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

Lemma jsafe_phi_bupd_age Z Jspec ge ora q n phi phiaged :
ext_spec_stable age (JE_spec _ Jspec) ->
age phi phiaged ->
le n (level phiaged) ->
@jsafe_phi_bupd Z Jspec ge n ora q phi ->
@jsafe_phi_bupd Z Jspec ge n ora q phiaged.