Goal:
  
  G1 : t
  G2 : t
  H : invariants G1
  ext := EdgeSet.diff (E G2) (E G1) : EdgeSet.t
  bs := border_set G1 ext : VSet.t
  s : VSet.t
  y : V.t
  z : V.t
  p : SPath G2 s y z
  _s_ : VSet.t
  _x_ : V.t
  _x1_ : V.t
  _projT1_ : Z
  _hz_ : VSet.In _x_ (V G1)
  e := (_x1_, _projT1_, _x_) : (V.t × Z) × V.t
  _he_ : EdgeSet.In e ext
  ============================
   (_x_ = e..s)


DEBUG:Going to execute:
<Coq.Init.Tauto.not_dep_intros>
Level 2: evaluation returns
<Coq.Init.Tauto.not_dep_intros>;
 repeat
  (match reverse goal with
   | id:?X1
     |- _ => <Coq.Init.Tauto.is_conj> flags X1; elim id; do 2 intro; clear id
   | id:_ <-> _ |- _ => elim id; do 2 intro; clear id
   | id:~ _ |- _ => red in id
   | id:?X1
     |- _ => <Coq.Init.Tauto.is_disj> flags X1; elim id; intro; clear id
   | _ =>
       <Coq.Init.Tauto.find_cut>
        ltac:(fun id0 id1 X2 => assert X2; [ exact (id0 id1) | clear id0 ])
   | id:?X1 -> ?X2
     |- _ =>
         <Coq.Init.Tauto.is_unit_or_eq> flags X1; Ltac.cut X2;
          [ intro; clear id
          | Ltac.cut X1; [ exact id | constructor 1; fail ] ]
   | id:?X1 -> ?X2
     |- _ => <Coq.Init.Tauto.flatten_contravariant_conj> flags X1 X2 id
   | id:?X1 <-> ?X2 -> ?X3
     |- _ =>
         assert ((X1 -> X2) -> (X2 -> X1) -> X3) by
          (do 2 intro; apply id; Ltac.split; Ltac.assumption); clear id
   | id:?X1 -> ?X2
     |- _ => <Coq.Init.Tauto.flatten_contravariant_disj> flags X1 X2 id
   | |- ?X1 => <Coq.Init.Tauto.is_conj> flags X1; Ltac.split
   | |- _ <-> _ => Ltac.split
   | |- ~ _ => red
   end; <Coq.Init.Tauto.not_dep_intros>)
where
flags := 
of type
tauto_flags of type tacvalue