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(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(*     A development written by Pierre Castéran for Coq V6.1  Coq : A product of inria : "http://pauillac.inria.fr/coq/coq-eng.html"  Pierre Castéran : A product of LaBRI :   LaBRI, Universite Bordeaux-I      |    12 place Puy Paulin 351 Cours de la Liberation        |    33000 Bordeaux F-33405 TALENCE Cedex             |    France France                            |    (+ 33) 5 56 81 15 80 tel : (+ 33) 5 56 84 69 31 fax : (+ 33) 5 56 84 66 69 email: casteran@labri.u-bordeaux.fr www: http://dept-info.labri.u-bordeaux.fr/~casteran  "Les rêves sont aussi beaux que la réalité, mais ils ne sont pas mieux". ( J.L.Borges )  *)
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.
Hint Resolve rmax_intro: searchtrees.
(* base cases *)

Lemma rmax_nil_nil : forall n : nat, RMAX (bin n NIL NIL) NIL n.
Hint Resolve rmax_1: searchtrees.