reserve
  X,x,y,z for set,
  k,n,m for Nat ,
  f for Function,
  p,q,r for FinSequence of NAT;

theorem Th1:
  for p,q being FinSequence holds p is_a_prefix_of q iff
  ex r being FinSequence st q = p^r
proof
  let p,q be FinSequence;
  thus p is_a_prefix_of q implies ex r being FinSequence st q = p^r
  by FINSEQ_1:80;
  given r being FinSequence such that
A1: q = p^r;
 dom p = Seg len p & p = q|dom p by A1,FINSEQ_1:21,def 3;
  hence thesis;
