raw.gt_tree x t} + {~ M.Raw.gt_tree x t}
  x : T.t
  t : M.Raw.tree elt
  l : M.Raw.tree elt
  k : M.Raw.key
  n : elt
  r : M.Raw.tree elt
  z : Int.Z_as_Int.t
  y : M.Raw.key
  p1 : T.lt x y
  p2 : M.Raw.gt_tree x l
  p3 : M.Raw.gt_tree x r
  H : M.Raw.In y (M.Raw.Node l k n r z)
  H1 : T.eq y k
  ============================
   (T.lt x y)


DEBUG:Going to execute:
let rec use_hyp H :=
            match type of H with
            | _ /\ _ => exact H || destruct_hyp H
            | _ * _ => exact H || destruct_hyp H
            | _ => try (solve [ inversion H ])
            end
           with do_intro := let H := fresh in
                            intro H; use_hyp H
           with destruct_hyp H := case H; clear H; do_intro; do_intro
           in
           let rec use_hyps :=
            match goal with
            | H:_ /\ _ |- _ => exact H || (destruct_hyp H; use_hyps)
            | H:_ * _ |- _ => exact H || (destruct_hyp H; use_hyps)
            | H:_ |- _ => solve [ inversion H ]
            | _ => idtac
            end
           in
           let do_atom := solve
           [ trivial
           with eq_true
           | Init.reflexivity
           | Init.symmetry; trivial
           | contradiction
           | congruence ]
           in
           let rec do_ccl :=
            try do_atom; repeat (do_intro; try do_atom); try arith_congr;
             (solve [ Init.split; do_ccl ])
           in
           (solve [ do_atom | use_hyps; do_ccl ]) ||
             fail "Cannot solve this goal"