theorem Th5:
  ex y st u#y=w
proof
  take y = (-u)+(w+w);
  u+y = (u+(-u))+(w+w) by RLVECT_1:def 3
    .= 0.V+(w+w) by RLVECT_1:5
    .= w+w by RLVECT_1:4;
  hence thesis by Def2;
end;
