Goal:
  
  A : Type
  B : Type
  f : nat → A → B
  f' : nat → A → B
  g : B → bool
  g' : B → bool
  l : list A
  hfg : ∀ (n : nat) (x : A), nth_error l n = Some x → g (f n x) → g' (f' n x)
  n : nat
  x : A
  H : nth_error l n = Some x
  ============================
   (nth_error l (0 + n) = Some x)


DEBUG:Going to execute:
do_atom