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
  b : sigma
        (λ index : sigma (λ _ : list B, sigma (λ _ : list A, list A)),
           OnOne2All P (pr1 index) (pr1 (pr2 index)) (pr2 (pr2 index)))
  H : NoConfusion_OnOne2All A B P
        {|
          pr1 := {| pr1 := idx0; pr2 := {| pr1 := idx1; pr2 := idx |} |};
          pr2 := a
        |} b
  ============================
   ({|
      pr1 := {| pr1 := idx0; pr2 := {| pr1 := idx1; pr2 := idx |} |};
      pr2 := a
    |} = b)


DEBUG:Going to execute:
let idx := fresh "idx" in
           destruct id as [idx id]; repeat CoreTactics.destruct_sigma idx;
            simpl in id
DEBUG LTAC Evaluated term: b
DEBUG LTAC Evaluated term: (sigma
                              (λ index : sigma
                                           (λ _ : list B,
                                              sigma (λ _ : list A, list A)),
                                 OnOne2All P (pr1 index) 
                                   (pr1 (pr2 index)) 
                                   (pr2 (pr2 index))))
Level 4: type of id
 has value 
(sigma
   (λ index : sigma (λ _ : list B, sigma (λ _ : list A, list A)),
      OnOne2All P (pr1 index) (pr1 (pr2 index)) (pr2 (pr2 index))))