Goal:
  
  G1 : t
  G2 : t
  on_edge : forall x y : V.t, EdgeOf G1 x y -> EdgeOf G2 x y
  weight_on_edge : forall (x y : V.t) (e : EdgeOf G1 x y),
                   (on_edge x y e).π1 >= e.π1
  ============================
   (forall (x y : V.t) (p : PathOf G1 x y), weight (map_path p) >= weight p)


DEBUG:Going to execute:
move  =>x y p; apply_funelim (map_path p); simp map_path