reserve X,Y,z,s for set, L,L1,L2,A,B for List of X, x for Element of X,
  O,O1,O2,O3 for Operation of X, a,b,y for Element of X, n,m for Nat;
reserve F,F1,F2 for filtering Operation of X;

theorem Th46:
  z in x.F implies z = x
  proof
    assume z in x.F; then
    [x,z] in F & F c= id X by Def21,RELAT_1:169;
    hence thesis by RELAT_1:def 10;
  end;
