Goal:
  
  G : t
  z : V.t
  fuel : nat
  IHfuel : forall (s : VSet.t) (x : V.t),
           VSet.cardinal s = fuel ->
           lsp00 fuel s x z =
           (if VSet.mem x s
            then
             fold_left max
               (map
                  (fun '(n, y) =>
                   (Some n +
                    lsp00 (VSet.cardinal (VSet.remove x s)) 
                      (VSet.remove x s) y z)%nbar) 
                  (succs x))
               (if is_left (V.eq_dec x z) then Some 0 else None)
            else if is_left (V.eq_dec x z) then Some 0 else None)
  s : VSet.t
  x : V.t
  n : Z
  y : V.t
  HH : Z.of_nat (VSet.cardinal (VSet.remove x s)) + 1 =
       Z.of_nat (VSet.cardinal s)
  H : Z.of_nat (VSet.cardinal s) = Z.of_nat fuel + 1
  cstr : 0 <= Z.of_nat fuel
  cstr0 : 0 <= Z.of_nat (VSet.cardinal s)
  cstr1 : 0 <= Z.of_nat (VSet.cardinal (VSet.remove x s))
  ============================
   (Z.of_nat (VSet.cardinal (VSet.remove x s)) = Z.of_nat fuel)


DEBUG:Going to execute:
<coq-core.plugins.micromega::Lia@0> $1