reserve G for Graph,
  k, m, n for Nat;
reserve G for non void Graph;

theorem
  for t being DecoratedTree, p being Node of t, k being Element of NAT
  holds p|k is Node of t
proof
  let t be DecoratedTree, p be Node of t, k be Element of NAT;
  p|k = p|Seg k by FINSEQ_1:def 16;
  then p|k is_a_prefix_of p by TREES_1:def 1;
  hence thesis by TREES_1:20;
end;
