End Min_Max_Elt.
Section Induction_Principles.

(* Specifications: *)
Lemma map_induction_max :
forall P : t elt -> Type,
(forall m, Empty m -> P m) ->
(forall m m', P m -> forall x e, Above x m -> Add x e m m' -> P m') ->
forall m, P m.
Lemma map_induction_min :
forall P : t elt -> Type,
(forall m, Empty m -> P m) ->
(forall m m', P m -> forall x e, Below x m -> Add x e m m' -> P m') ->
forall m, P m.