End RENUMBER.
Definition pnum (f: function) := postorder (successors_map f) f.(fn_entrypoint).
Definition reach (f: function) (pc: node) := reachable (successors_map f) f.(fn_entrypoint) pc.

(* Specifications: *)
Lemma transf_function_at:
forall f pc i,
f.(fn_code)!pc = Some i ->
reach f pc ->
(transf_function f).(fn_code)!(renum_pc (pnum f) pc) = Some(renum_instr (pnum f) i).