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 Th36:
  p^q is D-valued FinSequence implies
  p is FinSequence of D & q is FinSequence of D
proof
  assume p^q is D-valued FinSequence;
  then rng(p^q) c= D by RELAT_1:def 19;
  then
A1: rng p \/ rng q c= D by Th31;
  rng p c= rng p \/ rng q by XBOOLE_1:7;
  hence p is FinSequence of D by Def4,A1,XBOOLE_1:1;
  rng q c= rng p \/ rng q by XBOOLE_1:7;
  hence thesis by Def4,A1,XBOOLE_1:1;
end;
