Program Definition function_bounds := {|
  used_callee_save := RegSet.elements record_regs_of_function;
  bound_local := max_over_slots_of_funct local_slot;
  bound_outgoing := Z.max (max_over_instrs outgoing_space) (max_over_slots_of_funct outgoing_slot);
  bound_stack_data := Z.max f.(fn_stacksize) 0
|}.

Lemma record_regs_ok: forall r rl u, In r rl -> is_callee_save r = true -> RegSet.In r (record_regs u rl).