theorem Th92:
  x nin vf r implies r is x-omitting
  proof
    assume x nin vf r;
    then
A1: [x,s] nin rng r /\ [:Union X, the carrier of S:] by XTUPLE_0:def 12;
    [x,s] in [:Union X, the carrier of S:] by ZFMISC_1:87;
    then [x,s] nin rng r by A1,XBOOLE_0:def 4;
    hence Coim(r,[x,s]) = {} by FUNCT_1:72;
  end;
