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
  B is constant implies Union B = Intersection B
proof
  assume B is constant;
  then consider A being Subset of X such that
A1: for n being Nat holds B.n = A by VALUED_0:def 18;
  Union B = A by Th10,A1;
  hence thesis by Th11,A1;
end;
