reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;

theorem Th21:
  for r being D-valued FinSequence st len r = i+j
  ex p,q being FinSequence of D st len p = i & len q = j & r = p^q
proof
  let r be D-valued FinSequence;
  assume len r = i+j;
  then consider p,q being FinSequence such that
A1: len p = i & len q = j and
A2: r = p^q by Th20;
  p is FinSequence of D & q is FinSequence of D by A2,FINSEQ_1:36;
  hence thesis by A1,A2;
end;
