Goal:
  
  A : Type
  P : A -> Type
  p : A -> bool
  Hp : forall x : A, reflectT (P x) (p x)
  a : A
  ============================
   (reflectT (P a) (p a))


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