theorem Th79:
  for vS1 being Function holds (for y st y in dom vS1 holds vS1.y
= v.y) & dom vS misses dom vS1 implies for y st y in (dom vS1) \ {x} holds vS1|
  ((dom vS1) \ {x}).y = (v.vS).y
proof
  let vS1 be Function;
  assume that
A1: for y st y in dom vS1 holds vS1.y = v.y and
A2: dom vS misses dom vS1;
  let y such that
A3: y in (dom vS1) \ {x};
  y in dom vS1 /\ ((dom vS1) \ {x}) by A3,XBOOLE_0:def 4;
  then vS1|((dom vS1) \ {x}).y = vS1.y by FUNCT_1:48;
  then
A4: vS1|((dom vS1) \ {x}).y = v.y by A1,A3;
  not y in dom vS by A2,A3,XBOOLE_0:3;
  hence thesis by A4,FUNCT_4:11;
end;
