Definition cond_positivity (x:R) : bool :=
match Rle_dec 0 x with
| left _ => true
| right _ => false
end.

(** Sequential characterisation of continuity *)
Lemma continuity_seq :
forall (f:R -> R) (Un:nat -> R) (l:R),
continuity_pt f l -> Un_cv Un l -> Un_cv (fun i:nat => f (Un i)) (f l).