
theorem
  for G being _Graph for W1, W2 being Walk of G st W1 is_a_prefix_of W2
  holds W1.edges() c= W2.edges()
proof
  let G be _Graph, W1, W2 be Walk of G such that
A1: W1 c= W2;
  let x be object;
  assume x in W1.edges();
  then consider n being even Element of NAT such that
A2: 1 <= n and
A3: n <= len W1 and
A4: W1.n = x by GLIB_001:99;
  n in dom W1 by A2,A3,FINSEQ_3:25;
  then
A5: W2.n = x by A1,A4,GRFUNC_1:2;
  len W1 <= len W2 by A1,FINSEQ_1:63;
  then n <= len W2 by A3,XXREAL_0:2;
  hence thesis by A2,A5,GLIB_001:99;
end;
