Section fix_R.
Variable R : SRS nat.
Variables x0 y0 : list nat.
Definition Σ := x0 ++ y0 ++ sym R.
Notation "#" := (fresh Σ).
Definition R' := R ++ map (fun a => ([a], [a])) (# :: Σ).

Lemma correct1 x y :
incl x Σ -> incl y Σ ->
SR (R, x, y) -> PCSnf (R', x ++ [#], y ++ [#]).