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

theorem
  (inferior_setsequence(A (\+\) A1)).n c= A \+\ (inferior_setsequence A1 ).n
proof
  (inferior_setsequence(A (\+\) A1)).n = Intersection ((A (\+\) A1) ^\n) by Th1
    .= Intersection (A (\+\) (A1 ^\n)) by Th20;
  then (inferior_setsequence(A (\+\) A1)).n c= A \+\ Intersection (A1 ^\n) by
Th37;
  hence thesis by Th1;
end;
