Goal:
  
  G : t
  HI : invariants G
  HG : acyclic_no_loop G
  p : sigma
        (fun index : sigma (fun _ : VSet.t => sigma (fun _ : V.t => V.t)) =>
         SPath G (pr1 index) (pr1 (pr2 index)) (pr2 (pr2 index)))
  ============================
   (forall (x : V.t) (z : Z) (p0 : SPath G (V G) x (s G)),
    {|
      pr1 := {| pr1 := V G; pr2 := {| pr1 := x; pr2 := s G |} |}; pr2 := p0
    |} = p ->
    let H := CoreTactics.block in
    sweight p0 = z ->
    ~ VSet.In x (V G) -> let H0 := CoreTactics.block in z = 0)


DEBUG:Going to execute:
let xn := fresh id "'" in
           destruct id as [xn id]; DepElim.decompose_exists xn id;
            cbv beta iota delta [TODO projection TODO projection] in id, id';
            DepElim.decompose_exists id id'
DEBUG LTAC Evaluated term: p
DEBUG LTAC Evaluated term: (sigma
                              (fun
                                 index : sigma
                                           (fun _ : VSet.t =>
                                            sigma (fun _ : V.t => V.t)) =>
                               SPath G (pr1 index) 
                                 (pr1 (pr2 index)) 
                                 (pr2 (pr2 index))))
Level 2: type of id
 has value 
(sigma
   (fun index : sigma (fun _ : VSet.t => sigma (fun _ : V.t => V.t)) =>
    SPath G (pr1 index) (pr1 (pr2 index)) (pr2 (pr2 index))))