Goal:
  
  G1 : t
  G2 : t
  l : labelling
  Gl := relabel_on G1 G2 l : t
  H : invariants G1
  preserves_edges : forall e : EdgeSet.elt,
                    EdgeSet.In e (E G1) -> EdgeSet.In e (E G2)
  x : V.t
  y : V.t
  e : EdgeOf G1 x y
  ============================
   ((if EdgeSet.mem (x, e.π1, y) (E G1)
     then
      ((x, e.π1, y)..s, diff l (x, e.π1, y)..s (x, e.π1, y)..t,
       (x, e.π1, y)..t)
     else (x, e.π1, y)) = (x, diff l x y, y))


DEBUG:Going to execute:
move : e.π2  => /EdgeSet.mem_spec -> //=