Goal:
  
  A : Type
  B : Type
  C : Type
  P : A → B → C → Prop
  p : A → B → C → bool
  a : A
  l : list A
  Hp : ∀ (x : A) (y : B) (z : C), reflect (P x y z) (p x y z)
  IHl : ∀ (l' : list B) (l'' : list C),
          forallb3 p l l' l'' → Forall3 P l l' l''
  ============================
   (false → Forall3 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 ])