Inductive RMAX (t t' : nat_tree) (n : nat) : Prop :=
    rmax_intro :
      occ t n ->
      (forall p : nat, occ t p -> p <= n) ->
      (forall q : nat, occ t' q -> occ t q) ->
      (forall q : nat, occ t q -> occ t' q \/ n = q) ->
      ~ occ t' n -> search t' -> RMAX t t' n.Inductive RMAX (t t' : nat_tree) (n : nat) : Prop :=
    rmax_intro :
      occ t n ->
      (forall p : nat, occ t p -> p <= n) ->
      (forall q : nat, occ t' q -> occ t q) ->
      (forall q : nat, occ t q -> occ t' q \/ n = q) ->
      ~ occ t' n -> search t' -> RMAX t t' n.

Lemma rmax_t_NIL : forall (t : nat_tree) (n : nat), search (bin n t NIL) -> RMAX (bin n t NIL) t n.