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
  p^q is XFinSequence of D implies p is XFinSequence of D & q is
  XFinSequence of D
proof
  assume p^q is XFinSequence of D;
  then rng(p^q) c= D by RELAT_1:def 19;
  then
A1: rng p \/ rng q c= D by Th24;
  rng p c= rng p \/ rng q by XBOOLE_1:7;
  then rng p c= D by A1;
  hence p is XFinSequence of D by RELAT_1:def 19;
  rng q c= rng p \/ rng q by XBOOLE_1:7;
  then rng q c= D by A1;
  hence thesis by RELAT_1:def 19;
end;
