Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  idx : sigma (λ _ : list A, list A)
  a : All2_fold P (pr1 idx) (pr2 idx)
  b : sigma
        (λ index : sigma (λ _ : list A, list A),
           All2_fold P (pr1 index) (pr2 index))
  H : NoConfusion_All2_fold A P {| pr1 := idx; pr2 := a |} b
  ============================
   ({| pr1 := idx; pr2 := a |} = b)


DEBUG:Going to execute:
type of id