Goal:
  
  A : Type
  P : nat → A → A → Type
  idx0 : nat
  idx : sigma (λ _ : list A, list A)
  a : OnOne2i P (pr1 {| pr1 := idx0; pr2 := idx |})
        (pr1 (pr2 {| pr1 := idx0; pr2 := idx |}))
        (pr2 (pr2 {| pr1 := idx0; pr2 := idx |}))
  b : sigma
        (λ index : sigma (λ _ : nat, sigma (λ _ : list A, list A)),
           OnOne2i P (pr1 index) (pr1 (pr2 index)) (pr2 (pr2 index)))
  e : NoConfusion_OnOne2i A P
        {| pr1 := {| pr1 := idx0; pr2 := idx |}; pr2 := a |} b
  ============================
   (noConfusion_OnOne2i_obligation_2 A P
      {| pr1 := {| pr1 := idx0; pr2 := idx |}; pr2 := a |} b
      (noConfusion_OnOne2i_obligation_1 A P
         {| pr1 := {| pr1 := idx0; pr2 := idx |}; pr2 := a |} b e) = e)


DEBUG:Going to execute:
match type of id with
           | sigma ?P =>
               let idx := fresh "idx" in
               destruct id as [idx id]; repeat CoreTactics.destruct_sigma idx;
                simpl in id
           | _ => idtac
           end