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

Lemma jsafe_phi_bupd_downward {Z} {Jspec : juicy_ext_spec Z} {ge n z c phi} :
jsafe_phi_bupd Jspec ge (S n) z c phi ->
jsafe_phi_bupd Jspec ge n z c phi.