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:
apply : eq_sym