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)
  ly : Z
  Hly : lsp G (s G) y = Some ly
  Hpos : 0 <= ly
  Hlab : Z.of_nat (to_label (lsp G (s G) y)) = ly
  lx : Z
  Hlx : lsp G (s G) x = Some lx
  poskx : 0 <= lx
  Hlab' : Z.of_nat (to_label (lsp G (s G) x)) = lx
  z : Z
  xs : lsp G x (s G) = Some z
  K : Z
  xy : lsp G x y = Some K
  XX : correct_labelling G
         (to_label ∘ lsp (Subgraph1.G' G y x K) (s (Subgraph1.G' G y x K)))
  ============================
   (n <= K)


DEBUG:Going to execute:
apply HI