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 Th42;
  then A \+\ (superior_setsequence A1).n c= Union ((A (\+\) A1) ^\n) by Th20;
  hence thesis by Th2;
end;
