Theorem associativityNat : isAssociative_fun 0 add. Proof. intros n m x. unfold iterop_fun_fun. apply pathsinv0. rewrite 2 iterop_fun_nat. intermediate_path (stnsum (λ i : stn n, stnsum (x i))). - apply maponpaths. apply funextfun; intro. apply iterop_fun_nat. - now apply nat_plus_associativity'. Defined.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Algebra.Groups. Require Import UniMath.MoreFoundations.NegativePropositions.