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;
reserve D for set;

theorem Th19:
  for p,q being Sequence holds dom p c= dom(p^q)
proof
  let p,q be Sequence;
  dom(p^q) = (dom p)+^(dom q) by ORDINAL4:def 1;
  hence thesis by ORDINAL3:24;
end;
