(** - Any element of $A\subset E$ is of course also an element of $E$ itself.
 Map_embed takes setoid functions $X\to A$ to setoid functions $X\to E$ by embedding

 %\label{Mapembed}% *)
Definition Map_embed :
  forall (X E : Setoid) (A : part_set E) (f : Map X A), MAP X E.

(* Specifications: *)
Lemma Map_embed_prop : forall (A D : Setoid) (B : part_set A) (v : MAP D B) (i : D), in_part (Map_embed v i) B.