(* ⊕  ⊗  ∸    ⊞ ⊠ ⊟ *)
 
  Notation expoZ := (mscal Zmult 1).Fact expoZ_power n x : expoZ n (Z.of_nat x) = Z.of_nat (power n x).Fact mscal_Zplus n : mscal Zplus 0 n 1 = Z.of_nat n.Fact alpha_SSm_m_neq_0 : v <> 0%nat.Notation Hv' := alpha_SSm_m_neq_0.Notation f := (Z2Zp Hm).

(* Specifications: *)
Theorem alpha_nat_2lm_plus_j : nat2Zp Hv' (alpha_nat (2*l*m+j)) = nat2Zp Hv' (alpha_nat j) \/ nat2Zp Hv' (alpha_nat (2*l*m+j)) = Zp_opp Hv' (nat2Zp Hv' (alpha_nat j)).
Theorem alpha_nat_2lm_minus_j : nat2Zp Hv' (alpha_nat (2*l*m-j)) = nat2Zp Hv' (alpha_nat j) \/ nat2Zp Hv' (alpha_nat (2*l*m-j)) = Zp_opp Hv' (nat2Zp Hv' (alpha_nat j)).