
theorem
  for G being _Graph, W being Walk of G st W is minlength holds W is Path-like
proof
  let G be _Graph, W be Walk of G such that
A1: W is minlength and
A2: not W is Path-like;
  set s = the Path-like Subwalk of W;
  s is_Walk_from W.first(),W.last() by GLIB_001:def 32;
  then
A3: len W <= len s by A1;
  len s <= len W by GLIB_001:162;
  hence contradiction by A2,A3,Th35,XXREAL_0:1;
end;
