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;
reserve A for Abelian addGroup;
reserve a,b for Element of A;
reserve x for object;
reserve y,y1,y2,Y,Z for set;
reserve k for Nat;
reserve G for addGroup;
reserve a,g,h for Element of G;
reserve A for Subset of G;
reserve G for non empty addMagma,
  A,B,C for Subset of G;
reserve a,b,g,g1,g2,h,h1,h2 for Element of G;

theorem ThA16:
  {}(the carrier of G) + A = {} & A + {}(the carrier of G) = {}
proof
A1: now
    set x = the Element of A + {}(the carrier of G);
    assume A + {}(the carrier of G) <> {};
    then ex g1,g2 st x = g1 + g2 & g1 in A & g2 in {}(the carrier of G)
      by ThX8;
    hence contradiction;
  end;
  now
    set x = the Element of {}(the carrier of G) + A;
    assume {}(the carrier of G) + A <> {};
    then ex g1,g2 st x = g1 + g2 & g1 in {}(the carrier of G) & g2 in A
      by ThX8;
    hence contradiction;
  end;
  hence thesis by A1;
end;
