Goal:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  IHa : All2i
          (λ (i : nat) (x : A) (y : B),
             (if i <? S n then False else nth_error l (i - S n) = Some x)
             × R i x y) (S n) l r
  i : nat
  x0 : A
  y0 : B
  e : nth_error l (i - S n) = Some x0
  r1 : R i x0 y0
  ltb' : ¬ BinInt.Z.lt (BinInt.Z.of_nat i) (BinInt.Z.of_nat n)
  ltb : ¬ BinInt.Z.lt (BinInt.Z.of_nat i)
            (BinInt.Z.add (BinInt.Z.of_nat n) (BinNums.Zpos BinNums.xH))
  cstr : BinInt.Z.le BinNums.Z0 (BinInt.Z.of_nat i)
  cstr0 : BinInt.Z.le BinNums.Z0 (BinInt.Z.of_nat n)
  z2 : BinNums.Z
  H2 : BinInt.Z.lt BinNums.Z0
         (BinInt.Z.sub (BinInt.Z.of_nat i)
            (BinInt.Z.add (BinInt.Z.of_nat n) (BinNums.Zpos BinNums.xH)))
       ∧ z2 =
         BinInt.Z.sub (BinInt.Z.of_nat i)
           (BinInt.Z.add (BinInt.Z.of_nat n) (BinNums.Zpos BinNums.xH))
       ∨ BinInt.Z.le
           (BinInt.Z.sub (BinInt.Z.of_nat i)
              (BinInt.Z.add (BinInt.Z.of_nat n) (BinNums.Zpos BinNums.xH)))
           BinNums.Z0 ∧ z2 = BinNums.Z0
  z3 : BinNums.Z
  H3 : BinInt.Z.lt BinNums.Z0
         (BinInt.Z.sub (BinInt.Z.of_nat i) (BinInt.Z.of_nat n))
       ∧ z3 = BinInt.Z.sub (BinInt.Z.of_nat i) (BinInt.Z.of_nat n)
       ∨ BinInt.Z.le (BinInt.Z.sub (BinInt.Z.of_nat i) (BinInt.Z.of_nat n))
           BinNums.Z0 ∧ z3 = BinNums.Z0
  ============================
   (z3 = BinInt.Z.add z2 (BinNums.Zpos BinNums.xH))


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