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
  x : V.t
  y : V.t
  p : PathOf G1 x y
  ============================
   (forall (x y y' : V.t) (e : EdgeOf G1 x y') (p : PathOf G1 y' y),
    weight (map_path p) <= weight p ->
    weight (pathOf_step G2 x y' y (on_edge x y' e) (map_path p)) <=
    weight (pathOf_step G1 x y' y e p))


DEBUG:Going to execute:
<coq-equations.plugin::simp@0> $1 $2

Goals:
  
  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
  x : V.t
  y : V.t
  p : PathOf G1 x y
  ============================
   (forall x : V.t, weight (pathOf_refl G2 x) <= weight (pathOf_refl G1 x))

  
  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
  x : V.t
  y : V.t
  p : PathOf G1 x y
  ============================
   (forall (x y y' : V.t) (e : EdgeOf G1 x y') (p : PathOf G1 y' y),
    weight (map_path p) <= weight p ->
    weight (pathOf_step G2 x y' y (on_edge x y' e) (map_path p)) <=
    weight (pathOf_step G1 x y' y e p))


DEBUG:Going to execute:
cbn => //