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).
Hint Unfold Σ : core.

Lemma correct2 x1 x2 y1 y2 :
incl x1 Σ -> incl x2 Σ -> incl y1 Σ -> incl y2 Σ ->
PCSnf (R', x2 ++ [#] ++ x1, y2 ++ [#] ++ y1) -> SR (R, x1 ++ x2, y1 ++ y2).