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 Th17:
  (inferior_setsequence B).0 = Intersection B
proof
  (inferior_setsequence B).0 = meet {B.k : k >= 0} by Def2
    .= meet rng B by Th5
    .= Intersection B by Th8;
  hence thesis;
end;
