Proof with eauto with val_erasure regs_erasure.
destruct c; simpl.
repeat split...
Qed.
Hint Immediate core_erasure_refl: regs_erasure.

Lemma regs_erasure_set:
forall rs rs' v v' r
(Hrs_ren: regs_erasure rs rs')
(Hval: val_erasure v v'),
regs_erasure (rs # r <- v) (rs' # r <- v').