Goal:
  
  G : t
  HI : invariants G
  HG : acyclic_no_loop G
  n : Z
  x : V.t
  y : VSet.elt
  Vy : VSet.In y (V G)
  Hle : leq_vertices G n x y
  Vx : ~ VSet.In x (V G)
  Hx : x <> x
  XX : Z.of_nat
         (if is_left (right Hx)
          then
           if n <=? 0
           then (Z.to_nat (Z.of_nat (to_label (lsp G (s G) y)) - n) + 1)%nat
           else to_label (lsp G (s G) y)
          else to_label (lsp G (s G) x)) + n <=
       Z.of_nat
         (if is_left (V.eq_dec y x)
          then
           if n <=? 0
           then (Z.to_nat (Z.of_nat (to_label (lsp G (s G) y)) - n) + 1)%nat
           else to_label (lsp G (s G) y)
          else to_label (lsp G (s G) y))
  ============================
   False


DEBUG:Going to execute:
now apply Hx