Goal:
  
  A : Type
  B : Type
  f : nat → A → B
  f' : nat → A → B
  g : B → bool
  g' : B → bool
  l : list A
  ============================
   (∀ n : nat,
      (∀ (n0 : nat) (x : A),
         nth_error l n0 = Some x → g (f (n + n0) x) = g' (f' (n + n0) x))
      → forallb g (mapi_rec f l n) = forallb g' (mapi_rec f' l n))


DEBUG:Going to execute:
induction l

Goals:
  
  A : Type
  B : Type
  f : nat → A → B
  f' : nat → A → B
  g : B → bool
  g' : B → bool
  ============================
   (∀ n : nat,
      (∀ (n0 : nat) (x : A),
         nth_error [] n0 = Some x → g (f (n + n0) x) = g' (f' (n + n0) x))
      → forallb g (mapi_rec f [] n) = forallb g' (mapi_rec f' [] n))

  
  A : Type
  B : Type
  f : nat → A → B
  f' : nat → A → B
  g : B → bool
  g' : B → bool
  a : A
  l : list A
  IHl : ∀ n : nat,
          (∀ (n0 : nat) (x : A),
             nth_error l n0 = Some x → g (f (n + n0) x) = g' (f' (n + n0) x))
          → forallb g (mapi_rec f l n) = forallb g' (mapi_rec f' l n)
  ============================
   (∀ n : nat,
      (∀ (n0 : nat) (x : A),
         nth_error (a :: l) n0 = Some x
         → g (f (n + n0) x) = g' (f' (n + n0) x))
      → forallb g (mapi_rec f (a :: l) n) =
        forallb g' (mapi_rec f' (a :: l) n))


DEBUG:Going to execute:
cbn
DEBUG LTAC Evaluated term: l

Goals:
  
  A : Type
  B : Type
  f : nat → A → B
  f' : nat → A → B
  g : B → bool
  g' : B → bool
  ============================
   (∀ n : nat,
      (∀ (n0 : nat) (x : A),
         nth_error [] n0 = Some x → g (f (n + n0) x) = g' (f' (n + n0) x))
      → true = true)

  
  A : Type
  B : Type
  f : nat → A → B
  f' : nat → A → B
  g : B → bool
  g' : B → bool
  a : A
  l : list A
  IHl : ∀ n : nat,
          (∀ (n0 : nat) (x : A),
             nth_error l n0 = Some x → g (f (n + n0) x) = g' (f' (n + n0) x))
          → forallb g (mapi_rec f l n) = forallb g' (mapi_rec f' l n)
  ============================
   (∀ n : nat,
      (∀ (n0 : nat) (x : A),
         nth_error (a :: l) n0 = Some x
         → g (f (n + n0) x) = g' (f' (n + n0) x))
      → g (f n a) && forallb g (mapi_rec f l (S n)) =
        g' (f' n a) && forallb g' (mapi_rec f' l (S n)))


DEBUG:Going to execute:
auto

Goals:
  
  A : Type
  B : Type
  f : nat → A → B
  f' : nat → A → B
  g : B → bool
  g' : B → bool
  ============================
   (∀ n : nat,
      (∀ (n0 : nat) (x : A),
         nth_error [] n0 = Some x → g (f (n + n0) x) = g' (f' (n + n0) x))
      → true = true)

  
  A : Type
  B : Type
  f : nat → A → B
  f' : nat → A → B
  g : B → bool
  g' : B → bool
  a : A
  l : list A
  IHl : ∀ n : nat,
          (∀ (n0 : nat) (x : A),
             nth_error l n0 = Some x → g (f (n + n0) x) = g' (f' (n + n0) x))
          → forallb g (mapi_rec f l n) = forallb g' (mapi_rec f' l n)
  ============================
   (∀ n : nat,
      (∀ (n0 : nat) (x : A),
         nth_error (a :: l) n0 = Some x
         → g (f (n + n0) x) = g' (f' (n + n0) x))
      → g (f n a) && forallb g (mapi_rec f l (S n)) =
        g' (f' n a) && forallb g' (mapi_rec f' l (S n)))


DEBUG:Going to execute:
<coq-core.plugins.ltac::auto@0> $1 $2 $3