Goal:
  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  i0 : nat
  hd0 : A
  hd'0 : A
  tl0 : list A
  p0 : P i0 hd0 hd'0
  H : {|
        pr1 := i;
        pr2 :=
          {|
            pr1 := hd;
            pr2 := {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
          |}
      |} =
      {|
        pr1 := i0;
        pr2 :=
          {|
            pr1 := hd0;
            pr2 := {| pr1 := hd'0; pr2 := {| pr1 := tl0; pr2 := p0 |} |}
          |}
      |}
  ============================
   ({|
      pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
      pr2 := OnOne2i_hd P i hd hd' tl p
    |} =
    {|
      pr1 :=
        {| pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |} |};
      pr2 := OnOne2i_hd P i0 hd0 hd'0 tl0 p0
    |})


DEBUG:Going to execute:
set (rhs := y) in *; pattern sigma rhs; clearbody rhs; destruct H;
            simpl