Definition gamma (A : SRS) := map (fun '(x,y) => (x, rev y)) A.

(* Specifications: *)
Lemma sigma_eq  s A :
sigma s A = tau1 A ++ [s] ++ rev (tau2 (gamma A)).
Lemma tau2_gamma s A :
s el rev (tau2 (gamma A)) <-> s el tau2 A.
Lemma sigma_inv A s1 s x y :
sigma s1 A = x ++ [s] ++ y -> ~ s el x -> ~ s el y -> ~ s el sym A ->
s1 = s.
Lemma sigma_snoc A x y u v s s' :
sigma s A = x ++ [s] ++ y -> ~ s el x -> ~ s el y ->
sigma s' (A ++ [u/v]) = x ++ u ++ s' ++ v ++ y.