Goal:
  
  A : Type
  B : Type
  P : A → B → Type
  P' : ∀ (a : A) (b : B), P a b → Type
  t : A
  t' : B
  x : A
  y : B
  l : list A
  l' : list B
  r : P x y
  rs : All2 P l l'
  r0 : P' x y r
  H' : All2_dep P' rs
  IHH' : ∀ (n : nat) (H1 : nth_error l n = Some t) 
           (H2 : nth_error l' n = Some t'),
           P' t t' (All2_nth_error n t t' rs H1 H2)
  H1 : Some x = Some t
  H2 : Some y = Some t'
  k : (λ t0 : option A, match t0 with
                        | Some x => x
                        | None => x
                        end) (Some x) =
      (λ t0 : option A, match t0 with
                        | Some x => x
                        | None => x
                        end) (Some t)
  ============================
   (P' t t'
      (rew [λ X : Type, X]
           eq_trans
             (f_equal (λ f : B → Type, f y) (eq_trans eq_refl (f_equal P k)))
             (f_equal (P t)
                (f_equal
                   (λ t0 : option B,
                      match t0 with
                      | Some x => x
                      | None => y
                      end) H2)) in r))


DEBUG:Going to execute:
cbn in k