
theorem Th12:
  for X be set for p be FinSequence of bool X holds { Intersect (
rng MergeSequence(p,q)) where q is FinSequence of BOOLEAN : len q = len p } is
  Subset-Family of X
proof
  let X be set;
  let p be FinSequence of bool X;
  { Intersect (rng MergeSequence(p,q)) where q is FinSequence of BOOLEAN :
  len q = len p } c= bool X
  proof
    let z be object;
    assume z in { Intersect (rng MergeSequence(p,q)) where q is FinSequence
    of BOOLEAN : len q = len p };
    then
    ex q be FinSequence of BOOLEAN st z = Intersect (rng MergeSequence(p,q)
    ) & len q = len p;
    hence thesis;
  end;
  hence thesis;
end;
