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 Th38:
  B is constant & the_value_of B = A implies for n holds (
  inferior_setsequence B).n = A
proof
  assume
A1: B is constant & the_value_of B = A;
  let n;
  (inferior_setsequence(B)).n = meet {B.k : n <= k} by Def2;
  hence thesis by A1,Th14;
end;
