Goal:
  
  A : Type
  B : Type
  f : nat → A → B
  x : A
  l : list A
  IHl : ∀ n : nat,
          mapi_rec f (List.rev l) n =
          List.rev (mapi_rec (λ (k : nat) (x : A), f (#|l| + n - S k) x) l 0)
  n : nat
  k : nat
  x0 : A
  H0 : BinInt.Z.lt (BinInt.Z.of_nat k)
         (BinInt.Z.add (BinInt.Z.of_nat #|l|) BinNums.Z0)
  H : BinInt.Z.le BinNums.Z0 (BinInt.Z.of_nat k)
  cstr : BinInt.Z.le BinNums.Z0 (BinInt.Z.of_nat n)
  cstr0 : BinInt.Z.le BinNums.Z0 (BinInt.Z.of_nat #|l|)
  z1 : BinNums.Z
  H1 : BinInt.Z.lt BinNums.Z0
         (BinInt.Z.sub
            (BinInt.Z.add
               (BinInt.Z.add (BinInt.Z.of_nat #|l|) (BinNums.Zpos BinNums.xH))
               (BinInt.Z.of_nat n))
            (BinInt.Z.add (BinInt.Z.of_nat k) (BinNums.Zpos BinNums.xH)))
       ∧ z1 =
         BinInt.Z.sub
           (BinInt.Z.add
              (BinInt.Z.add (BinInt.Z.of_nat #|l|) (BinNums.Zpos BinNums.xH))
              (BinInt.Z.of_nat n))
           (BinInt.Z.add (BinInt.Z.of_nat k) (BinNums.Zpos BinNums.xH))
       ∨ BinInt.Z.le
           (BinInt.Z.sub
              (BinInt.Z.add
                 (BinInt.Z.add (BinInt.Z.of_nat #|l|)
                    (BinNums.Zpos BinNums.xH)) (BinInt.Z.of_nat n))
              (BinInt.Z.add (BinInt.Z.of_nat k) (BinNums.Zpos BinNums.xH)))
           BinNums.Z0 ∧ z1 = BinNums.Z0
  z2 : BinNums.Z
  H2 : BinInt.Z.lt BinNums.Z0
         (BinInt.Z.sub
            (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.of_nat k) (BinNums.Zpos BinNums.xH)))
       ∧ z2 =
         BinInt.Z.sub
           (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.of_nat k) (BinNums.Zpos BinNums.xH))
       ∨ BinInt.Z.le
           (BinInt.Z.sub
              (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.of_nat k) (BinNums.Zpos BinNums.xH)))
           BinNums.Z0 ∧ z2 = BinNums.Z0
  ============================
   (z2 = z1)


DEBUG:Going to execute:
idtac