 reserve x,y,X,Y for set;
reserve G for non empty multMagma,
  D for set,
  a,b,c,r,l for Element of G;
reserve M for non empty multLoopStr;
reserve H for non empty SubStr of G,
  N for non empty MonoidalSubStr of G;

theorem
  0 is_a_unity_wrt addnat & addnat is uniquely-decomposable
proof
  the_unity_wrt addnat = 0 & ex n being Element of NAT st n is_a_unity_wrt
  addnat by Th40,Th43,SETWISEO:def 2;
  hence 0 is_a_unity_wrt addnat by BINOP_1:def 8;
  thus thesis by Def20,Th43;
end;
