Goal:
  
  T : Type
  Listable_T : Listable T
  FinitelyListable_T : FinitelyListable T
  v : T
  x : T
  xs : list T
  IHxs : forall offset n : nat,
         forallb (fun '(n0, t) => n0 == find_index t)
           (combine (seq offset (length xs)) xs) ->
         nth_error xs n = Some v -> find_index v = offset + n
  offset : nat
  n : nat
  Hnth : nth_error (x :: xs) n = Some v
  ============================
   (offset <> find_index x -> false -> find_index v = offset + n)


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 ])