Goal:
  
  G : t
  c : nat
  IH : forall m : nat,
       (m < c)%nat ->
       forall s : VSet.t,
       VSet.cardinal s = m ->
       forall (x y : V.t) (n : Z),
       lsp0 s x y = Some n -> exists p : SPath s x y, sweight p = n
  s : VSet.t
  e : VSet.cardinal s = c
  x : V.t
  y : V.t
  n : Z
  Hx : VSet.mem x s = true
  e0 : x = y
  H : (if is_left (left e0) then Some 0 else None) = Some n
  ============================
   (exists p : SPath s x y, sweight p = n)


DEBUG:Going to execute:
apply some_inj in H