reserve n,m,k for Nat,
  x,X for set,
  A for Subset of X,
  A1,A2 for SetSequence of X;

theorem
  A \ (superior_setsequence A1).n c= (superior_setsequence(A (\) A1)).n
proof
  A \ (superior_setsequence A1).n = A \ Union (A1 ^\n) by Th2;
  then A \ (superior_setsequence A1).n c= Union (A (\) (A1 ^\n)) by Th40;
  then A \ (superior_setsequence A1).n c= Union ((A (\) A1) ^\n) by Th18;
  hence thesis by Th2;
end;
