Goal:
  
  A : Type
  B : Type
  P : B → A → A → Type
  idx : sigma (λ _ : list B, sigma (λ _ : list A, list A))
  a : OnOne2All P (pr1 idx) (pr1 (pr2 idx)) (pr2 (pr2 idx))
  b : sigma
        (λ index : sigma (λ _ : list B, sigma (λ _ : list A, list A)),
           OnOne2All P (pr1 index) (pr1 (pr2 index)) (pr2 (pr2 index)))
  e : NoConfusion_OnOne2All A B P {| pr1 := idx; pr2 := a |} b
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P {| pr1 := idx; pr2 := a |} b
      (noConfusion_OnOne2All_obligation_1 A B P {| pr1 := idx; pr2 := a |} b
         e) = e)


DEBUG:Going to execute:
fun id =>
             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