reserve x, y for set;
reserve D for non empty set;
reserve UN for Universe;
reserve C for Category;
reserve O for non empty Subset of the carrier of C;

theorem Th6:
  comp Trivial-addLoopStr = op1
proof
  reconsider f = comp Trivial-addLoopStr as Function of {{}}, {{}};
  for x being object st x in {{}} holds op1.x = f.x
  proof
    let x be object;
    assume x in {{}};
    then reconsider x as Element of Trivial-addLoopStr;
    x = {} by TARSKI:def 1;
    then op1.x = -x by Th2,TARSKI:def 1
      .= f.x by VECTSP_1:def 13;
    hence thesis;
  end;
  hence thesis by FUNCT_2:12;
end;
