reserve k,n for Nat,
  x,y,z,y1,y2 for object,X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for XFinSequence;

theorem
  rng p c= dom f implies f*p is XFinSequence
proof
  assume rng p c= dom f;
  then dom(f*p) = len p by RELAT_1:27;
  hence thesis by ORDINAL1:def 7;
end;
