Lemma K_0_eqn {M:ExactCategory} (E : ShortExactSequence M) : K_0_class (Ob2 E) = K_0_class (Ob1 E) + K_0_class (Ob3 E). Proof. apply iscompsetquotpr. apply generated_binopeqrel_intro. apply hinhpr. exists E. split; reflexivity. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.Free_Monoids_and_Groups.