Qed.

Lemma CV_extensionality : forall Un Un', (forall n, Un n = Un' n) ->  forall l, Un_cv Un l -> Un_cv Un' l.
Ltac ring_exact_R hyp :=
match type of hyp with
| Rlt ?X1 ?X2 => (stepr X2; trivial; ring) || (stepl X1; trivial; ring)
| Rle ?X1 ?X2 => (stepr X2; trivial; ring) || (stepl X1; trivial; ring)
| ~(@eq R ?X1 ?X2) => (stepr X2; trivial; ring) || (stepl X1; trivial; ring)
| ?X3 => fail 1
end.