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 after_external_erase :
forall v v' c c' m m' c2
(HeraseCores: core_erasure c c')
(HeraseVal: optionval_erasure v v')
(HeraseMem: mem_erasure m m')
(Hafter_external: after_external the_ge v c m = Some c2),
exists (c2' : state),
after_external the_ge v' c' m' = Some c2' /\
core_erasure c2 c2'.