Goal:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b0 : All2i R n (x :: l) (y :: r)
  b'' : nat
  b''0 : list A
  b' : list B
  b : All2i R b'' b''0 b'
  ============================
   ({|
      pr1 := {| pr1 := n; pr2 := {| pr1 := x :: l; pr2 := y :: r |} |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := b''0; pr2 := b' |} |}; pr2 := b
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b0
      → let H0 := CoreTactics.block in All2i_cons r0 a = b0)


DEBUG:Going to execute:
destruct p

Goals:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b0 : All2i R n [] []
  b'' : nat
  ============================
   ({| pr1 := {| pr1 := n; pr2 := {| pr1 := []; pr2 := [] |} |}; pr2 := b0 |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := []; pr2 := [] |} |};
      pr2 := All2i_nil
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n [] [] All2i_nil b0
      → let H0 := CoreTactics.block in All2i_nil = b0)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b0 : All2i R n [] []
  b'' : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R b'' x y
  b : All2i R (S b'') l r
  ============================
   ({| pr1 := {| pr1 := n; pr2 := {| pr1 := []; pr2 := [] |} |}; pr2 := b0 |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := x :: l; pr2 := y :: r |} |};
      pr2 := All2i_cons r0 b
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n [] [] All2i_nil b0
      → let H0 := CoreTactics.block in All2i_nil = b0)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b0 : All2i R n (x :: l) (y :: r)
  b'' : nat
  ============================
   ({|
      pr1 := {| pr1 := n; pr2 := {| pr1 := x :: l; pr2 := y :: r |} |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := []; pr2 := [] |} |};
      pr2 := All2i_nil
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b0
      → let H0 := CoreTactics.block in All2i_cons r0 a = b0)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b0 : All2i R n (x :: l) (y :: r)
  b'' : nat
  x0 : A
  y0 : B
  l0 : list A
  r1 : list B
  r2 : R b'' x0 y0
  b : All2i R (S b'') l0 r1
  ============================
   ({|
      pr1 := {| pr1 := n; pr2 := {| pr1 := x :: l; pr2 := y :: r |} |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := x0 :: l0; pr2 := y0 :: r1 |} |};
      pr2 := All2i_cons r2 b
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b0
      → let H0 := CoreTactics.block in All2i_cons r0 a = b0)


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b0 : All2i R n [] []
  b'' : nat
  ============================
   ({| pr1 := {| pr1 := n; pr2 := {| pr1 := []; pr2 := [] |} |}; pr2 := b0 |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := []; pr2 := [] |} |};
      pr2 := All2i_nil
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n [] [] All2i_nil b0
      → let H0 := CoreTactics.block in All2i_nil = b0)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b0 : All2i R n [] []
  b'' : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R b'' x y
  b : All2i R (S b'') l r
  ============================
   ({| pr1 := {| pr1 := n; pr2 := {| pr1 := []; pr2 := [] |} |}; pr2 := b0 |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := x :: l; pr2 := y :: r |} |};
      pr2 := All2i_cons r0 b
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n [] [] All2i_nil b0
      → let H0 := CoreTactics.block in All2i_nil = b0)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b0 : All2i R n (x :: l) (y :: r)
  b'' : nat
  ============================
   ({|
      pr1 := {| pr1 := n; pr2 := {| pr1 := x :: l; pr2 := y :: r |} |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := []; pr2 := [] |} |};
      pr2 := All2i_nil
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b0
      → let H0 := CoreTactics.block in All2i_cons r0 a = b0)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b0 : All2i R n (x :: l) (y :: r)
  b'' : nat
  x0 : A
  y0 : B
  l0 : list A
  r1 : list B
  r2 : R b'' x0 y0
  b : All2i R (S b'') l0 r1
  ============================
   ({|
      pr1 := {| pr1 := n; pr2 := {| pr1 := x :: l; pr2 := y :: r |} |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := x0 :: l0; pr2 := y0 :: r1 |} |};
      pr2 := All2i_cons r2 b
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b0
      → let H0 := CoreTactics.block in All2i_cons r0 a = b0)


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

Goals:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b0 : All2i R n [] []
  b'' : nat
  ============================
   ({| pr1 := {| pr1 := n; pr2 := {| pr1 := []; pr2 := [] |} |}; pr2 := b0 |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := []; pr2 := [] |} |};
      pr2 := All2i_nil
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n [] [] All2i_nil b0
      → let H0 := CoreTactics.block in All2i_nil = b0)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b0 : All2i R n [] []
  b'' : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R b'' x y
  b : All2i R (S b'') l r
  ============================
   ({| pr1 := {| pr1 := n; pr2 := {| pr1 := []; pr2 := [] |} |}; pr2 := b0 |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := x :: l; pr2 := y :: r |} |};
      pr2 := All2i_cons r0 b
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n [] [] All2i_nil b0
      → let H0 := CoreTactics.block in All2i_nil = b0)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b0 : All2i R n (x :: l) (y :: r)
  b'' : nat
  ============================
   ({|
      pr1 := {| pr1 := n; pr2 := {| pr1 := x :: l; pr2 := y :: r |} |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := []; pr2 := [] |} |};
      pr2 := All2i_nil
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b0
      → let H0 := CoreTactics.block in All2i_cons r0 a = b0)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b0 : All2i R n (x :: l) (y :: r)
  b'' : nat
  x0 : A
  y0 : B
  l0 : list A
  r1 : list B
  r2 : R b'' x0 y0
  b : All2i R (S b'') l0 r1
  ============================
   ({|
      pr1 := {| pr1 := n; pr2 := {| pr1 := x :: l; pr2 := y :: r |} |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := x0 :: l0; pr2 := y0 :: r1 |} |};
      pr2 := All2i_cons r2 b
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b0
      → let H0 := CoreTactics.block in All2i_cons r0 a = b0)


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

Goals:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b0 : All2i R n [] []
  b'' : nat
  ============================
   ({| pr1 := {| pr1 := n; pr2 := {| pr1 := []; pr2 := [] |} |}; pr2 := b0 |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := []; pr2 := [] |} |};
      pr2 := All2i_nil
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n [] [] All2i_nil b0
      → let H0 := CoreTactics.block in All2i_nil = b0)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b0 : All2i R n [] []
  b'' : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R b'' x y
  b : All2i R (S b'') l r
  ============================
   ({| pr1 := {| pr1 := n; pr2 := {| pr1 := []; pr2 := [] |} |}; pr2 := b0 |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := x :: l; pr2 := y :: r |} |};
      pr2 := All2i_cons r0 b
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n [] [] All2i_nil b0
      → let H0 := CoreTactics.block in All2i_nil = b0)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b0 : All2i R n (x :: l) (y :: r)
  b'' : nat
  ============================
   ({|
      pr1 := {| pr1 := n; pr2 := {| pr1 := x :: l; pr2 := y :: r |} |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := []; pr2 := [] |} |};
      pr2 := All2i_nil
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b0
      → let H0 := CoreTactics.block in All2i_cons r0 a = b0)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b0 : All2i R n (x :: l) (y :: r)
  b'' : nat
  x0 : A
  y0 : B
  l0 : list A
  r1 : list B
  r2 : R b'' x0 y0
  b : All2i R (S b'') l0 r1
  ============================
   ({|
      pr1 := {| pr1 := n; pr2 := {| pr1 := x :: l; pr2 := y :: r |} |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := x0 :: l0; pr2 := y0 :: r1 |} |};
      pr2 := All2i_cons r2 b
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b0
      → let H0 := CoreTactics.block in All2i_cons r0 a = b0)


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b0 : All2i R n [] []
  b'' : nat
  ============================
   ({| pr1 := {| pr1 := n; pr2 := {| pr1 := []; pr2 := [] |} |}; pr2 := b0 |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := []; pr2 := [] |} |};
      pr2 := All2i_nil
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n [] [] All2i_nil b0
      → let H0 := CoreTactics.block in All2i_nil = b0)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b0 : All2i R n [] []
  b'' : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R b'' x y
  b : All2i R (S b'') l r
  ============================
   ({| pr1 := {| pr1 := n; pr2 := {| pr1 := []; pr2 := [] |} |}; pr2 := b0 |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := x :: l; pr2 := y :: r |} |};
      pr2 := All2i_cons r0 b
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n [] [] All2i_nil b0
      → let H0 := CoreTactics.block in All2i_nil = b0)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b0 : All2i R n (x :: l) (y :: r)
  b'' : nat
  ============================
   ({|
      pr1 := {| pr1 := n; pr2 := {| pr1 := x :: l; pr2 := y :: r |} |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := []; pr2 := [] |} |};
      pr2 := All2i_nil
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b0
      → let H0 := CoreTactics.block in All2i_cons r0 a = b0)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b0 : All2i R n (x :: l) (y :: r)
  b'' : nat
  x0 : A
  y0 : B
  l0 : list A
  r1 : list B
  r2 : R b'' x0 y0
  b : All2i R (S b'') l0 r1
  ============================
   ({|
      pr1 := {| pr1 := n; pr2 := {| pr1 := x :: l; pr2 := y :: r |} |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := x0 :: l0; pr2 := y0 :: r1 |} |};
      pr2 := All2i_cons r2 b
    |}
    → let H := CoreTactics.block in
      NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b0
      → let H0 := CoreTactics.block in All2i_cons r0 a = b0)


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim