Goal:
  
  A : Type
  P : nat → A → Type
  n : nat
  a : A
  l : list A
  l' : list A
  IHl : ∀ (n : nat) (l' : list A),
          Alli P n (l ++ l') → Alli P n l × Alli P (#|l| + n) l'
  X : P n a
  X0 : Alli P (S n) (l ++ l')
  cstr : BinInt.Z.le BinNums.Z0 (BinInt.Z.of_nat n)
  cstr0 : BinInt.Z.le BinNums.Z0 (BinInt.Z.of_nat #|l|)
  ============================
   (BinInt.Z.add (BinInt.Z.of_nat #|l|)
      (BinInt.Z.add (BinInt.Z.of_nat n) (BinNums.Zpos BinNums.xH)) =
    BinInt.Z.add (BinInt.Z.add (BinInt.Z.of_nat #|l|) (BinInt.Z.of_nat n))
      (BinNums.Zpos BinNums.xH))


DEBUG:Going to execute:
<coq-core.plugins.zify::TRANS@1>