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 0_G = 1
proof
A1: for n st n * (0_G) = 0_G & n <> 0 holds 1 <= n by NAT_1:14;
  ( not 0_G is being_of_order_0)& 1 * (0_G) = 0_G by Lm4;
  hence thesis by A1,Def11;
end;
