Goal:
  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  x : X
  a0 : Y
  ys : list Y
  ys' : list Y
  r0 : R n x a0
  x0 : list X
  x1 : list X
  a : All2i R (S n) x0 ys
  a1 : All2i R (S n + #|x0|) x1 ys'
  IHys : ∀ (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'
  ============================
   (All2i R n (x :: x0) (a0 :: ys))


DEBUG:Going to execute:
<coq-core.plugins.ltac::constructor@0>

Goals:
  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  x : X
  a0 : Y
  ys : list Y
  ys' : list Y
  r0 : R n x a0
  x0 : list X
  x1 : list X
  a : All2i R (S n) x0 ys
  a1 : All2i R (S n + #|x0|) x1 ys'
  IHys : ∀ (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'
  ============================
   (R n x a0)

  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  x : X
  a0 : Y
  ys : list Y
  ys' : list Y
  r0 : R n x a0
  x0 : list X
  x1 : list X
  a : All2i R (S n) x0 ys
  a1 : All2i R (S n + #|x0|) x1 ys'
  IHys : ∀ (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'
  ============================
   (All2i R (S n) x0 ys)


DEBUG:Going to execute:
auto

Goals:
  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  x : X
  a0 : Y
  ys : list Y
  ys' : list Y
  r0 : R n x a0
  x0 : list X
  x1 : list X
  a : All2i R (S n) x0 ys
  a1 : All2i R (S n + #|x0|) x1 ys'
  IHys : ∀ (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'
  ============================
   (R n x a0)

  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  x : X
  a0 : Y
  ys : list Y
  ys' : list Y
  r0 : R n x a0
  x0 : list X
  x1 : list X
  a : All2i R (S n) x0 ys
  a1 : All2i R (S n + #|x0|) x1 ys'
  IHys : ∀ (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'
  ============================
   (All2i R (S n) x0 ys)


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