Goal:
  
  A : Type
  P : A → Type
  f : A → A
  x : A
  l : list A
  p : P x
  X : All P l
  H : ∀ x : A, P x → f x = x
  H0 : map f l = l
  ============================
   (f x :: map f l = x :: l)


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