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

theorem Th50:
  (inferior_setsequence(A (/\) A1)).n = A /\ (inferior_setsequence A1).n
proof
  (inferior_setsequence(A (/\) A1)).n = Intersection ((A (/\) A1) ^\n) by Th1
    .= Intersection (A (/\) (A1 ^\n)) by Th16
    .= A /\ Intersection (A1 ^\n) by Th33
    .= A /\ (inferior_setsequence A1).n by Th1;
  hence thesis;
end;
