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
  ============================
   (let H := CoreTactics.block in
    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
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |} = {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |})


DEBUG:Going to execute:
destruct p

Goals:
  
  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
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |})

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |})

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |})

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |})


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
  
  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
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |})

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |})

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |})

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |})


DEBUG:Going to execute:
DepElim.simplify_dep_elim; DepElim.simplify_IH_hyps;
            DepElim.unblock_dep_elim

Goals:
  
  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
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |})

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |})

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |})

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |})


DEBUG:Going to execute:
DepElim.simplify_dep_elim; DepElim.simplify_IH_hyps

Goals:
  
  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
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |})

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |})

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |})

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |})


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
  
  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
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |})

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |})

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |})

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |})


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim