proposition: Lemma preserves_powers (a : A) (n : nat) : f (Str_nth n (powers a)) = Str_nth n (powers (f a)).
proof: Proof. rewrite 2!(Str_nth_powers _ id). apply preserves_nat_pow. Qed.
imports: Coq.setoid_ring.Ring Coq.Arith.Factorial MathClasses.misc.workaround_tactics MathClasses.interfaces.abstract_algebra MathClasses.interfaces.additional_operations MathClasses.interfaces.orders MathClasses.interfaces.naturals MathClasses.interfaces.integers MathClasses.theory.nat_pow MathClasses.theory.int_pow MathClasses.theory.streams