Notation the_ge := (@the_ge the_program).

Lemma at_external_erase: forall rs rs' m m' ef vs (Herase: core_erasure (State rs m) (State rs' m')) (Hmem_erase: mem_erasure m m') (Hat_external: at_external the_ge (State rs m) = Some (ef, vs)), exists vs', at_external the_ge (State rs' m') = Some (ef, vs') /\ val_erasure_list vs vs'.