Goal:
  
  A : Type
  P : nat → A → Type
  x : A
  l : list A
  IHl : ∀ k : nat,
          Alli P k l
          → Alli (λ k' : nat, P (Nat.pred #|l| - k' + k)) 0 (List.rev l)
  k : nat
  X : Alli P k l × Alli P (#|l| + k) [x]
  ============================
   (Alli (λ k' : nat, P (Nat.pred #|l ++ [x]| - k' + k)) 0
      (List.rev (l ++ [x])))


DEBUG:Going to execute:
intuition
Level 0: Backtrace:

In environment
A : Type
P : nat → A → Type
x : A
l : list A
IHl : ∀ k : nat,
        Alli P k l
        → Alli (λ k' : nat, P (Nat.pred #|l| - k' + k)) 0 (List.rev l)
k : nat
X : Alli P k (l ++ [x])
Unable to unify "Alli ?M2496 ?M2497 (?M2498 :: ?M2499)" with
 "Alli (λ k' : nat, P (Nat.pred #|l ++ [x]| - k' + k)) 0
    (List.rev (l ++ [x]))".
Level 0: Backtrace:

In environment
A : Type
P : nat → A → Type
x : A
l : list A
IHl : ∀ k : nat,
        Alli P k l
        → Alli (λ k' : nat, P (Nat.pred #|l| - k' + k)) 0 (List.rev l)
k : nat
X : Alli P k (l ++ [x])
Unable to unify "Alli ?M2496 ?M2497 (?M2498 :: ?M2499)" with
 "Alli (λ k' : nat, P (Nat.pred #|l ++ [x]| - k' + k)) 0
    (List.rev (l ++ [x]))".
DEBUG LTAC Evaluated term: Alli_app