Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  a : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  idx2 : list A
  idx1 : list A
  b : All2_fold P idx2 idx1
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} = {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |})


DEBUG:Going to execute:
destruct p

Goals:
    A : Type  P : list A → list A → A → A → Type
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
    → let H0 := CoreTactics.block in
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |} =
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |})

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  b : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P b p
      |}
    → let H0 := CoreTactics.block in
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |} =
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P b p
      |})

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  a : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} = {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |})

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  a : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  d0 : A
  d'0 : A
  Γ0 : list A
  Γ'0 : list A
  b : All2_fold P Γ0 Γ'0
  p0 : P Γ0 Γ'0 d0 d'0
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |}
      {|
        pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
        pr2 := All2_fold_cons P b p0
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} =
      {|
        pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
        pr2 := All2_fold_cons P b p0
      |})


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
    A : Type  P : list A → list A → A → A → Type
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
    → let H0 := CoreTactics.block in
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |} =
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |})

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  b : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P b p
      |}
    → let H0 := CoreTactics.block in
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |} =
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P b p
      |})

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  a : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} = {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |})

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  a : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  d0 : A
  d'0 : A
  Γ0 : list A
  Γ'0 : list A
  b : All2_fold P Γ0 Γ'0
  p0 : P Γ0 Γ'0 d0 d'0
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |}
      {|
        pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
        pr2 := All2_fold_cons P b p0
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} =
      {|
        pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
        pr2 := All2_fold_cons P b p0
      |})


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

Goals:
    A : Type  P : list A → list A → A → A → Type
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
    → let H0 := CoreTactics.block in
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |} =
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |})

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  b : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P b p
      |}
    → let H0 := CoreTactics.block in
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |} =
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P b p
      |})

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  a : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} = {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |})

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  a : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  d0 : A
  d'0 : A
  Γ0 : list A
  Γ'0 : list A
  b : All2_fold P Γ0 Γ'0
  p0 : P Γ0 Γ'0 d0 d'0
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |}
      {|
        pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
        pr2 := All2_fold_cons P b p0
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} =
      {|
        pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
        pr2 := All2_fold_cons P b p0
      |})


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

Goals:
    A : Type  P : list A → list A → A → A → Type
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
    → let H0 := CoreTactics.block in
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |} =
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |})

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  b : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P b p
      |}
    → let H0 := CoreTactics.block in
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |} =
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P b p
      |})

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  a : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} = {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |})

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  a : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  d0 : A
  d'0 : A
  Γ0 : list A
  Γ'0 : list A
  b : All2_fold P Γ0 Γ'0
  p0 : P Γ0 Γ'0 d0 d'0
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |}
      {|
        pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
        pr2 := All2_fold_cons P b p0
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} =
      {|
        pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
        pr2 := All2_fold_cons P b p0
      |})


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
    A : Type  P : list A → list A → A → A → Type
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
    → let H0 := CoreTactics.block in
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |} =
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |})

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  b : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P b p
      |}
    → let H0 := CoreTactics.block in
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |} =
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P b p
      |})

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  a : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} = {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |})

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  a : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  d0 : A
  d'0 : A
  Γ0 : list A
  Γ'0 : list A
  b : All2_fold P Γ0 Γ'0
  p0 : P Γ0 Γ'0 d0 d'0
  ============================
   (let H := CoreTactics.block in
    NoConfusion_All2_fold A P
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |}
      {|
        pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
        pr2 := All2_fold_cons P b p0
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |} =
      {|
        pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
        pr2 := All2_fold_cons P b p0
      |})


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim