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


DEBUG:Going to execute:
simpl