Fact A_plus u v : A (u+v)%nat = A u ⊠ A v.
Fact A_mult u v : A (u*v)%nat = MZ_expo u (A v).
Fact A_plus_mult m n k l :
(m = n + l * k)%nat
-> A m = A n ⊠ MZ_expo l (A k).
Fact MZ_det_B : MZ_det B = 1.
Definition Pell x y := x*x -b*x*y+y*y=1.

(* Specifications: *)
Theorem alpha_Pell n : Pell (α (S n)) (α n).
Fact A_iA n : A n ⊠ iA n = MZ_one.