Goal:
  
  G : t
  fuel : nat
  s : VSet.t
  x : V.t
  z : V.t
  IHfuel : forall (s : VSet.t) (x z : V.t),
           lsp00_fast fuel s x z = lsp00 fuel s x z
  ============================
   (EdgeSet.fold
      (fun '(src, w, tgt) (acc : Nbar.t) =>
       if is_left (V.eq_dec src x)
       then max acc (Some w + lsp00_fast fuel (VSet.remove x s) tgt z)
       else acc) (E G) (if is_left (V.eq_dec x z) then Some 0 else None) =
    fold_left max
      (map (fun '(n, y) => (Some n + lsp00 fuel (VSet.remove x s) y z)%nbar)
         (succs x)) (if is_left (V.eq_dec x z) then Some 0 else None))


DEBUG:Going to execute:
trivial; hnf; intros; (solve
            [ do
            ![ solve
             [ trivial | apply : eq_sym ; trivial ]
             | discriminate
             | contradiction
             | Ltac.split ]
            | case not_locked_false_eq_true; Ltac.assumption
            | match goal with
              | H:~ _ |- _ => solve [ case H; trivial ]
              end ])