Goal:
  
  A : Type
  B : Type
  C : Type
  D : Type
  R : A → B → bool
  f : C → A
  g : D → B
  ============================
   (forallb2 R (map f []) (map g []) =
    forallb2 (λ (x : C) (y : D), R (f x) (g y)) [] [])


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 ])