theorem Th2:
  for vS1 being Function st x in dom vS1 holds (vS1|((dom vS1) \ {x
  })) +* (x .--> vS1.x) = vS1
proof
  let vS1 be Function;
  assume x in dom vS1;
  then (dom vS1 \ {x}) \/ {x} = dom vS1 \/ {x} & {x} c= dom vS1 by XBOOLE_1:39
,ZFMISC_1:31;
  then (dom vS1 \ {x}) \/ {x} = dom vS1 by XBOOLE_1:12;
  hence thesis by FUNCT_7:14;
end;
