Goal:
  
  A : Type
  B : Type
  f : nat → A → B
  x : A
  l : list A
  IHl : ∀ n k : nat,
          k ≤ n
          → List.rev (mapi_rec f l (n - k)) =
            mapi_rec (λ (k0 : nat) (x : A), f (Nat.pred #|l| + n - k0) x)
              (List.rev l) k
  n : nat
  k : nat
  H : BinInt.Z.le (BinInt.Z.of_nat k) (BinInt.Z.of_nat n)
  cstr : BinInt.Z.le BinNums.Z0 (BinInt.Z.of_nat k)
  cstr0 : BinInt.Z.le BinNums.Z0 (BinInt.Z.of_nat n)
  cstr1 : BinInt.Z.le BinNums.Z0 (BinInt.Z.of_nat #|l|)
  z2 : BinNums.Z
  H2 : BinInt.Z.lt BinNums.Z0
         (BinInt.Z.sub
            (BinInt.Z.add (BinInt.Z.of_nat #|l|) (BinNums.Zpos BinNums.xH))
            (BinNums.Zpos BinNums.xH))
       ∧ z2 =
         BinInt.Z.sub
           (BinInt.Z.add (BinInt.Z.of_nat #|l|) (BinNums.Zpos BinNums.xH))
           (BinNums.Zpos BinNums.xH)
       ∨ BinInt.Z.le
           (BinInt.Z.sub
              (BinInt.Z.add (BinInt.Z.of_nat #|l|) (BinNums.Zpos BinNums.xH))
              (BinNums.Zpos BinNums.xH)) BinNums.Z0 ∧ 
         z2 = BinNums.Z0
  z3 : BinNums.Z
  H3 : BinInt.Z.lt BinNums.Z0
         (BinInt.Z.sub (BinInt.Z.add z2 (BinInt.Z.of_nat n))
            (BinInt.Z.of_nat k))
       ∧ z3 =
         BinInt.Z.sub (BinInt.Z.add z2 (BinInt.Z.of_nat n))
           (BinInt.Z.of_nat k)
       ∨ BinInt.Z.le
           (BinInt.Z.sub (BinInt.Z.add z2 (BinInt.Z.of_nat n))
              (BinInt.Z.of_nat k)) BinNums.Z0 ∧ z3 = BinNums.Z0
  z4 : BinNums.Z
  H4 : BinInt.Z.lt BinNums.Z0
         (BinInt.Z.sub (BinInt.Z.of_nat n) (BinInt.Z.of_nat k))
       ∧ z4 = BinInt.Z.sub (BinInt.Z.of_nat n) (BinInt.Z.of_nat k)
       ∨ BinInt.Z.le (BinInt.Z.sub (BinInt.Z.of_nat n) (BinInt.Z.of_nat k))
           BinNums.Z0 ∧ z4 = BinNums.Z0
  ============================
   (BinInt.Z.add (BinInt.Z.of_nat #|l|) z4 = z3)


DEBUG:Going to execute:
<coq-core.plugins.micromega::Lia@0> $1