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
  H : ∀ (n : nat) (x : A), P n x → f x = x
  H0 : map f tl = tl
  ============================
   (f hd :: map f tl = hd :: tl)


DEBUG:Going to execute:
match goal with
           | |- _ → _ => intro; t_tauto_intuit
           | |- _ => t_reduce; t_solver
           end