Goal:
  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  idx2 : list A
  idx1 : list A
  b : OnOne2 P idx2 idx1
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd tl tl' a
                                      |}
                                      {|
                                        pr1 := {| pr1 := idx2; pr2 := idx1 |};
                                        pr2 := b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
             pr2 := OnOne2_tl P hd tl tl' a
           |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |} e) = e)


DEBUG:Going to execute:
simpl in H

Goals:
  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  idx2 : list A
  idx1 : list A
  b : OnOne2 P idx2 idx1
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd' :: tl
                                          |};
                                        pr2 := OnOne2_hd P hd hd' tl p
                                      |}
                                      {|
                                        pr1 := {| pr1 := idx2; pr2 := idx1 |};
                                        pr2 := b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
             pr2 := OnOne2_hd P hd hd' tl p
           |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  idx2 : list A
  idx1 : list A
  b : OnOne2 P idx2 idx1
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd tl tl' a
                                      |}
                                      {|
                                        pr1 := {| pr1 := idx2; pr2 := idx1 |};
                                        pr2 := b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
             pr2 := OnOne2_tl P hd tl tl' a
           |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |} e) = e)


DEBUG:Going to execute:
DepElim.simplify_equations_in H

Goals:
  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  idx2 : list A
  idx1 : list A
  b : OnOne2 P idx2 idx1
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd' :: tl
                                          |};
                                        pr2 := OnOne2_hd P hd hd' tl p
                                      |}
                                      {|
                                        pr1 := {| pr1 := idx2; pr2 := idx1 |};
                                        pr2 := b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
             pr2 := OnOne2_hd P hd hd' tl p
           |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  idx2 : list A
  idx1 : list A
  b : OnOne2 P idx2 idx1
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd tl tl' a
                                      |}
                                      {|
                                        pr1 := {| pr1 := idx2; pr2 := idx1 |};
                                        pr2 := b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
             pr2 := OnOne2_tl P hd tl tl' a
           |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |} e) = e)


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

Goals:
  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  idx2 : list A
  idx1 : list A
  b : OnOne2 P idx2 idx1
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd' :: tl
                                          |};
                                        pr2 := OnOne2_hd P hd hd' tl p
                                      |}
                                      {|
                                        pr1 := {| pr1 := idx2; pr2 := idx1 |};
                                        pr2 := b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
             pr2 := OnOne2_hd P hd hd' tl p
           |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  idx2 : list A
  idx1 : list A
  b : OnOne2 P idx2 idx1
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd tl tl' a
                                      |}
                                      {|
                                        pr1 := {| pr1 := idx2; pr2 := idx1 |};
                                        pr2 := b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
             pr2 := OnOne2_tl P hd tl tl' a
           |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |} e) = e)


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