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


DEBUG:Going to execute:
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 ]