Definition fib_mat := mat2 1 1 1 0.

Lemma fib_n :
forall n : nat,
power Mat2 matrix fib_mat (S n) =
mat2 (Z_of_nat (shift_Fib (S (S n)))) (Z_of_nat (shift_Fib (S n)))
(Z_of_nat (shift_Fib (S n))) (Z_of_nat (shift_Fib n)).