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 Th26:
 for y being object holds
  Intersection(F,Ch,y) c= Intersection(F,Ch|X9,y)
proof let y be object;
  let z be object such that
A1: z in Intersection(F,Ch,y);
  now
    let x such that
A2: x in dom (Ch|X9) and
A3: Ch|X9.x=y;
    x in dom Ch/\X9 by A2,RELAT_1:61;
    then
A4: x in dom Ch by XBOOLE_0:def 4;
    Ch.x=y by A2,A3,FUNCT_1:47;
    hence z in F.x by A1,A4,Def2;
  end;
  hence thesis by A1,Def2;
end;
