Goal:
  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  y : Y
  r0 : R n a0 y
  x : list Y
  x0 : list Y
  a : All2i R (S n) xs x
  a1 : All2i R (S n + #|xs|) xs' x0
  IHxs : ∀ (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'
  ============================
   (All2i R n (a0 :: xs) ?Goal × All2i R (S (n + #|xs|)) xs' ?Goal0)


DEBUG:Going to execute:
fun => <coq-core.plugins.ltac::split@0>

Goals:
  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  y : Y
  r0 : R n a0 y
  x : list Y
  x0 : list Y
  a : All2i R (S n) xs x
  a1 : All2i R (S n + #|xs|) xs' x0
  IHxs : ∀ (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'
  ============================
   (All2i R n (a0 :: xs) ?Goal)

  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  y : Y
  r0 : R n a0 y
  x : list Y
  x0 : list Y
  a : All2i R (S n) xs x
  a1 : All2i R (S n + #|xs|) xs' x0
  IHxs : ∀ (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'
  ============================
   (All2i R (S (n + #|xs|)) xs' ?Goal0)


DEBUG:Going to execute:
eauto

Goals:
  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  y : Y
  r0 : R n a0 y
  x : list Y
  x0 : list Y
  a : All2i R (S n) xs x
  a1 : All2i R (S n + #|xs|) xs' x0
  IHxs : ∀ (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'
  ============================
   (All2i R n (a0 :: xs) ?Goal)

  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  a0 : X
  xs : list X
  xs' : list X
  y : Y
  r0 : R n a0 y
  x : list Y
  x0 : list Y
  a : All2i R (S n) xs x
  a1 : All2i R (S n + #|xs|) xs' x0
  IHxs : ∀ (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'
  ============================
   (All2i R (S (n + #|xs|)) xs' ?Goal0)


DEBUG:Going to execute:
<coq-core.plugins.ltac::eauto@0> $1 $2 $3