reserve X,Y,x,y for set;
reserve A for non empty Poset;
reserve a,a1,a2,a3,b,c for Element of A;
reserve S,T for Subset of A;
reserve f for Choice_Function of BOOL(the carrier of A);
reserve fC,fC1,fC2 for Chain of f;

theorem
  fC1 meets fC2
proof
  f.(the carrier of A) in fC1 & f.(the carrier of A) in fC2 by Th37;
  hence thesis by XBOOLE_0:3;
end;
