Goal:
    A : Type  B : Type  C : Type  P : A → B → C → Type
  ============================
   (All (λ z : C, All2 (λ (x : A) (y : B), P x y z) [] []) []
    → ([] = []) + All2 (λ (x : A) (y : B), All (P x y) []) [] [])


DEBUG:Going to execute:
first
[ All2_All_swap_t_step
| let H1 := fresh in
  let H2 := fresh in
  eapply All2_impl;
   [ eapply All2_prod
   | intros * [H1 H2]; constructor; (first [ exact H1 | exact H2 ]) ];
   (let IH' := fresh in
    eauto; edestruct IH as [IH'| IH']; try (apply IH'; clear IH'); clear IH) ]