Goal:
  
  A : Type
  B : Type
  P : B → A → A → Type
  idx0 : list B
  idx1 : list A
  idx : list A
  a : OnOne2All P idx0 idx1 idx
  idx2 : sigma (λ _ : list B, sigma (λ _ : list A, list A))
  b : OnOne2All P (pr1 idx2) (pr1 (pr2 idx2)) (pr2 (pr2 idx2))
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 := {| pr1 := idx0; pr2 := {| pr1 := idx1; pr2 := idx |} |};
          pr2 := a
        |} {| pr1 := idx2; pr2 := b |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 := {| pr1 := idx0; pr2 := {| pr1 := idx1; pr2 := idx |} |};
        pr2 := a
      |} {| pr1 := idx2; pr2 := b |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 := {| pr1 := idx0; pr2 := {| pr1 := idx1; pr2 := idx |} |};
           pr2 := a
         |} {| pr1 := idx2; pr2 := b |} e) = e)


DEBUG:Going to execute:
type of id