Goal:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2All A B P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := b0 :: bs;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd :: tl'
                                              |}
                                          |};
                                        pr2 :=
                                          OnOne2All_tl P b0 bs hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := idx3;
                                            pr2 :=
                                              {| pr1 := idx4; pr2 := idx2 |}
                                          |};
                                        pr2 := b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2All_obligation_2 A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
        (noConfusion_OnOne2All_obligation_1 A B P
           {|
             pr1 :=
               {|
                 pr1 := b0 :: bs;
                 pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
               |};
             pr2 := OnOne2All_tl P b0 bs hd tl tl' a
           |}
           {|
             pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
             pr2 := b
           |} e) = e)


DEBUG:Going to execute:
simpl in H

Goals:
  
  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|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2All 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 := idx3;
                                            pr2 :=
                                              {| pr1 := idx4; pr2 := idx2 |}
                                          |};
                                        pr2 := b
                                      |}),
      let H0 := CoreTactics.block in
      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 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
        (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 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
             pr2 := b
           |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2All A B P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := b0 :: bs;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd :: tl'
                                              |}
                                          |};
                                        pr2 :=
                                          OnOne2All_tl P b0 bs hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := idx3;
                                            pr2 :=
                                              {| pr1 := idx4; pr2 := idx2 |}
                                          |};
                                        pr2 := b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2All_obligation_2 A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
        (noConfusion_OnOne2All_obligation_1 A B P
           {|
             pr1 :=
               {|
                 pr1 := b0 :: bs;
                 pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
               |};
             pr2 := OnOne2All_tl P b0 bs hd tl tl' a
           |}
           {|
             pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
             pr2 := b
           |} e) = e)


DEBUG:Going to execute:
DepElim.simplify_equations_in H

Goals:
  
  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|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2All 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 := idx3;
                                            pr2 :=
                                              {| pr1 := idx4; pr2 := idx2 |}
                                          |};
                                        pr2 := b
                                      |}),
      let H0 := CoreTactics.block in
      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 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
        (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 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
             pr2 := b
           |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2All A B P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := b0 :: bs;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd :: tl'
                                              |}
                                          |};
                                        pr2 :=
                                          OnOne2All_tl P b0 bs hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := idx3;
                                            pr2 :=
                                              {| pr1 := idx4; pr2 := idx2 |}
                                          |};
                                        pr2 := b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2All_obligation_2 A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
        (noConfusion_OnOne2All_obligation_1 A B P
           {|
             pr1 :=
               {|
                 pr1 := b0 :: bs;
                 pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
               |};
             pr2 := OnOne2All_tl P b0 bs hd tl tl' a
           |}
           {|
             pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
             pr2 := b
           |} e) = e)


DEBUG:Going to execute:
fun e =>
             repeat progress (autounfold with equations in e; simpl in e)

Goals:
  
  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|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2All 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 := idx3;
                                            pr2 :=
                                              {| pr1 := idx4; pr2 := idx2 |}
                                          |};
                                        pr2 := b
                                      |}),
      let H0 := CoreTactics.block in
      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 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
        (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 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
             pr2 := b
           |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2All A B P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := b0 :: bs;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd :: tl'
                                              |}
                                          |};
                                        pr2 :=
                                          OnOne2All_tl P b0 bs hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := idx3;
                                            pr2 :=
                                              {| pr1 := idx4; pr2 := idx2 |}
                                          |};
                                        pr2 := b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2All_obligation_2 A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
        (noConfusion_OnOne2All_obligation_1 A B P
           {|
             pr1 :=
               {|
                 pr1 := b0 :: bs;
                 pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
               |};
             pr2 := OnOne2All_tl P b0 bs hd tl tl' a
           |}
           {|
             pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
             pr2 := b
           |} e) = e)


DEBUG:Going to execute:
repeat progress (autounfold with equations in e; simpl in e)