Goal:
  
  A : Type
  P : A → Prop
  p : A → bool
  a : A
  l : list A
  Hp : ∀ x : A, reflect (P x) (p x)
  IHl : forallb p l → Forall P l
  ============================
   (p a && forallb p l → Forall P (a :: l))


DEBUG:Going to execute:
trivial; hnf; intros; (solve
            [ do
            ![ solve
             [ trivial | apply : eq_sym ; trivial ]
             | discriminate
             | contradiction
             | Ltac.split ]
            | case not_locked_false_eq_true; Ltac.assumption
            | match goal with
              | H:¬ _ |- _ => solve [ case H; trivial ]
              end ])