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
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P
        (pr1 {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |})
        (pr1 (pr2 {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |}))
        (pr2 (pr2 {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |}))
  H : NoConfusion_OnOne2All A B P
        {|
          pr1 := {| pr1 := idx0; pr2 := {| pr1 := idx1; pr2 := idx |} |};
          pr2 := a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   ({|
      pr1 := {| pr1 := idx0; pr2 := {| pr1 := idx1; pr2 := idx |} |};
      pr2 := a
    |} =
    {|
      pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
      pr2 := b
    |})


DEBUG:Going to execute:
type of id