Goal:
  
  A : Type
  B : Type
  R : A → B → Type
  l : list A
  a : B
  r1 : list B
  r2 : list B
  h1' : list A
  h1 : list B
  h : All2 R h1' h1
  ============================
   ({| pr1 := l; pr2 := a :: r1 ++ r2 |} = {| pr1 := h1'; pr2 := h1 |}
    → let H := CoreTactics.block in
      (∀ (l : list A) (r2 : list B),
         All2 R l (r1 ++ r2)
         → ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 r1 × All2 R l2 r2)
      → let H0 := CoreTactics.block in
        ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 (a :: r1) × All2 R l2 r2)


DEBUG:Going to execute:
destruct p

Goals:
  
  A : Type
  B : Type
  R : A → B → Type
  l : list A
  a : B
  r1 : list B
  r2 : list B
  ============================
   ({| pr1 := l; pr2 := a :: r1 ++ r2 |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      (∀ (l : list A) (r2 : list B),
         All2 R l (r1 ++ r2)
         → ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 r1 × All2 R l2 r2)
      → let H0 := CoreTactics.block in
        ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 (a :: r1) × All2 R l2 r2)

  
  A : Type
  B : Type
  R : A → B → Type
  l : list A
  a : B
  r1 : list B
  r2 : list B
  x : A
  y : B
  l0 : list A
  l' : list B
  r : R x y
  h : All2 R l0 l'
  ============================
   ({| pr1 := l; pr2 := a :: r1 ++ r2 |} =
    {| pr1 := x :: l0; pr2 := y :: l' |}
    → let H := CoreTactics.block in
      (∀ (l : list A) (r2 : list B),
         All2 R l (r1 ++ r2)
         → ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 r1 × All2 R l2 r2)
      → let H0 := CoreTactics.block in
        ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 (a :: r1) × All2 R l2 r2)


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
  
  A : Type
  B : Type
  R : A → B → Type
  l : list A
  a : B
  r1 : list B
  r2 : list B
  ============================
   ({| pr1 := l; pr2 := a :: r1 ++ r2 |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      (∀ (l : list A) (r2 : list B),
         All2 R l (r1 ++ r2)
         → ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 r1 × All2 R l2 r2)
      → let H0 := CoreTactics.block in
        ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 (a :: r1) × All2 R l2 r2)

  
  A : Type
  B : Type
  R : A → B → Type
  l : list A
  a : B
  r1 : list B
  r2 : list B
  x : A
  y : B
  l0 : list A
  l' : list B
  r : R x y
  h : All2 R l0 l'
  ============================
   ({| pr1 := l; pr2 := a :: r1 ++ r2 |} =
    {| pr1 := x :: l0; pr2 := y :: l' |}
    → let H := CoreTactics.block in
      (∀ (l : list A) (r2 : list B),
         All2 R l (r1 ++ r2)
         → ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 r1 × All2 R l2 r2)
      → let H0 := CoreTactics.block in
        ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 (a :: r1) × All2 R l2 r2)


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

Goals:
  
  A : Type
  B : Type
  R : A → B → Type
  l : list A
  a : B
  r1 : list B
  r2 : list B
  ============================
   ({| pr1 := l; pr2 := a :: r1 ++ r2 |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      (∀ (l : list A) (r2 : list B),
         All2 R l (r1 ++ r2)
         → ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 r1 × All2 R l2 r2)
      → let H0 := CoreTactics.block in
        ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 (a :: r1) × All2 R l2 r2)

  
  A : Type
  B : Type
  R : A → B → Type
  l : list A
  a : B
  r1 : list B
  r2 : list B
  x : A
  y : B
  l0 : list A
  l' : list B
  r : R x y
  h : All2 R l0 l'
  ============================
   ({| pr1 := l; pr2 := a :: r1 ++ r2 |} =
    {| pr1 := x :: l0; pr2 := y :: l' |}
    → let H := CoreTactics.block in
      (∀ (l : list A) (r2 : list B),
         All2 R l (r1 ++ r2)
         → ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 r1 × All2 R l2 r2)
      → let H0 := CoreTactics.block in
        ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 (a :: r1) × All2 R l2 r2)


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

Goals:
  
  A : Type
  B : Type
  R : A → B → Type
  l : list A
  a : B
  r1 : list B
  r2 : list B
  ============================
   ({| pr1 := l; pr2 := a :: r1 ++ r2 |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      (∀ (l : list A) (r2 : list B),
         All2 R l (r1 ++ r2)
         → ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 r1 × All2 R l2 r2)
      → let H0 := CoreTactics.block in
        ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 (a :: r1) × All2 R l2 r2)

  
  A : Type
  B : Type
  R : A → B → Type
  l : list A
  a : B
  r1 : list B
  r2 : list B
  x : A
  y : B
  l0 : list A
  l' : list B
  r : R x y
  h : All2 R l0 l'
  ============================
   ({| pr1 := l; pr2 := a :: r1 ++ r2 |} =
    {| pr1 := x :: l0; pr2 := y :: l' |}
    → let H := CoreTactics.block in
      (∀ (l : list A) (r2 : list B),
         All2 R l (r1 ++ r2)
         → ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 r1 × All2 R l2 r2)
      → let H0 := CoreTactics.block in
        ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 (a :: r1) × All2 R l2 r2)


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
  
  A : Type
  B : Type
  R : A → B → Type
  l : list A
  a : B
  r1 : list B
  r2 : list B
  ============================
   ({| pr1 := l; pr2 := a :: r1 ++ r2 |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      (∀ (l : list A) (r2 : list B),
         All2 R l (r1 ++ r2)
         → ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 r1 × All2 R l2 r2)
      → let H0 := CoreTactics.block in
        ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 (a :: r1) × All2 R l2 r2)

  
  A : Type
  B : Type
  R : A → B → Type
  l : list A
  a : B
  r1 : list B
  r2 : list B
  x : A
  y : B
  l0 : list A
  l' : list B
  r : R x y
  h : All2 R l0 l'
  ============================
   ({| pr1 := l; pr2 := a :: r1 ++ r2 |} =
    {| pr1 := x :: l0; pr2 := y :: l' |}
    → let H := CoreTactics.block in
      (∀ (l : list A) (r2 : list B),
         All2 R l (r1 ++ r2)
         → ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 r1 × All2 R l2 r2)
      → let H0 := CoreTactics.block in
        ∑ l1 l2 : list A, l = l1 ++ l2 × All2 R l1 (a :: r1) × All2 R l2 r2)


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim