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

Lemma pures_same_jm_ ge m tp Phi (compat : mem_compatible_with tp m Phi)
i (cnti : containsThread tp i) :
pures_same (m_phi (jm_(ge := ge) cnti compat)) Phi.