Goal:
  
  G : t
  HI : invariants G
  HG : acyclic_no_loop G
  y_0 : V.t
  x_0 : V.t
  Vx : VSet.In x_0 (V G)
  Vy : VSet.In y_0 (V G)
  Hxs : lsp G x_0 y_0 = None
  K : Z
  z : VSet.elt
  Hz : VSet.In z (V G')
  p : PathOf G (s G) z
  w : 0 <= weight p
  ============================
   (∥ 0 <= weight (to_G' p) ∥)


DEBUG:Going to execute:
repeat
            match goal with
            | H:∥ _ ∥ |- _ => case H; clear H; intro H
            end; try eapply sq