reserve m,n for Nat;
reserve i,j for Integer;
reserve S for non empty addMagma;
reserve r,r1,r2,s,s1,s2,t,t1,t2 for Element of S;
reserve G for addGroup-like non empty addMagma;
reserve e,h for Element of G;
reserve G for addGroup;
reserve f,g,h for Element of G;
reserve u for UnOp of G;

theorem
  ord h * h = 0_G
proof
  per cases;
  suppose
    h is being_of_order_0;
    then ord h = 0 by Def11;
    hence thesis by Def7;
  end;
  suppose
    h is not being_of_order_0;
    hence thesis by Def11;
  end;
end;
