Goal:
  
  A : Type
  B : Type
  f : nat → B
  a : A
  l : list A
  IHl : ∀ f : nat → B,
          mapi_rec (λ (i : nat) (_ : A), f i) l 0 = unfold #|l| f
  ============================
   (S #|l| = #|l ++ [a]|)


DEBUG:Going to execute:
rewrite app_length /=
DEBUG LTAC Evaluated term: mapi_rec_app
DEBUG LTAC Evaluated term: mapi_rec_app
DEBUG LTAC Evaluated term: (f 0 :: ?l)
DEBUG LTAC Evaluated term: (mapi (λ (i : nat) (_ : A), f i) (a :: l))
DEBUG LTAC Evaluated term: mapi_irrel_list