Goal:
  
  ============================
   (∀ (A : Type) (l : list A) (n0 : {n : nat | n < #|l|}) 
      (hd : A) (tl : list A),
      hd :: tl = l
      → ∀ (filtered_var := proj1_sig n0) (n : nat),
          S n = filtered_var → (λ n1 : nat, n1 < #|tl|) n)


DEBUG:Going to execute:
Tactics.program_simplify; try typeclasses eauto  10 with program