Goal:
    A : Type  B : Type  P : nat → A → B → Type  n : nat  x : A  n0 : nat
  ============================
   (None = Some x → ∑ c : B, nth_error [] n = Some c × P (n0 + n)%nat x c)


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 ])