Definition iterop_list_step (runax : isrunit op unel) (x:X) (xs:list X) : iterop_list (x::xs) = op x (iterop_list xs). Proof. generalize x; clear x. apply (list_ind (λ xs, ∏ x : X, iterop_list (x :: xs) = op x (iterop_list xs))). { intro x. simpl. apply pathsinv0,runax. } intros y rest IH x. reflexivity. Defined.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Algebra.Groups. Require Import UniMath.MoreFoundations.NegativePropositions.