Goal:
  
  A : Type
  B : Type
  f : nat → A → option B
  g : nat → A → option B
  l : list A
  P : nat → A → Type
  n : nat
  Ha : Alli P n l
  Hfg : ∀ (i : nat) (x : A) (t : B), P i x → f i x = Some t → g i x = Some t
  ============================
   (∀ t : list B,
      map_option_out (mapi_rec f l n) = Some t
      → map_option_out (mapi_rec g l n) = Some t)


DEBUG:Going to execute:
induction Ha

Goals:
  
  A : Type
  B : Type
  f : nat → A → option B
  g : nat → A → option B
  P : nat → A → Type
  n : nat
  Hfg : ∀ (i : nat) (x : A) (t : B), P i x → f i x = Some t → g i x = Some t
  ============================
   (∀ t : list B,
      map_option_out (mapi_rec f [] n) = Some t
      → map_option_out (mapi_rec g [] n) = Some t)

  
  A : Type
  B : Type
  f : nat → A → option B
  g : nat → A → option B
  P : nat → A → Type
  n : nat
  hd : A
  tl : list A
  p : P n hd
  Ha : Alli P (S n) tl
  Hfg : ∀ (i : nat) (x : A) (t : B), P i x → f i x = Some t → g i x = Some t
  IHHa : ∀ t : list B,
           map_option_out (mapi_rec f tl (S n)) = Some t
           → map_option_out (mapi_rec g tl (S n)) = Some t
  ============================
   (∀ t : list B,
      map_option_out (mapi_rec f (hd :: tl) n) = Some t
      → map_option_out (mapi_rec g (hd :: tl) n) = Some t)


DEBUG:Going to execute:
try constructor
DEBUG LTAC Evaluated term: Ha