intros.
simpl in |- *.
red in |- *.
intros b.
simpl in |- *.
auto with algebra.
Qed.
Hint Resolve Map_embed_eats_Map_to_equal_subsets: algebra.

Lemma Map_to_equal_subsets_inj :
forall (A B : Setoid) (X Y : part_set A) (H H' : X =' Y in _)
(f g : Map B X),
Map_to_equal_subsets H f =' Map_to_equal_subsets H' g in _ ->
f =' g in MAP _ _.