reserve x for set,
  t,t1,t2 for DecoratedTree;
reserve C for set;
reserve X,Y for non empty constituted-DTrees set;

theorem Th32:
  for n being Nat, r being FinSequence ex q being
  FinSequence st q = r|Seg n & q is_a_prefix_of r
proof
  let n be Nat, r be FinSequence;
  r|Seg n is FinSequence by FINSEQ_1:15;
  then consider q being FinSequence such that
A1: q = r|Seg n;
  q is_a_prefix_of r by A1,TREES_1:def 1;
  hence thesis by A1;
end;
