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)).