Definition Pphi_pow :=
let mkpow x p :=
match p with xH => x | _ => rpow x (Cp_phi (Npos p)) end in
let mkopp_pow x p := ropp (mkpow x p)  in
let mkmult_pow r x p := rmul r (mkpow x p) in
Pphi_avoid mkpow mkopp_pow mkmult_pow.

Lemma local_mkpow_ok r p :
match p with
| xI _ => rpow r (Cp_phi (Npos p))
| xO _ => rpow r (Cp_phi (Npos p))
| 1 => r
end == pow_pos rmul r p.