Definition nat_nat_fun_ind {X : abgr} (x : X) (n m : nat) : nat_nat_to_monoid_fun x (make_dirprod (n + m)%nat m) = nat_nat_to_monoid_fun x (make_dirprod n O).
Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups.