proposition: Lemma Str_nth_powers_help (n : nat) (c : A) : Str_nth n (powers_help c) = c * a ^ (f n).
proof: Proof. revert c. induction n using peano_naturals.nat_induction; intros c; unfold Str_nth in *; simpl. rewrite rings.preserves_0, nat_pow_0. ring. rewrite rings.preserves_plus, rings.preserves_1. rewrite nat_pow_S, IHn. ring. 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