Goal:
  
  A : Type
  P : nat → A → Type
  p : nat → A → bool
  Hp : ∀ (i : nat) (x : A), reflectT (P i x) (p i x)
  n : nat
  hd : A
  tl : list A
  p0 : P n hd
  X : Alli P (S n) tl
  IHX : is_true (alli p (S n) tl)
  ============================
   (is_true (p n hd && alli p (S n) tl))


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 ])