Goal:
    A : Type  P : A → Prop  Q : A → Prop  a : A  l' : list A
  ============================
   (All P []
    → All Q (a :: l')
      → 0 = S #|l'| → All2 (λ x y : A, P x ∧ Q y) [] (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 ])