Section Inclusion.
Variable E : Setoid.
Comments "The relation of belonging is compatible with equality:".
intros A; try assumption.
exact (Pred_compatible_prf (E:=E) (p:=A)).
Qed.

Lemma in_part_comp_r :
forall (x : E) (A B : part_set E), in_part x A -> Equal A B -> in_part x B.