Goal:
  
  A : Type
  B : Type
  C : Type
  g : nat → B → C
  f : nat → A → B
  k : nat
  a : A
  l : list A
  IHl : ∀ k : nat,
          mapi_rec g (mapi_rec f l k) k =
          mapi_rec (λ (k0 : nat) (x : A), g k0 (f k0 x)) l k
  ============================
   (g k (f k a) :: mapi_rec (λ (k : nat) (x : A), g k (f k x)) l (S k) =
    g k (f k a) :: mapi_rec (λ (k : nat) (x : A), g k (f k x)) l (S k))


DEBUG:Going to execute:
solve
[ trivial
with eq_true
| reflexivity
| symmetry; trivial
| contradiction
| congruence ]