theorem Lem8:
  for p,q,r being FinSequence st p^q is_a_prefix_of r holds p is_a_prefix_of r
  proof
    let p,q,r be FinSequence;
    assume p^q is_a_prefix_of r;
    then consider n being FinSequence such that
A1: r = p^q^n by TREES_1:1;
    r = p^(q^n) by A1,FINSEQ_1:32;
    hence p is_a_prefix_of r by TREES_1:1;
  end;
