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