theorem
  v1 - w = v2 - w implies v1 = v2
proof
  assume v1 - w = v2 - w;
  then - (v1 - w) = w - v2 by RLVECT_1:33;
  then w - v1 = w - v2 by RLVECT_1:33;
  hence thesis by RLVECT_1:23;
end;
