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 D1,D2 being set st D1 c= D2 holds D1* c= D2*
proof
  let D1,D2 be set such that
A1: D1 c= D2;
  let x be object;
  assume x in D1*;
  then reconsider p = x as FinSequence of D1 by Def11;
  rng p c= D1 by Def4;
  then x is FinSequence of D2 by Def4,A1,XBOOLE_1:1;
  hence thesis by Def11;
end;
