reserve n,m,k,k1,k2,i,j for Nat;
reserve x,y,z for object,X,Y,Z for set;
reserve A for Subset of X;
reserve B,A1,A2,A3 for SetSequence of X;
reserve Si for SigmaField of X;
reserve S,S1,S2,S3 for SetSequence of Si;

theorem Th18:
  (superior_setsequence B).0 = Union B
proof
  (superior_setsequence B).0 = union {B.k : 0 <= k} by Def3
    .= union rng B by Th5
    .= Union B by CARD_3:def 4;
  hence thesis;
end;
