Goal:
  
  f : EdgeSet.elt -> VSet.t -> VSet.t
  prpf : Proper (eq ==> VSet.Equal ==> VSet.Equal) f
  _a_ : EdgeSet.elt
  _l_ : list EdgeSet.elt
  ih : Proper (VSet.Equal ==> VSet.Equal)
         (fold_left (fun (a : VSet.t) (e : EdgeSet.elt) => f e a) _l_)
  _x_ : VSet.t
  _y_ : VSet.t
  a : VSet.elt
  ============================
   (VSet.In a
      (fold_left (fun (a : VSet.t) (e : EdgeSet.elt) => f e a) _l_
         (f _a_ _y_)) <->
    VSet.In a
      (fold_left (fun (a : VSet.t) (e : EdgeSet.elt) => f e a) _l_
         (f _a_ _y_)))


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 ]