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
  x0 : V.t
  y0 : V.t
  y' : V.t
  e : EdgeOf G1 x0 y'
  p0 : PathOf G1 y' y0
  H : weight (map_path p0) <= weight p0
  ============================
   ((on_edge x0 y' e).π1 + weight (map_path p0) <= e.π1 + weight p0)


DEBUG:Going to execute:
solve
[ do
![ solve
 [ trivial | apply : eq_sym ; trivial ]
 | discriminate
 | contradiction
 | Ltac.split ]
| case not_locked_false_eq_true; Ltac.assumption
| match goal with
  | H:~ _ |- _ => solve [ case H; trivial ]
  end ]