Definition classify_cmp' ty1 ty2 :=
  match stupid_typeconv ty1, stupid_typeconv ty2 with
  | Tpointer _ _ , Tpointer _ _ => cmp_case_pp
  | Tpointer _ _ , Tint _ si _ => cmp_case_pi si
  | Tint _ si _, Tpointer _ _ => cmp_case_ip si
  | Tpointer _ _ , Tlong _ _ => cmp_case_pl
  | Tlong _ _ , Tpointer _ _ => cmp_case_lp
  | _, _ => cmp_default
  end.

Lemma classify_cmp_eq: classify_cmp = classify_cmp'.