Section SOUNDNESS.
Variable p: program.
Variable tp: program.
Variable used: IS.t.
Hypothesis USED_VALID: valid_used_set p used.
Hypothesis TRANSF: match_prog_1 used p tp.
Let ge := Genv.globalenv p.
Let tge := Genv.globalenv tp.
Let pm := prog_defmap p.
Definition kept (id: ident) : Prop := IS.In id used.
(** Relating [Genv.find_symbol] operations in the original and transformed program *)

Lemma transform_find_symbol_1:
forall id b,
Genv.find_symbol ge id = Some b -> kept id -> exists b', Genv.find_symbol tge id = Some b'.