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
  hd'0 : A
  tl0 : list A
  p0 : P b hd0 hd'0
  e : #|bs0| = #|tl0|
  e1 : {|
         pr1 := b0;
         pr2 :=
           {|
             pr1 := bs;
             pr2 :=
               {|
                 pr1 := hd;
                 pr2 :=
                   {|
                     pr1 := hd';
                     pr2 := {| pr1 := tl; pr2 := {| pr1 := p; pr2 := e0 |} |}
                   |}
               |}
           |}
       |} =
       {|
         pr1 := b;
         pr2 :=
           {|
             pr1 := bs0;
             pr2 :=
               {|
                 pr1 := hd0;
                 pr2 :=
                   {|
                     pr1 := hd'0;
                     pr2 :=
                       {| pr1 := tl0; pr2 := {| pr1 := p0; pr2 := e |} |}
                   |}
               |}
           |}
       |}
  ============================
   (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 := hd'0 :: tl0 |}
          |};
        pr2 := OnOne2All_hd P b bs0 hd0 hd'0 tl0 p0 e
      |}
      (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 := hd'0 :: tl0 |}
             |};
           pr2 := OnOne2All_hd P b bs0 hd0 hd'0 tl0 p0 e
         |} e1) = e1)


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