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;
reserve a, b, c, d, e, f for object;

theorem
 for X being FinSequence-membered set ex Y being non empty set st X c= Y*
proof
 let X be FinSequence-membered set;
  set Z = {rng f where f is Element of X: f in X};
 take Y = succ union Z;
 let x be object;
 assume
A1: x in X;
  then reconsider x as FinSequence by Def18;
  rng x in {rng f where f is Element of X: f in X} by A1;
  then rng x c= Y by ORDINAL3:1,SETFAM_1:41;
  then x is FinSequence of Y by Def4;
 hence thesis by Def11;
end;
