Definition e := (y0 ++ [#;$]) / [$].
Definition P := [d ; e] ++ R ++ [ ([#] / [#] )] ++ map (fun a => [a] / [a]) Sigma.

Lemma P_inv c :
c el P ->
c = d \/ c = e \/ c el R \/ c = ( [#] / [#] ) \/ exists a, a el Sigma /\ c = [a] / [a].