{R : Ring} (e : R) `{IsIdempotent R e} (n : nat) : (1 <= n)%nat -> rng_power e n = e. Proof. intros L; induction L. - snrapply rng_mult_one_r. - rhs_V rapply rng_idem. exact (ap (e *.) IHL). Defined.
Require Import Basics.Overture Basics.Tactics Basics.PathGroupoids. Require Import Basics.Equivalences Basics.Trunc Types.Sigma WildCat.Core. Require Import Nat.Core Rings.Ring.