Section Update2Rel.
Variables A B : Type.
Variable R : relation A.
Hypothesis A_eq_dec : forall x y : A, {x = y} + {x <> y}.
Hypothesis R_dec : forall x y : A, {R x y} + {~ R x y}.

Lemma filter_rel_related :
forall n n' ns,
In n' (filter_rel R_dec n ns) ->
In n' ns /\ R n n'.