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
  Intersection B c= Union B
proof
  meet rng B c= union rng B by SETFAM_1:2;
  then Intersection B c= union rng B by Th8;
  hence thesis by CARD_3:def 4;
end;
