Goal:
  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  hd'0 : A
  tl0 : list A
  p0 : P hd0 hd'0
  ============================
   ({|
      pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
      pr2 := OnOne2_hd P hd hd' tl p
    |} =
    {|
      pr1 :=
        {|
          pr1 :=
            pr1
              {|
                pr1 := hd;
                pr2 := {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
              |}
            :: pr1
                 (pr2
                    (pr2
                       {|
                         pr1 := hd;
                         pr2 :=
                           {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                       |}));
          pr2 :=
            pr1
              (pr2
                 {|
                   pr1 := hd;
                   pr2 := {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                 |})
            :: pr1
                 (pr2
                    (pr2
                       {|
                         pr1 := hd;
                         pr2 :=
                           {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                       |}))
        |};
      pr2 :=
        OnOne2_hd P
          (pr1
             {|
               pr1 := hd;
               pr2 := {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
             |})
          (pr1
             (pr2
                {|
                  pr1 := hd;
                  pr2 := {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                |}))
          (pr1
             (pr2
                (pr2
                   {|
                     pr1 := hd;
                     pr2 :=
                       {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                   |})))
          (pr2
             (pr2
                (pr2
                   {|
                     pr1 := hd;
                     pr2 :=
                       {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                   |})))
    |})


DEBUG:Going to execute:
simpl