Goal:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e0 : #|bs| = #|tl|
  b : B
  bs0 : list B
  hd0 : A
  tl0 : list A
  tl' : list A
  b1 : OnOne2All P bs0 tl0 tl'
  e : False
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
      |}
      {|
        pr1 :=
          {|
            pr1 := b :: bs0;
            pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |}
          |};
        pr2 := OnOne2All_tl P b bs0 hd0 tl0 tl' b1
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
             |};
           pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
         |}
         {|
           pr1 :=
             {|
               pr1 := b :: bs0;
               pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |}
             |};
           pr2 := OnOne2All_tl P b bs0 hd0 tl0 tl' b1
         |} e) = e)


DEBUG:Going to execute:
fun H =>
             match type of H with
             | ?R ?x ?y =>
                 let rhs := fresh in
                 set (rhs := y) in *; pattern sigma rhs; clearbody rhs;
                  destruct H; simpl
             end