Hint Resolve regs_erasure_get regs_erasure_refl regs_erasure_set
: regs_erasure.
Notation the_ge := (@the_ge the_program).
(** ** Result about at_external, after_external and initial_core *)

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'.