Goal:
  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  l : list Y
  a2' : nat
  a2'0 : list X
  a2 : list Y
  a : All2i R a2' a2'0 a2
  ============================
   ({| pr1 := n; pr2 := {| pr1 := a0 :: xs ++ xs'; pr2 := l |} |} =
    {| pr1 := a2'; pr2 := {| pr1 := a2'0; pr2 := a2 |} |}
    → let H := CoreTactics.block in
      (∀ (n : nat) (xs' : list X) (l : list Y),
         All2i R n (xs ++ xs') l
         → ∑ ys ys' : list Y,
             l = ys ++ ys' × All2i R n xs ys × All2i R (n + #|xs|) xs' ys')
      → let H0 := CoreTactics.block in
        ∑ ys ys' : list Y,
          l = ys ++ ys'
          × All2i R n (a0 :: xs) ys × All2i R (n + #|a0 :: xs|) xs' ys')


DEBUG:Going to execute:
destruct p

Goals:
  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  l : list Y
  a2' : nat
  ============================
   ({| pr1 := n; pr2 := {| pr1 := a0 :: xs ++ xs'; pr2 := l |} |} =
    {| pr1 := a2'; pr2 := {| pr1 := []; pr2 := [] |} |}
    → let H := CoreTactics.block in
      (∀ (n : nat) (xs' : list X) (l : list Y),
         All2i R n (xs ++ xs') l
         → ∑ ys ys' : list Y,
             l = ys ++ ys' × All2i R n xs ys × All2i R (n + #|xs|) xs' ys')
      → let H0 := CoreTactics.block in
        ∑ ys ys' : list Y,
          l = ys ++ ys'
          × All2i R n (a0 :: xs) ys × All2i R (n + #|a0 :: xs|) xs' ys')

  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  l : list Y
  a2' : nat
  x : X
  y : Y
  l0 : list X
  r : list Y
  r0 : R a2' x y
  a : All2i R (S a2') l0 r
  ============================
   ({| pr1 := n; pr2 := {| pr1 := a0 :: xs ++ xs'; pr2 := l |} |} =
    {| pr1 := a2'; pr2 := {| pr1 := x :: l0; pr2 := y :: r |} |}
    → let H := CoreTactics.block in
      (∀ (n : nat) (xs' : list X) (l : list Y),
         All2i R n (xs ++ xs') l
         → ∑ ys ys' : list Y,
             l = ys ++ ys' × All2i R n xs ys × All2i R (n + #|xs|) xs' ys')
      → let H0 := CoreTactics.block in
        ∑ ys ys' : list Y,
          l = ys ++ ys'
          × All2i R n (a0 :: xs) ys × All2i R (n + #|a0 :: xs|) xs' ys')


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  l : list Y
  a2' : nat
  ============================
   ({| pr1 := n; pr2 := {| pr1 := a0 :: xs ++ xs'; pr2 := l |} |} =
    {| pr1 := a2'; pr2 := {| pr1 := []; pr2 := [] |} |}
    → let H := CoreTactics.block in
      (∀ (n : nat) (xs' : list X) (l : list Y),
         All2i R n (xs ++ xs') l
         → ∑ ys ys' : list Y,
             l = ys ++ ys' × All2i R n xs ys × All2i R (n + #|xs|) xs' ys')
      → let H0 := CoreTactics.block in
        ∑ ys ys' : list Y,
          l = ys ++ ys'
          × All2i R n (a0 :: xs) ys × All2i R (n + #|a0 :: xs|) xs' ys')

  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  l : list Y
  a2' : nat
  x : X
  y : Y
  l0 : list X
  r : list Y
  r0 : R a2' x y
  a : All2i R (S a2') l0 r
  ============================
   ({| pr1 := n; pr2 := {| pr1 := a0 :: xs ++ xs'; pr2 := l |} |} =
    {| pr1 := a2'; pr2 := {| pr1 := x :: l0; pr2 := y :: r |} |}
    → let H := CoreTactics.block in
      (∀ (n : nat) (xs' : list X) (l : list Y),
         All2i R n (xs ++ xs') l
         → ∑ ys ys' : list Y,
             l = ys ++ ys' × All2i R n xs ys × All2i R (n + #|xs|) xs' ys')
      → let H0 := CoreTactics.block in
        ∑ ys ys' : list Y,
          l = ys ++ ys'
          × All2i R n (a0 :: xs) ys × All2i R (n + #|a0 :: xs|) xs' ys')


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

Goals:
  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  l : list Y
  a2' : nat
  ============================
   ({| pr1 := n; pr2 := {| pr1 := a0 :: xs ++ xs'; pr2 := l |} |} =
    {| pr1 := a2'; pr2 := {| pr1 := []; pr2 := [] |} |}
    → let H := CoreTactics.block in
      (∀ (n : nat) (xs' : list X) (l : list Y),
         All2i R n (xs ++ xs') l
         → ∑ ys ys' : list Y,
             l = ys ++ ys' × All2i R n xs ys × All2i R (n + #|xs|) xs' ys')
      → let H0 := CoreTactics.block in
        ∑ ys ys' : list Y,
          l = ys ++ ys'
          × All2i R n (a0 :: xs) ys × All2i R (n + #|a0 :: xs|) xs' ys')

  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  l : list Y
  a2' : nat
  x : X
  y : Y
  l0 : list X
  r : list Y
  r0 : R a2' x y
  a : All2i R (S a2') l0 r
  ============================
   ({| pr1 := n; pr2 := {| pr1 := a0 :: xs ++ xs'; pr2 := l |} |} =
    {| pr1 := a2'; pr2 := {| pr1 := x :: l0; pr2 := y :: r |} |}
    → let H := CoreTactics.block in
      (∀ (n : nat) (xs' : list X) (l : list Y),
         All2i R n (xs ++ xs') l
         → ∑ ys ys' : list Y,
             l = ys ++ ys' × All2i R n xs ys × All2i R (n + #|xs|) xs' ys')
      → let H0 := CoreTactics.block in
        ∑ ys ys' : list Y,
          l = ys ++ ys'
          × All2i R n (a0 :: xs) ys × All2i R (n + #|a0 :: xs|) xs' ys')


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

Goals:
  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  l : list Y
  a2' : nat
  ============================
   ({| pr1 := n; pr2 := {| pr1 := a0 :: xs ++ xs'; pr2 := l |} |} =
    {| pr1 := a2'; pr2 := {| pr1 := []; pr2 := [] |} |}
    → let H := CoreTactics.block in
      (∀ (n : nat) (xs' : list X) (l : list Y),
         All2i R n (xs ++ xs') l
         → ∑ ys ys' : list Y,
             l = ys ++ ys' × All2i R n xs ys × All2i R (n + #|xs|) xs' ys')
      → let H0 := CoreTactics.block in
        ∑ ys ys' : list Y,
          l = ys ++ ys'
          × All2i R n (a0 :: xs) ys × All2i R (n + #|a0 :: xs|) xs' ys')

  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  l : list Y
  a2' : nat
  x : X
  y : Y
  l0 : list X
  r : list Y
  r0 : R a2' x y
  a : All2i R (S a2') l0 r
  ============================
   ({| pr1 := n; pr2 := {| pr1 := a0 :: xs ++ xs'; pr2 := l |} |} =
    {| pr1 := a2'; pr2 := {| pr1 := x :: l0; pr2 := y :: r |} |}
    → let H := CoreTactics.block in
      (∀ (n : nat) (xs' : list X) (l : list Y),
         All2i R n (xs ++ xs') l
         → ∑ ys ys' : list Y,
             l = ys ++ ys' × All2i R n xs ys × All2i R (n + #|xs|) xs' ys')
      → let H0 := CoreTactics.block in
        ∑ ys ys' : list Y,
          l = ys ++ ys'
          × All2i R n (a0 :: xs) ys × All2i R (n + #|a0 :: xs|) xs' ys')


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  l : list Y
  a2' : nat
  ============================
   ({| pr1 := n; pr2 := {| pr1 := a0 :: xs ++ xs'; pr2 := l |} |} =
    {| pr1 := a2'; pr2 := {| pr1 := []; pr2 := [] |} |}
    → let H := CoreTactics.block in
      (∀ (n : nat) (xs' : list X) (l : list Y),
         All2i R n (xs ++ xs') l
         → ∑ ys ys' : list Y,
             l = ys ++ ys' × All2i R n xs ys × All2i R (n + #|xs|) xs' ys')
      → let H0 := CoreTactics.block in
        ∑ ys ys' : list Y,
          l = ys ++ ys'
          × All2i R n (a0 :: xs) ys × All2i R (n + #|a0 :: xs|) xs' ys')

  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  l : list Y
  a2' : nat
  x : X
  y : Y
  l0 : list X
  r : list Y
  r0 : R a2' x y
  a : All2i R (S a2') l0 r
  ============================
   ({| pr1 := n; pr2 := {| pr1 := a0 :: xs ++ xs'; pr2 := l |} |} =
    {| pr1 := a2'; pr2 := {| pr1 := x :: l0; pr2 := y :: r |} |}
    → let H := CoreTactics.block in
      (∀ (n : nat) (xs' : list X) (l : list Y),
         All2i R n (xs ++ xs') l
         → ∑ ys ys' : list Y,
             l = ys ++ ys' × All2i R n xs ys × All2i R (n + #|xs|) xs' ys')
      → let H0 := CoreTactics.block in
        ∑ ys ys' : list Y,
          l = ys ++ ys'
          × All2i R n (a0 :: xs) ys × All2i R (n + #|a0 :: xs|) xs' ys')


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim