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;
reserve i for Element of NAT;

theorem Th66:
  for X being ConstructorDB
  for x,y being Element of X holds x in y ref iff y in x occur
  proof
    let X be ConstructorDB;
    let x,y be Element of X;
    hereby
      assume x in y ref; then
      [y,x] in @the ref-operation of X by RELAT_1:169; then
      [x,y] in (@the ref-operation of X)~ by RELAT_1:def 7;
      hence y in x occur by RELAT_1:169;
    end;
    assume y in x occur; then
    [x,y] in (@the ref-operation of X)~ by RELAT_1:169; then
    [y,x] in @the ref-operation of X by RELAT_1:def 7;
    hence x in y ref by RELAT_1:169;
  end;
