Section SRH_SR.
Local Notation "A <<= B" := (incl A B) (at level 70).
Local Notation symbol := nat.
Local Notation string := (string nat).
Local Notation SRS := (SRS nat).
Variables (R : SRS) (x0 : string) (a0 : symbol).
Notation Sigma :=  (a0 :: x0 ++ sym R).
Definition P :=
R ++ map (fun a => [a; a0] / [a0]) Sigma ++ map (fun a => [a0; a] / [a0]) Sigma.

Lemma cons_incl X (a : X) (A B : list X) : a :: A <<= B -> A <<= B.