Goal:
  
  G : t
  HI : invariants G
  HG : acyclic_no_loop G
  p'' : VSet.t
  p' : sigma (fun _ : V.t => V.t)
  p : SPath G (pr1 {| pr1 := p''; pr2 := p' |})
        (pr1 (pr2 {| pr1 := p''; pr2 := p' |}))
        (pr2 (pr2 {| pr1 := p''; pr2 := p' |}))
  ============================
   (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
    |} = {| pr1 := {| pr1 := p''; pr2 := p' |}; pr2 := 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:
fun id id' =>
             hnf in id;
              match type of id with
              | sigma _ =>
                  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'
              | _ =>
                  cbv beta iota delta [TODO projection TODO projection]
                   in id, id'
              end