Goal:
  
  A : Type
  P : nat → A → Type
  f : A → A
  n : nat
  hd : A
  tl : list A
  p : P n hd
  X : Alli P (S n) tl
  IHX : (∀ (n : nat) (x : A), P n x → f x = x) → map f tl = tl
  H : ∀ (n : nat) (x : A), P n x → f x = x
  ============================
   (f hd :: map f tl = hd :: tl)


DEBUG:Going to execute:
<Coq.Init.Tauto.find_cut>
            ltac:(fun id0 id1 X2 =>
                    assert X2; [ exact (id0 id1) | clear id0 ])
Level 2: evaluation returns
<coq-core.plugins.tauto::is_disj@0>
where
tauto_flags := 
of type
tauto_flags
X1 := ∀ (n : nat) (x : A), P n x → f x = x
of type
constr of type tacvalue

Level 2: Backtrace:

Tactic failure.
Level 2: Backtrace:

Tactic failure.
Level 1: Backtrace:

Tactic failure.
Level 1: Backtrace:

Tactic failure.
Level 1: Backtrace:

Tactic failure.
Level 1: Backtrace:

Tactic failure.