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
  ============================
   (forall (x : V.t) (projT1 : Z),
    VSet.In z (V G1) ->
    let e := (x, projT1, y) in
    EdgeSet.In e ext -> VSet.In (first_in G1 G2 p) bs)


DEBUG:Going to execute:
fun c =>
             let elimc := get_first_elim c in
             let elimfn := match elimc with
                           | fun_elim => constr:(f)
                           end in
             let elimn := match elimc with
                          | fun_elim => constr:(n)
                          end in
             let elimt := make_refine elimn elimc in
             CoreTactics.apply_args c elimt
              ltac:(fun elimc => unshelve refine_ho elimc; cbv beta)