reserve x, x1, x2, y, z, X9 for set,
  X, Y for finite set,
  n, k, m for Nat,
  f for Function;
reserve F,Ch for Function;

theorem Th30:
 for x,y being object holds
  x in Ch"{y} implies Intersection(F,Ch,y) c= F.x
proof let x,y be object;
  assume
A1: x in Ch"{y};
  then
A2: x in dom Ch by FUNCT_1:def 7;
  Ch.x in {y} by A1,FUNCT_1:def 7;
  then
A3: Ch.x=y by TARSKI:def 1;
  let z be object;
  assume z in Intersection(F,Ch,y);
  hence thesis by A2,A3,Def2;
end;
