Goal:
  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ (l' : list B) (k : nat),
         All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k xs l'
         → All2i R k xs (map2 g xs l')
  ============================
   (∀ k : nat,
      All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k (x :: xs) []
      → All2i R k (x :: xs) [])


DEBUG:Going to execute:
trivial; hnf; intros