Definition pures_same phi1 phi2 := forall loc k pp, phi1 @ loc = PURE k pp <-> phi2 @ loc = PURE k pp.

Lemma jsafe_phi_bupd_age_to Z Jspec ge ora q n l phi :
ext_spec_stable age (JE_spec _ Jspec) ->
le n l ->
@jsafe_phi_bupd Z Jspec ge n ora q phi ->
@jsafe_phi_bupd Z Jspec ge n ora q (age_to l phi).