Section LINEARIZATION.
Variable prog: LTL.program.
Variable tprog: Linear.program.
Hypothesis TRANSF: match_prog prog tprog.
Let ge := Genv.globalenv prog.
Let tge := Genv.globalenv tprog.
Proof (Genv.find_funct_transf_partial TRANSF).
Proof (Genv.find_funct_ptr_transf_partial TRANSF).
Proof (Genv.find_symbol_transf_partial TRANSF).
Proof (Genv.senv_transf_partial TRANSF).
(** * Correctness of reachability analysis *)
(** The entry point of the function is reachable. *)
(** The successors of a reachable instruction are reachable. *)
(** * Properties of node enumeration *)
(** An enumeration of CFG nodes is correct if the following conditions hold: - All nodes for reachable basic blocks must be in the list. - The list is without repetition (so that no code duplication occurs).  We prove that the result of the [enumerate] function satisfies both conditions. *)

Lemma check_reachable_correct:
forall f reach s pc i,
check_reachable f reach s = true ->
f.(LTL.fn_code)!pc = Some i ->
reach!!pc = true ->
Nodeset.In pc s.