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


DEBUG:Going to execute:
destruct p

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

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


DEBUG:Going to execute:
DepElim.simpl_dep_elim

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

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

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

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


DEBUG:Going to execute:
DepElim.simplify_dep_elim

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

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


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim