reserve i,j,n,k,m for Nat,
     a,b,x,y,z for object,
     F,G for FinSequence-yielding FinSequence,
     f,g,p,q for FinSequence,
     X,Y for set,
     D for non empty set;

theorem Th46:
  doms {} = { {} }
proof
  reconsider f={} as FinSequence-yielding FinSequence;
  for i st i in dom f holds f.i in dom (f.i);
  then ex p be FinSequence st p=f & len p = len f &
    for i st i in dom p holds p.i in dom (f.i);
  then
A1: {} in doms f by Def8;
  doms f c= { {} }
  proof
    let y be object;
    assume y in doms f;
    then ex p be FinSequence st p=y & len p = len f &
    for i st i in dom p holds p.i in dom (f.i) by Def8;
    then y=f;
    hence thesis by TARSKI:def 1;
  end;
  hence thesis by A1,ZFMISC_1:33;
end;
