Goal:
  
  A : Type
  B : Type
  f : A → B
  a : A
  l : list A
  p : B → bool
  IHl : ∀ (f : A → B) (p : B → bool),
          forallb p (map f l) = forallb (λ x : A, p (f x)) l
  ============================
   (p (f a) && forallb p (map f l) = p (f a) && forallb (λ x : A, p (f x)) l)


DEBUG:Going to execute:
match reverse goal with
           | id:(?X1 → ?X2) → ?X3
             |- _ =>
                 Ltac.cut X3;
                  [ intro; clear id; t_tauto_intuit
                  | Ltac.cut (X1 → X2);
                     [ exact
                     id
                     | generalize (λ y : X2, id (λ x : X1, y)); intro; clear
                        id; (solve [ t_tauto_intuit ]) ] ]
           | id:¬ ?X1 → ?X3
             |- _ =>
                 Ltac.cut X3;
                  [ intro; clear id; t_tauto_intuit
                  | Ltac.cut (¬ X1);
                     [ exact
                     id
                     | clear id; intro; (solve [ t_tauto_intuit ]) ] ]
           | |- ?X1 =>
                 <Coq.Init.Tauto.is_disj> flags X1; (solve
                  [ Ltac.left; t_tauto_intuit | Ltac.right; t_tauto_intuit ])
           end