
theorem Th1:
  for G being real-weighted WGraph, EL be FF:ELabeling of G, W
  being Walk of G st W is trivial holds W is_augmenting_wrt EL
proof
  let G be real-weighted WGraph, EL be FF:ELabeling of G;
  let W be Walk of G;
  assume
A1: W is trivial;
  now
    let n be odd Nat;
    assume n < len W;
    then n < 1 by A1,GLIB_001:126;
    hence
    (W.(n+1) DJoins W.n, W.(n+2), G implies EL.(W.(n+1)) < (the_Weight_of
G).(W.(n+1))) & (not W.(n+1) DJoins W.n,W.(n+2), G implies 0 < EL.(W.(n+1)))
by ABIAN:12;
  end;
  hence thesis;
end;
