Ltac reify_goal lvar lexpr lterm:=
(*idtac lvar; idtac lexpr; idtac lterm;*)
match lexpr with
nil => idtac
| ?e1::?e2::_ =>
match goal with
|- (?op ?u1 ?u2) =>
change (op
(@PEeval Z _ _ _ _ _ _ _ _ _ (@gen_phiZ _ _ _ _ _ _ _ _ _) N
(fun n:N => n) (@pow_N _ _ _ _ _ _ _ _ _)
lvar e1)
(@PEeval Z _ _ _ _ _ _ _ _ _ (@gen_phiZ _ _ _ _ _ _ _ _ _) N
(fun n:N => n) (@pow_N _ _ _ _ _ _ _ _ _)
lvar e2))
end
end.

(* Specifications: *)
Lemma comm: forall (R:Type)`{Ring R}(c : Z) (x : R),
x * (gen_phiZ c) == (gen_phiZ c) * x.