(* lemmes sur map_replace : *)

(* Specifications: *)
Lemma map_replace_mapget_ins_true_0 :
forall (m : Map bool) (a : ad) (b : bool),
MapGet bool m a = Some b ->
MapGet bool (map_replace bool m a true) a = Some true.
Lemma map_replace_mapget_ins_true_1 :
forall (m : Map bool) (a a' : ad),
MapGet bool m a = Some true ->
MapGet bool (map_replace bool m a' true) a = Some true.
Lemma map_replace_mapget_true_inv :
forall (m : Map bool) (a b : ad),
MapGet bool (map_replace bool m a true) b = Some true ->
b = a \/ MapGet bool m b = Some true.