reserve
  a for natural Number,
  k,l,m,n,k1,b,c,i for Nat,
  x,y,z,y1,y2 for object,
  X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for FinSequence;
reserve D for set;

theorem
  for D being non empty set ex p being FinSequence of D st len p = a
proof
  let D be non empty set;
  reconsider a as Element of NAT by ORDINAL1:def 12;
  set y = the Element of D;
  set p = Seg a --> y;
A1: dom p = Seg a by FUNCOP_1:13;
  then reconsider p as FinSequence by Def2;
  rng p c= {y} & {y} c= D by FUNCOP_1:13,ZFMISC_1:31;
  then reconsider q=p as FinSequence of D by Def4,XBOOLE_1:1;
  take q;
  thus thesis by A1,Def3;
end;
