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;

theorem
  -({}(the carrier of G)) = {}
proof
  thus -({}(the carrier of G)) c= {}
  proof
    let x be object;
    assume x in -({}(the carrier of G));
    then ex a st x = -a & a in {}the carrier of G;
    hence thesis;
  end;
  thus thesis;
end;
