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
  ============================
   (∀ 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 H := 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:
change (let _ := CoreTactics.block in T)

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:
try simpl in H; DepElim.simplify_equations_in H
DEBUG LTAC Evaluated term: (∀ (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)

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:
try simpl in H