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

theorem Th51:
  (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 Th17
    .= A \/ Intersection (A1 ^\n) by Th34
    .= A \/ (inferior_setsequence A1).n by Th1;
  hence thesis;
end;
